Quantitative Finance Collector is a blog on Quantitative finance codes, methods in math finance focusing on derivative pricing, quantitative trading and quantitative risk management.
Sep
2
I was asked how to improve the convergence speed of Greeks calculation with Monte Carlo simulation. Besides those variance reduction techniques such as antithetic, or low discrepancy random numbers, one efficient way is to use pathwise derivative instead of finite difference.
1, Finite Difference approximation
This is the most widely used & straightforward method, as its name suggests, basically, to estimate dy/dx, we increase x by a very small quantity to x1, re-calculate the option value y1, and then estimate the sensitivity as (y-y1)/(x1-x). Thus this method requires us to calculate the option value at least twice (three times for central difference method), and obviously is a big challenge when we have to simulate lots of times.
2, pathwise derivative estimate
contrary to finite difference approximation, pathwise derivative estimate derivative directly, without simulating multiple times. It takes advantage of additional information about the dynamics and parameter dependence of a simulated process. Simply put, by the chain rule, if we could find another variable z such that
, and there are solutions to the two derivatives at the right hand side, the pathwise derivative estimator can be applied, and for most cases, stock price S(T) for European option or S(tau) for American option is an excellent choice of z, tau is the optimal timing for exercise. Please read the chapter 7 of Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) (v. 53)
for detail.
1, Finite Difference approximation
This is the most widely used & straightforward method, as its name suggests, basically, to estimate dy/dx, we increase x by a very small quantity to x1, re-calculate the option value y1, and then estimate the sensitivity as (y-y1)/(x1-x). Thus this method requires us to calculate the option value at least twice (three times for central difference method), and obviously is a big challenge when we have to simulate lots of times.
2, pathwise derivative estimate
contrary to finite difference approximation, pathwise derivative estimate derivative directly, without simulating multiple times. It takes advantage of additional information about the dynamics and parameter dependence of a simulated process. Simply put, by the chain rule, if we could find another variable z such that
, and there are solutions to the two derivatives at the right hand side, the pathwise derivative estimator can be applied, and for most cases, stock price S(T) for European option or S(tau) for American option is an excellent choice of z, tau is the optimal timing for exercise. Please read the chapter 7 of Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) (v. 53) for detail.
Aug
31
Heard of this app few weeks ago but never tried as I am using Gphone (Indeed there is an app for android Gphone, however I didn't download it as it is not developed by MathWorks and received bad feedbacks). So if you happen to have an i-toy, try to connect to your MATLAB remotely from your iPhone, iPad, or iPod touch.
Features
Command-line access to MATLAB running on your computer
Access to your MATLAB workspace
Ability to view MATLAB figures on your iPhone
Record of commands typed on the iPhone in your command history
Custom keyboard
Ability to connect to MATLAB running on Windows, Mac, and Linux
Download the free app Matlab Mobile for Iphone at http://itunes.apple.com/us/app/matlab-mobile/id370976661?mt=8
Features
Command-line access to MATLAB running on your computer
Access to your MATLAB workspace
Ability to view MATLAB figures on your iPhone
Record of commands typed on the iPhone in your command history
Custom keyboard
Ability to connect to MATLAB running on Windows, Mac, and Linux
Download the free app Matlab Mobile for Iphone at http://itunes.apple.com/us/app/matlab-mobile/id370976661?mt=8
Aug
31
This guest post is brought to you by Options University.
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John J. Halpin
Dear MathFinance.cn readers,
Options University is giving away $797 worth of Options Education For F.R.E.E. to the next 200 traders.
And trust me. This is not a trick, or a gimmick.
If you are wondering why we are doing this, well, with the economy being in the toilet, Options University wants to show that we're here to help you weather the storm.
So the next 200 students that follow the link below will be armed with some of the most powerful, portfolio-boosting investment education on the planet.
Follow the link below to get your hands on Options 101 and the Advanced Options Home Study Courses (the convenient online editions):
==> Get Your Free Option Trading Course
The only potentially bad news is that the amount of editions released for f.r.e.e. has to be limited to only 200, as these particular home study courses continue to be their best selling education products. But for those of you who are fast enough, please enjoy two of the best selling options education courses for f.r.e.e.
John J. Halpin
Aug
30
Today is the British bank holiday, I am the only one sitting in the big office, no mood to do my research...
Like usual, open Browser, visit Google, since I have been looking for an internship recently, I type "Quant Jobs" and Google provides query suggestions in the search box automatically based on the hot searching terms. While I notice something interesting, Google.co.uk suggests me the terms "Quant Jobs in India" like below
then I switch to Google.com, still,
Like usual, open Browser, visit Google, since I have been looking for an internship recently, I type "Quant Jobs" and Google provides query suggestions in the search box automatically based on the hot searching terms. While I notice something interesting, Google.co.uk suggests me the terms "Quant Jobs in India" like below
then I switch to Google.com, still,
Aug
27
VBA week...
Option Pricing Models and Volatility Using Excel-VBA is the best book I have read this year, recommended by a friend of mine couple of days ago. I didn't look positive at it at the beginning as there are dozes of books on similar topics and to be honest, I never heard of the author (now I know he works in industry). However, the more pages I dig, the less willing to stop & happier I feel as the author explains the volatility staff relevant to option pricing SOOOOO well and in plain language. More importantly, there are accompanying VBA codes for almost every example, if that's no enough, the author provides VBA solutions to the exercise as well, which encourage the readers to practice & make our hands dirty, unlike many other books do.
The book starts with complex number, how to write macro code for it; followed by selected root-finding algorithms, and weighted least square regression; then introduces numerical integration, tree-building, black scholes, Heston model, GARCH, implied volatility, parameter estimation, etc. Preview is worth a thousand words, check yourself below:
Option Pricing Models and Volatility Using Excel-VBA is the best book I have read this year, recommended by a friend of mine couple of days ago. I didn't look positive at it at the beginning as there are dozes of books on similar topics and to be honest, I never heard of the author (now I know he works in industry). However, the more pages I dig, the less willing to stop & happier I feel as the author explains the volatility staff relevant to option pricing SOOOOO well and in plain language. More importantly, there are accompanying VBA codes for almost every example, if that's no enough, the author provides VBA solutions to the exercise as well, which encourage the readers to practice & make our hands dirty, unlike many other books do.The book starts with complex number, how to write macro code for it; followed by selected root-finding algorithms, and weighted least square regression; then introduces numerical integration, tree-building, black scholes, Heston model, GARCH, implied volatility, parameter estimation, etc. Preview is worth a thousand words, check yourself below:
Quantitative Finance Collector is simply a record of my financial engineering learning journey as a master in quantitative finance, a PhD candidate in finance and a Quantitative researcher, with most of the entries written at school. 
