Here you can download for free a high quality Black-Scholes option calculator aimed at students and researchers. It prices vanilla, barrier (discretely and continuously monitored) and arithmetic Asian options, all in three flavours (European, American and Bermudan) and all with both finite differences and Monte Carlo, for immediate comparison and validation. This isn't your typical basic spec, European vanilla binomial tree or Monte Carlo calculator. For one, it includes a few things that you will not find anywhere else (for free) and that even large libraries like QuantLib do not (like American Asian option pricing for example). This is for people who are interested in the numerical methods used for option pricing. I imagine that it could be used to graphically illustrate the comparative effectiveness of some of the general tools used in practice (see the links below for some examples). At the same time emphasis has been placed on maximizing the accuracy of the calculations, so it can also be used to produce highly accurate benchmark prices for the all the options covered, should you want to compare with your results. There is no market volatility input and calibration since it is not meant as a trading tool, but purely as an educational aid.
This is a PC (Windows) application I wrote a long time ago (and never finished) which I decided to patch up and resurrect here. It was written from scratch neither using nor based on any third party code (with a couple of exceptions mentioned below) so it can be used as an independent reference to check against other implementations. You will (or should anyway!) forgive the old-fashioned interface when you realize that the PDE and QMC based prices and Greeks it produces agree to more digits than you could imagine. I had some fun with it anyway, Monte Carlo results cannot be that accurate, right? Or that you can run one billion MC replications in a few seconds to check ultimate convergence to the PDE result, or solve a two-dimensional PDE for an Asian on a 1000x1000x200 space-time grid in less than a second, get extremely accurate benchmark solutions for Bermudan options, etc.
It is still an old app though based solely on GBM, aimed at students or researchers working on numerical methods.
Click on the links below for some mini-presentations of the pricer in action. Please note that these are not meant to be stand-alone tutorials on each subject, nor do they fully expand on exactly how things are done. They are just sample demonstrations of what you can experiment with using the pricer and if you are working on one of the techniques involved then hopefully the test cases presented could be useful for comparisons. Please don't hesitate to get in touch for more information / clarifications.
As mentioned above, the pricing engine was written by me and is not based on nor incorporating any third party code, with the following exceptions:
Comments and any questions regarding the implementation (I don't have time to expand here at the moment) are very welcome. The application has gone through a reasonable amount of testing but only by me, so it is certain that there are remaining issues (hopefully not too many!). Please do let me know of any problem you may find. Also do not forget to have a look at the included "Read me" file which has more information and should help with any features of the program that may not be immediately obvious or intuitive. Enjoy!
This is a PC (Windows) application I wrote a long time ago (and never finished) which I decided to patch up and resurrect here. It was written from scratch neither using nor based on any third party code (with a couple of exceptions mentioned below) so it can be used as an independent reference to check against other implementations. You will (or should anyway!) forgive the old-fashioned interface when you realize that the PDE and QMC based prices and Greeks it produces agree to more digits than you could imagine. I had some fun with it anyway, Monte Carlo results cannot be that accurate, right? Or that you can run one billion MC replications in a few seconds to check ultimate convergence to the PDE result, or solve a two-dimensional PDE for an Asian on a 1000x1000x200 space-time grid in less than a second, get extremely accurate benchmark solutions for Bermudan options, etc.
It is still an old app though based solely on GBM, aimed at students or researchers working on numerical methods.
Click on the links below for some mini-presentations of the pricer in action. Please note that these are not meant to be stand-alone tutorials on each subject, nor do they fully expand on exactly how things are done. They are just sample demonstrations of what you can experiment with using the pricer and if you are working on one of the techniques involved then hopefully the test cases presented could be useful for comparisons. Please don't hesitate to get in touch for more information / clarifications.
- Sample valuation comparisons - Literature comparisons for options with no analytical solution, such as American/Bermudan Asians with discrete or continuous sampling using the PDE solver. PDE-Monte Carlo cross-validation examples.
- Non-uniform grids
- Smoothing techniques
- Sobol quasi-random sequences
- Brownian bridge path construction
- Longstaff-Schwartz least-squares fitting for Monte Carlo pricing of options with early exercise
- Likelihood Ratio Greeks - Continuous Barrier monitoring adjustment
- Time-discretizations of stochastic processes
- Discrete barrier options with Crank-Nicolson (plus help)
As mentioned above, the pricing engine was written by me and is not based on nor incorporating any third party code, with the following exceptions:
- The Singular Value Decomposition module used for the least-squares fitting phase of the Longstaff-Schwartz algorithm is the one from Numerical Recipes. One of their pseudo-random generators is also used.
- The Sobol sequence generator was initially based on the sample code published by Frances Kuo and Stephen Joe here, but only a few lines survive from that (reworked to provide numbers in batches for parallelized runs). The direction numbers needed by the generator and bundled with the pricer are also courtesy of Joe & Kuo (their recommended choice). (Copyright (c) 2008, Frances Y. Kuo and Stephen Joe. All rights reserved.)
Comments and any questions regarding the implementation (I don't have time to expand here at the moment) are very welcome. The application has gone through a reasonable amount of testing but only by me, so it is certain that there are remaining issues (hopefully not too many!). Please do let me know of any problem you may find. Also do not forget to have a look at the included "Read me" file which has more information and should help with any features of the program that may not be immediately obvious or intuitive. Enjoy!
Copyright (c) 2016, Ace Numerics. All rights reserved.