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BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) Kwon LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) Kwon LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
FINANCIAL DATA ANALYSIS Financial System Objective Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of the options. Data & Calculations Google (Dec 17, 2010) priced at 590.80 Expiration Jan 28, 2010 Strike price Last traded price of call Last traded price of put 150 439.05 0.05 200 417.00 0.15 250 323.60 NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) Kwon LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonNEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0 NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonNEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0 NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonNEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0 NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) Kwon LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012 WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) Kwon LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0OPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. FINANCE | BRIAN(KI HYUN) KWON Posts about Finance written by briankwon21. Financial System. Objective. Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of theoptions.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
NORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the general formula for the probability density function of the normal distribution, meanMLE 78.51333 varMLE 373.5298 where MLE stands for Maximum Likelihood Estimation (MLE) Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.070063685 0.070064 1.918647 0.0707 65 16 0.242214363 0.172151 3.736397 0.1728 70 12 0.329790838 0.087576 0.098319 0.0882 75 15 0.427876012BRIAN(KI HYUN) KWON
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 = 24.213. Using Black-Scholes formula to calculate prices of calloptions with
GAMMA DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the gamma distribution, (assume μ=0) gammaMLE 1.47832419 BetaMLE 53.10968586 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.411068088 0.411068 35.30924 0.4294 65 16 0.523212857 0.112145 0.04014 0.1305 70 12 0.556659535 0.033447 9.719404 0.0518 75 15 0.588160397 0.031501 22.34287 0.0499 80 18NEWSVENDOR PROBLEM
Problem Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money WEIBULL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Using the formula for the probability density function of the weibull distribution, (assume that μ=0) Estimated γ-value: 4.32572193 rMLE 4.7545346 aMLE 85.7666969 Bin Frequency Cumulative p hat T Rounded p hat 50 15 0.073993741 0.073993741 1.37104603 0.0741 65 16 0.234806278 0.160812537 2.734651783 0.161 70 12 0.316598566 0.081792288 0.005891072 0.0819 75 15 0.410488565 LOGNORMAL DISTRIBUTION FOR THE NEWSVENDOR PROBLEM Bin. Frequency. Cumulative. p hat. T. Rounded p hat. 50. 15. 0.079310182. 0.07931. 0.80961. 0.0843. 65. 16. 0.30303536. 0.223725. 9.187184. 0.2275. 70. 12. 0BRIANKWON21
Read all of the posts by briankwon21 on Brian(Ki Hyun) KwonOPTIMIZATION
Posts about Optimization written by briankwon21. Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school.BRIAN(KI HYUN) KWON
Problem. Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to hisschool.
BRIAN(KI HYUN) KWON
September 11, 2011
REVERSE SINGLY & DOUBLY LINKED LISTSBy briankwon21
class SNode{
public String value; public SNode next; public SNode(String value){ this.value = value;}
public String toString(){ String string = value;if(next != null){
string += " -> " + next.toString();}
return string;
}
}
class DNode{
public String value; public DNode prev; public DNode next; public DNode(String value){ this.value = value;}
public String toString(){ String string = value;if(next != null){
string += " <-> " + next.toString();}
return string;
}
}
public class LinkedList { public static SNode reverse(SNode node){ SNode head,current_node,next_current_node,tail;head = node;
current_node = head.next;tail = head;
while(current_node != null){ next_current_node = current_node.next; current_node.next = head; head = current_node; current_node = next_current_node;}
tail.next = null;
return head;
}
public static SNode reverse_recursion(SNode node) { if(node.next==null) {return node;
}
SNode next_node = node.next; SNode current_node = node; SNode head = reverse_recursion(node.next); next_node.next = current_node; current_node.next=null;return head;
}
public static DNode reverse(DNode node){ if(node.next==null) {return node;
}
DNode next_node = node.next; DNode head = reverse(node.next); DNode current_node = next_node.prev; next_node.prev = next_node.next; next_node.next = current_node; if(current_node.prev==null) { current_node.next=null; current_node.prev=next_node;}
return head;
}
public static void main(String args){ SNode one = new SNode("1"); SNode two = new SNode("2"); SNode three = new SNode("3");one.next = two;
two.next = three;
System.out.println(one); System.out.println("-- reversed Singly-linked-list by iteration --"); SNode reversedList = reverse(one); System.out.println(reversedList + "\n"); reverse(reversedList); System.out.println(one); System.out.println("-- reversed Singly-linked-list by recursion --"); System.out.println(reverse_recursion(one) + "\n"); DNode first = new DNode("1"); DNode second = new DNode("2"); DNode third = new DNode("3"); first.prev = null; first.next = second; second.prev = first; second.next = third; third.prev = second; third.next = null; System.out.println(first); System.out.println("-- reversed doubly-linked-list --"); DNode reversed = reverse(first); System.out.println(reversed); System.out.println("-- re-reversed doubly-linked-list --"); DNode re_reversed = reverse(reversed); System.out.println(re_reversed);}
}
OUTPUT
1 -> 2 -> 3
-- reversed Singly-linked-list by iteration --3 -> 2 -> 1
1 -> 2 -> 3
-- reversed Singly-linked-list by recursion --3 -> 2 -> 1
1 <-> 2 <-> 3
-- reversed doubly-linked-list --3 <-> 2 <-> 1
-- re-reversed doubly-linked-list --1 <-> 2 <-> 3
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| posted in Algorithms -------------------------September 7, 2011
NEWSVENDOR PROBLEM
By briankwon21
PROBLEM
Tommy has been buying papers from the local newspaper company and selling it to the public at a local intersection close to his school. Unsold papers are recycled and Tommy does not get a penny out of those papers recycled. Tommy buys 125 papers each day and found that he is not making much money out of this business venture and has decided to give it up. Debbie, Tommy’s best-friend decided that she would havea go at this.
Tommy has been buying papers from the local newspaper company for $0.20 each and selling it to the public for $0.80 each. He has kept a record of the demand for the last 150 days. Determine how much Debbie should order so that she maximizes her profit. If Debbie has used this order quantity for the last 150 days, what would Debbie’s total profit (or loss) would have been?DATA
Numbers of newspapers sold by Tommy for the past 150 days: DATAANALYSIS
Fit a distribution function for the demand using the supplied demanddata.
NORMAL
WEIBULL
LOGNORMAL
GAMMA
Normal: 0.477
Weibull: 0.716
Lognormal: 0.007
Gamma: 0
RECOMMENDATION
Weibull distribution has the largest p-value. Therefore, weibull distribution has the best fit for the data. Optimal quantity to maximize expected profit (x*) = 1-F(x*)=c/s=0.2/0.8=0.25F(x*)=0.75
1-exp(-(x*/a)^r)=0.75exp(-(x*/a)^r)=0.25
x*=a*(-ln(0.25))^(1/r)=B14*(-LN(0.25))^(1/B13)x*=91.86593688
x*~=92
Therefore, Debbie should order the quantity of 92 to maximize theprofit.
THE TOTAL PROFIT WOULD BE $ _6380.8__0_Leave a comment
| posted in Optimization -------------------------September 7, 2011
FINANCIAL DATA ANALYSISBy briankwon21
FINANCIAL SYSTEM
OBJECTIVE
Increase likelihood of profit through comparison of official prices of traded options and theoretical prices of the options.DATA & CALCULATIONS
Google (Dec 17, 2010) priced at 590.80 Expiration Jan 28, 2010Strike price
Last traded price of call Last traded price of put150
439.05
0.05
200
417.00
0.15
250
323.60
0.10
300
295.43
0.05
350
239.88
0.05
400
191.45
0.15
450
142.50
0.23
500
92.68
1.00
550
46.90
5.50
600
15.50
23.90
650
3.20
62.34
700
0.60
107.00
750
0.15
152.61
800
0.10
304.00
850
0.05
269.80
900
0.05
419.70
Month (2010)
Volatility
September
19.668
August
25.109
July
31.764
June
27.512
May
32.564
April
23.032
March
19.394
February
16.385
January
22.486
Estimated Volatility (average volatility of 2010) = (19.668+25.109+31.764+27.512+32.564+23.032+19.394+16.385+22.486)/9 =24.213
Using Black-Scholes formula to calculate prices of call options with Annualized interest rate= 0.11% 252 trading days per year,t=42/252;
s=590.80;
k=150:50:900;
v=0.24213;
r=0.0011;
d1=(log(s./k)+(r+v^2/2)*t)./(v*t^0.5); d2=(log(s./k)+(r-v^2/2)*t)./(v*t^0.5); C=-normcdf(d2,0,1).*k.*exp(-r*t)+normcdf(d1,0,1)*sStrike price
Last traded price of call Price of call (Black-Scholes) Absolute differences Percentage of differences (%)150
439.05
440.83
1.78
0.41
200
417.00
390.84
-26.16
-6.27
250
323.60
340.85
17.25
5.33
300
295.43
290.86
-4.57
-1.55
350
239.88
240.86
0.98
0.41
400
191.45
190.87
-0.58
-0.3
450
142.50
140.93
-1.57
-1.1
500
92.68
91.90
-0.78
-0.84
550
46.90
48.60
1.7
3.62
600
15.50
19.20
3.7
23.87
650
3.20
5.46
2.26
70.63
700
0.60
1.12
0.52
86.67
750
0.15
0.17
0.02
13.33
800
0.10
0.02
-0.08
-80
850
0.05
0
-0.05
-100
900
0.05
0
-0.05
-100
Using put-call parity to calculate prices of put options,t=42/252;
s=590.80;
k=150:50:900;
v=0.24213;
r=0.0011;
d1=(log(s./k)+(r+v^2/2)*t)./(v*t^0.5); d2=(log(s./k)+(r-v^2/2)*t)./(v*t^0.5); P=(1-normcdf(d2,0,1)).*k.*exp(-r*t)-(1-normcdf(d1,0,1))*sStrike price
Last traded price of put Price of put (Black-Scholes) Absolute differences Percentage differences (%)150
0.05
0
-0.05
-100
200
0.15
0
-0.15
-100
250
0.10
0
-0.10
-100
300
0.05
0
-0.05
-100
350
0.05
0
-0.05
-100
400
0.15
0
-0.15
-100
450
0.23
0.04
-0.19
-82.61
500
1.00
1.01
0.01
1
550
5.50
7.70
2.2
40
600
23.90
28.29
4.39
18.37
650
62.34
64.54
2.2
3.53
700
107.00
110.19
3.19
2.98
750
152.61
159.24
6.63
4.344
800
304.00
209.07
-94.93
-31.23
850
269.80
259.05
-10.75
-3.98
900
419.70
309.04
-110.66
-26.37
ANALYSIS
In order to increase likelihood of profit through purchase of options, we might want to buy options where theoretical prices are lower. They are indicated by red font color (those with positive absolute differences). Among those options which are likely to provide profits, we might want to lean toward the ones with the highest positive percentage differences. However, we also have to take into account that the ones with small option prices are more likely to have large percentage difference because changes in a few pennies will yield the huge differences. This directly relates to high risk of investment. Therefore, for this analysis, we will ignore the option prices with lower than $10. The most attractive options are ones that have higher option prices but have higher percentage of differences or that have lower option prices but have higher absolute differences compared to similar range of prices. For call option, options with strike price of 250 and 600 which fit into the category are good investments. Option prices with strike price of 650 or higher are too low. They have high volatility and therefore they are risky. For put option, options with strike price of 600 and 750 stand out. Relative to neighbor strike prices, they have higher absolute and percentage differences. Until now we have analyzed the options with lower theoretical prices under an assumption that we are only purchasing the options. If we are allowed to short sell the options, we can also utilize the options with negative absolute differences where the theoretical prices are higher. For call option, strike price with 200 fits exactly into our criteria, so this would be the only one to be shorted. For put option, we can eliminate the one with strike price 850, and we are left with 800 and 900. We can invest in either of them or both. The decision would be very subjective. The following is the summary of which ones should be considered forinvestment.
When purchasing the call options:Strike price
Last traded price of call Price of call (Black-Scholes) Absolute differences Percentage of differences (%)250
323.60
340.85
17.25
5.33
600
15.50
19.20
3.7
23.87
When purchasing the put options:Strike price
Last traded price of call Price of call (Black-Scholes) Absolute differences Percentage of differences (%)600
23.90
28.29
4.39
18.37
750
152.61
159.24
6.63
4.344
When short selling the call options:Strike price
Last traded price of call Price of call (Black-Scholes) Absolute differences Percentage of differences (%)200
417.00
390.84
-26.16
-6.27
When short selling the put options:Strike price
Last traded price of call Price of call (Black-Scholes) Absolute differences Percentage of differences (%)800
304.00
209.07
-94.93
-31.23
900
419.70
309.04
-110.66
-26.37
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