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ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. WHAT IS THE RISK-NEUTRAL MEASURE? WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. WHAT IS THE RISK-NEUTRAL MEASURE? WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. WHAT IS THE RISK-NEUTRAL MEASURE? expected winnings = 0.75 * £2 + 0.25 * £0 = £1.50. This is the definition of the risk-neutral measure: The risk neutral measure is the set of probabilities for which the given market prices of a collection of trades would be equal to the expectations of the winnings or losses of each trade. Remark: It is risk-neutral becausein this
QUANTS – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. ROBERT – FERMAT'S LAST SPREADSHEET Robert. Mathematician (PhD in Probability Theory). Art lover (spent one excellent year studying painting and ceramics at Batley Art College). Ex investment banker (2yrs of fixed-income exotics trading, 5 yrs of quantitative research, 2 yrs of inflation structuring). Nowbusy as a
PYTHON – FERMAT'S LAST SPREADSHEET Posts about Python written by Robert. One of the great things about Python is the way you can easily juggle items around in collections -- lists, dictionaries, sets -- and the shortcuts you get when youcombine them.
THE EASY ROUTE TO RISK-NEUTRAL MEASURE PRICING The easy route to risk-neutral measure pricing. Robert Derivatives, Finance, Mathematics, Probability Theory, Quants August 7, 2017. The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and whichBOND LADDERS
A portfolio that is long bonds may actually benefit from a sell off! The explanation is that you benefit when you reinvest the coupons that your portfolio pays: the bonds you buy are cheaper. This is a problem of reinvestment risk, and the concept of a bond ladder should be better known as a standard building block for a bond portfolio – it THE EFFICIENT FRONTIER FOR FINANCIAL MODELLING There is a trade off between the explanatory powers of a model and its complexity: the more a model explains, the more complex it will be. Would you disagree with that? Before you answer, let me make a claim: Mathematics is about revealing patterns that simplify. The mathematician's work is actually based on producing simplicity, ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a WHY DOES THE YIELD CURVE SLOPE UPWARDS? In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a very simplepiece of algebra).
FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
GALOIS THEORY FOR DUMMIES A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
WHY DOES THE YIELD CURVE SLOPE UPWARDS? In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a very simplepiece of algebra).
FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
GALOIS THEORY FOR DUMMIES A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
WHY DOES THE YIELD CURVE SLOPE UPWARDS? In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a very simplepiece of algebra).
TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading.MATHEMATICS
The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here). WHAT IS THE RISK-NEUTRAL MEASURE? expected winnings = 0.75 * £2 + 0.25 * £0 = £1.50. This is the definition of the risk-neutral measure: The risk neutral measure is the set of probabilities for which the given market prices of a collection of trades would be equal to the expectations of the winnings or losses of each trade. Remark: It is risk-neutral becausein this
A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
A WALKTHROUGH GUIDE TO BUILDING YOURSELF A LINUX SYSTEM HDD installation — with all the details. Well, that was the big picture. Here we go through it all with the full details of every step. All the sequences are nicely laid out for a Frugal install of Puppy 4.3.1 here.. But before you go there, note my comments on that page too: you need to ‘manage flags’ in GParted and make the partition boot-able, and you should answer ‘no’ whenever A QUANT TRADING MODEL FOR SWAP SPREADS The model uses a linear regression of the 10-year swap spread onto: The model is effectively using the 5-year swap spread as part of the signal generation for the 10-year spread. The use of LIBOR, S&P and Bank stocks are not surprising if you have read my post: they are indicators of activities which can move swap spreads.HOW TO READ THE FT
Since moving back to a front office seat I have been a keen reader of the Financial Times. Regular reading of economic and finance journalism and analysis is a must if you want to understand the themes discussed around the trading floor.. If you have tried and failed to get into the FT, it may be because (like me once) you weren’t able to see any shape and form in the way things are gathered HOW TO CALCULATE CARRY How to calculate carry. Robert Finance, Trading January 11, 2012. January 11, 2012. Positive carry can be an obsession for fixed-income investors. For a simple explanation of carry for a bond position have a look at this well-written post: click here. Tagged.BOND LADDERS
A portfolio that is long bonds may actually benefit from a sell off! The explanation is that you benefit when you reinvest the coupons that your portfolio pays: the bonds you buy are cheaper. This is a problem of reinvestment risk, and the concept of a bond ladder should be better known as a standard building block for a bond portfolio – it THE EASY ROUTE TO RISK-NEUTRAL MEASURE PRICING The easy route to risk-neutral measure pricing. Robert Derivatives, Finance, Mathematics, Probability Theory, Quants August 7, 2017. The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD What is the intuition behind the output, let’s take your simple ATM with 100 normal vol. So, around 0.4*vol*sqrt(mat), say we use 100 of vol and 1 year , so 0.4*100*1, so around 40bps why would that be below50bps
A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD What is the intuition behind the output, let’s take your simple ATM with 100 normal vol. So, around 0.4*vol*sqrt(mat), say we use 100 of vol and 1 year , so 0.4*100*1, so around 40bps why would that be below50bps
A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread.PHD MATHEMATICS
For anyone interested, here are a few links to academic articles I wrote during my PhD on probability theory. I would say that one of the most pleasing parts of the work I completed for my thesis was that we managed to find the right mathematical way to describe a complex problem, which essentially made ROBERT – FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here). PYTHON – FERMAT'S LAST SPREADSHEET Posts about Python written by Robert. One of the great things about Python is the way you can easily juggle items around in collections -- lists, dictionaries, sets -- and the shortcuts you get when youcombine them.
WHAT IS THE RISK-NEUTRAL MEASURE? Here is a short list of the most common 'big-concept' questions that I was asked throughout my years as a quant (whether coming from people on the trading floor, in control functions, or from newcomers to the team), in no particular order: What is the risk-neutral measure? What is arbitrage-free pricing? What is a change THE EASY ROUTE TO RISK-NEUTRAL MEASURE PRICING The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here). In this post I want to look again at risk-neutral pricing. It A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
INTUITION FOR THE FORWARD FX EQUATION Every quant knows the expression that defines a forward FX rate on date t with maturity T: where B_f is the foreign discount factor and B_d is the domestic discount factor. But what is the best way to explain this intuitively? Here is my suggestion. Let's pick an example pair, say EUR and CHF, and see MARTINGALE – FERMAT'S LAST SPREADSHEET Posts about martingale written by Robert. Here is a short list of the most common 'big-concept' questions that I was asked throughout my years as a quant (whether coming from people on the trading floor, in control functions, or from newcomers to the team), in no particular order: What is the risk-neutral measure? WHY DOES THE YIELD CURVE SLOPE UPWARDS? In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
FERMAT'S LAST SPREADSHEET The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here).ABOUT ROBERT HARDY
Welcome to my Blog! Here you'll find my various articles and thoughts on topics from mathematics, finance, trading, computing, languages, calculating, computing and education. A little bit about me: after completing my undergraduate degree in Pure Mathematics at the University of Bath, I did my masters degree at Trinity College, Cambridge. And that's where the UNDERSTANDING TRADER JARGON In this post I present some tips on how to understand fixed-income trader jargon. If you are a quant working closely with swaps or options traders (as I was once), then you won't get very far in a discussion unless you have a certain amount of fluency with the following terms. Some were passed on TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. WHAT DOES ‘REDUCE THE BALANCE SHEET’ MEAN? This post is a LeanPost: it will be developed further depending on feedback from my readers. See my note here on what a LeanPost is. Many companies are these days talking about reducing the balance sheet. Another term used is de-leveraging. In the simplest terms, this just means that a company is reducing the number of GALOIS THEORY FOR DUMMIES CALCULATING OPTION PRICES IN YOUR HEAD Pricing an at-the-money option: well-known and easy. For an at-the-money call or put (ie where K=F), the price is the same, let’s call it ATMPrice. The BS formula reduces to a simpler: ATMPrice = 1/sqrt (2*PI) * vol * sqrt (Maturity) which is very well approximated by: ATMPrice = 0.4 * vol * sqrt (Maturity). Here is anexample in action:
FACTS, RULES OF THUMB, AND INTUITION FOR SWAP SPREADSSEE MORE ON FERMATSLASTSPREADSHEET.COM A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
ITO’S PRODUCT AND QUOTIENT RULES AS DESCRIBED BY A TRADER Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes typeof
TRADING – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread. Here is an unordered list of why . Continue reading. QUANTS – FERMAT'S LAST SPREADSHEET The N-year swap spread is defined as: N-yr swap spread := N-yr swap rate - N-yr government bond yield. Since most quants spend much less time on the bond market than on the swaps market, they often don't come to appreciate the central importance of the swap spread.PHD MATHEMATICS
PhD Mathematics. For anyone interested, here are a few links to academic articles I wrote during my PhD on probability theory. I would say that one of the most pleasing parts of the work I completed for my thesis was that we managed to find the right mathematical way to describe a complex problem, which essentially made . WHAT IS THE RISK-NEUTRAL MEASURE? expected winnings = 0.75 * £2 + 0.25 * £0 = £1.50. This is the definition of the risk-neutral measure: The risk neutral measure is the set of probabilities for which the given market prices of a collection of trades would be equal to the expectations of the winnings or losses of each trade. Remark: It is risk-neutral becausein this
ROBERT – FERMAT'S LAST SPREADSHEET Robert. Mathematician (PhD in Probability Theory). Art lover (spent one excellent year studying painting and ceramics at Batley Art College). Ex investment banker (2yrs of fixed-income exotics trading, 5 yrs of quantitative research, 2 yrs of inflation structuring). Nowbusy as a
PYTHON – FERMAT'S LAST SPREADSHEET Posts about Python written by Robert. One of the great things about Python is the way you can easily juggle items around in collections -- lists, dictionaries, sets -- and the shortcuts you get when youcombine them.
A FAST-MOVING INTRODUCTION TO ADVANCED PROBABILITY THEORY Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory. I was taught undergraduate probability theory by one of the best. Williams's book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formaltheoretical
MARTINGALE – FERMAT'S LAST SPREADSHEET Posts about martingale written by Robert. Here is a short list of the most common 'big-concept' questions that I was asked throughout my years as a quant (whether coming from people on the trading floor, in control functions, or from newcomers to the team), in no particular order: What is the risk-neutral measure? THE EASY ROUTE TO RISK-NEUTRAL MEASURE PRICING The easy route to risk-neutral measure pricing. Robert Derivatives, Finance, Mathematics, Probability Theory, Quants August 7, 2017. The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which WHY DOES THE YIELD CURVE SLOPE UPWARDS? In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a very simplepiece of algebra).
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Over the years I have written quite a few posts on finance and financial mathematics, based on the work I was doing at the time as a derivatives quant within various investment banks. Some of my post popular posts have been: How to calculate option prices in your head How to understand fixed-income trader jargon … Continue readingIntroduction →
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December 29, 2011August 7, 2017 SETTING UP A SPARK CLUSTER ON AWS On 7th December 2017 I gave a presentation at CodeNode (London UK) in which I showed how to set up a Spark cluster on AWS spot-requested instances. You can find the meeting notes on the Full Stack Quants website -- there is a link to a video recording of the session as well as links … Continue reading Setting up a Spark cluster on AWS →Robert Big data
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December 9, 2017
SMALLTALK COLLECTIONS FOR PYTHON CODERS One of the great things about Python is the way you can easily juggle items around in collections -- lists, dictionaries, sets -- and the shortcuts you get when you combine them. For example, to get a unique collection of elements in a list: list(set(my_list)) will do it. Similar things happen in Smalltalk but these … Continue reading Smalltalk collections for Python coders →Robert Computing
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August 8, 2017August 8, 2017 NOTES ON DEBUGGING WITH GDB Nice collection of tutorials here. PDF crib sheet here. Nice collection of suggestions in StackOverflow here. Some code for GDB which displays STL containers in a more friendly way, halfway down here. Nice tutorial which gives a bit more depth on tui here.Robert
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August 7, 2017
SETTING UP QUANTLIB IN LINUXHaving written a
walk-through on how to set up a Linux system ready for compiling software (see here), … Continue reading Setting up QuantLibin Linux →
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August 7, 2017
THE EASY ROUTE TO RISK-NEUTRAL MEASURE PRICING The principle of pricing in the risk-neutral measure is the foundation of quantitative analysis. I have already written a post which gives an intuitive description of the concept of a risk premium and which discusses some aspects of the risk-neutral approach (see here). In this post I want to look again at risk-neutral pricing. It … Continue reading The easy route to risk-neutral measure pricing →Robert
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August 7, 2017
TDD AND YOUR SOLUTION DOMAIN What does TDD achieve? If you are pair programming, TDD is excellent because it keeps the pair communicating on the same level. If you have an idea then you have to represent it as a test and the other person can follow your idea more easily. Should you always write a test first? I think … Continue reading TDD and your solution domain →Robert
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August 7, 2017August 7, 2017 WHAT IS FUNCTIONAL PROGRAMMING AND WHAT DOES IT DO FOR YOU? This is a good example here of a bad explanation of FP: basically saying that FP is intelligent whilst non-FP is dumb. I recently read a couple of blog posts by Kris Jenkins which give his answers to the questions: What is functional programming? Which languages could be said to be functional programming languages? I … Continue reading What is Functional Programming and what does it do for you? →Robert
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