Bookshelf

Returned from Waterstones bookstore on Trafalgar Square with a these Wilmott's books. No electronic copy can replace a "taste" of original old paper book!

Hypothetical Risk Valuation System

IT systems of banks and investment funds are versatile. They have been grown for years and today financial institutions increasingly rely on the quality of their quantitative technology. Such a trend has made computational finance topmost important.

Computational finance is a cross-disciplinary field that focuses on the financial services industry and relies on mathematical finance, numerical methods and computer simulations to make investment decisions and facilitates portfolio risk management.

Despite the fact banks tend to develop risk valuation systems in-house all of them can generally fit into the given below schema.

How the system works

Credit Risk Modelling Slides

A good overview of credit crisis of 2007-2009 and credit risk modelling of CDO's using copula correlation models.

Copula approach to Default Correlation and the Credit Crisis of 2008/2009 from Robbin Tops

Quant Bookshelf

A good resource with a list of readings for those who are interested in better understanding quants to speak the same language at least! ;)
http://www.quantstart.com/

Quantitative Finance Videos

Nathan Whitehead made a list of videos related to quantitative finance. Most are based on the book "Paul Wilmott on Quantitative Finance, 2nd Edition". And some are from "The Concepts and Practice of Mathematical Finance" by Mark Joshi.

Modern Portfolio Theory References

Recently I've got to refresh MPT knowledge and hence there are few references to share.

Biography 

• http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1990/markowitz-bio.html
• http://news.stanford.edu/news/2006/june7/memldant-060706.html 

MPT and Markowitz Model 

• http://mertens.com.ua/books/files/finmrkts_ch06.doc
• http://www.thedigeratilife.com/blog/index.php/2009/05/14/modern-portfolio-theory-manage-risk-diversification/ 

Operations Research 

• http://en.wikipedia.org/wiki/Quadratic_programming 
• http://en.wikipedia.org/wiki/Lagrange_multiplier 

Python Implementation

• http://travisvaught.blogspot.com/2011/09/modern-portfolio-theory-python.html
• https://github.com/tvaught/experimental/blob/master/portfolio_metrics/mpt.py

Black Scholes Option Pricing

Background

Major break-through in the valuation of derivatives came with two finance professors at MIT, Black and Scholes, came out with a formula that related the price of a call option to the price of the stock to which the option applies. Even though the model is not used by financial institutions today it still contains ideas that used in financial modelling.

The Black-Scholes formula is a partial differential equation that can be used to price the present value of an option under certain assumptions. The equation describes the Markov process of underlying asset price and it looks as given below:

There is an analytical solution of the equation, the walkthrough is given in this video:

Monte Carlo Simulation

Assuming the Brownian motion over this short period will be a normal (Gaussian) distribution with a mean of 0 and a variance of the time interval the iterative formula will be as follows:

Let's take the case of Option Call holder. The favourable cases of underlying asset movement (F) is given on the picture below:

Below you can find an implementation of Monte Carlo simulation of option pricing in python.

The program will generate a number of asset price paths. At option expiry time obviously the price will differ. Option price then will be the average of all gains received at expiry time.

Usefull Links

1. J.Hull Futures, Options and Other Derivatives 
2. http://pyvideo.org/video/1154/derivatives-analytics-with-python-numpy-0
3. https://www.enthought.com/store/ 
4. http://www.python.org/download/releases/2.7/ 
5. http://www.youtube.com/watch?v=i0sGAds8ztI&list=TLJV-9_NNgcRU 
6. http://www.personal.psu.edu/alm24/undergrad/bingqianMonteCarlo.pdf 
7. http://www.automatedtrader.net/glossary/Black-Scholes

JP Morgan Heads HPC

JP Morgan is now able to run risk analysis and price its global credit portfolio in near real-time after implementing High Performance Computing (HPC) capabilities.
Prior to the implementation, JP Morgan would take eight hours to do a complete risk run, and an hour to run a present value, on its entire book. If anything went wrong with the analysis, there was no time to re-run it. It has now reduced that to about 238 seconds, with an FPGA time of 12 seconds.
Read full article here

Parallel Programming for Quantitative Finance

Investment banks like calculations that require powerful computational resources. In many cases Monte-Carlo simulations are run on huge GRID systems that cost a lot.
Such systems are usually home grown and really look expensive to replicate elsewhere.

Few monthes ago I read an article in RISK magazine that outlined the same problem and as an option a  chipper and more flexible approach was mentioned that is based on multi-core CPU and GPU.
http://www.nvidia.co.uk/content/EMEAI/PDF/risk-magazine-tesla-april2013.pdf

GPU programming probably is not too complex although it definitely requires some background desk devs or quants might not have. A company Xcelerit http://www.xcelerit.com/ made an attempt to ease the parallel programming. They provide SDK that allows quants develop and execute their C++ programs on a high-performance environment.

Furthermore they have a library that comes with base statistics functions, market data adapters and a number of interfaces for commonly used software packages, e.g. MATLAB, Excel.
http://www.xcelerit.com/xcelerit-forges-new-tools-for-quantitative-finance/

They also outlined some case studies of inefficiencies of sequential program execution on a GRID compared to multi-core CPU architectures.
http://blog.xcelerit.com/efficiently-using-computing-grids-in-the-financial-industry/

Examples of SDK usage
http://blog.xcelerit.com/xcelerit-sdk-user-experience/

HSBC usage
http://blog.xcelerit.com/hsbc-run-risk-in-real-time-with-xcelerit-and-gpus/

Let's see whether this attempt of Xcelerit will have a successful continuation.