Tuesday, June 26, 2012

Variance Reduction Techniques

Variance Reduction Techniques are usually applied to increase precision of probabilistic estimates, such as interpolations/extrapolations off historical data. While it is very much valued in the field of datamining, when it comes to financial economics, number crunching is usually only a part of the profit-desired solution, as known and unknown risks never go away. For example, "...investment banks use very complicated Monte Carlo simulations to price esoteric mortgage-backed securities." (Wolfram)

Common Random Numbers
This is a popular method of variance reduction for simulation studies where 2+ systems are compared. The basic idea is to apply two or more configuration inputs to the tested system.

The method of common random numbers (also known as the method of correlated sampling, the method of matched pairs, or the method of matched sampling) does not always work. It can backfire if the the engineer of the Monte Carlo simulation creates a negative, rather than positive, correlation between the two random variables and .
Source: Wolfram

Option Delta

In financial engineering, CRN are sometimes used to estimate option delta when an explicit solution isn't available. Example below:

C: value of a Call option
S: value of underlying asset

Let epsilon: 0+, i.e. very small positive value, then the finite-difference ratio:

C(S +/- epsilon) are estimated using the same set of CRNs.

source: Variance Reduction Methods, Haugh

Saturday, June 16, 2012

Inrtoduction to C++ for financial engineers (Book Review)

Introduction to C++ for financial engineers by Daniel J. Duffy (2006) is meant to be a starter course in C++ code writing for those in quantitative financial, i.e. according to the author; it is not the case. I am truly disappointed with it, and have decided to drop the book after the 3rd chapter.

Lack of detailed guidance

A number of code excerpts were presented without the mention of additionally needed libraries; e.g. the Black Scholes example lacked the Cumulative Distribution Function, which I ended up getting from Espen Haug. This would not have been possible if I was a complete newbie to C++.

Lack of original content 

I found nothing interesting, new off the book.

A free alternative

Bernt Arne Odegaard has made available a booklet Recipes, off the collection C++ in Finance. It is pretty easy to understand, free, and has got interesting content.

Friday, June 8, 2012

Quantitative Election Forecasts with Nate Silver

Nate Silver, an American statistician originally known for PECOTA (Baseball player performance forecast), has stepped into the realms of Quantitative Politics.

The accuracy of his November 2008 presidential election predictions—he correctly predicted the winner of 49 of the 50 states—won Silver further attention and commendation.

The Election Forecast Model

In the article Baseball Analyst Draws Fans by Crunching Election Numbers, Bialik mentions how Silver allocates varying weighting with respect to poll accuracy as predictive variables. At the same time he has added economic indicators into the mix, that an "economic index, which is scaled on a similar basis to gross domestic product and now reads at 2.2 percent, exerts a gravitational pull on the forecast." (FiveThirtyEight, NY Times) So according to his latest blog post, Obama has a slight lead in the presidential race.

How do we make a profit off this information?

Betting markets.
According to Intrade, the market implies 53.3% chance of Obama winning, at this point in time (June 8, 2012).
According to Betfair, the market implies 57.5% chance of Obama winning, at this point in time (June 8, 2012).

It's a potentially arbitrage opportunity, if the differential overcomes the transaction costs.

Thursday, June 7, 2012

Black Scholes in Excel

This is thanks to the awesome Espen Haug, author of Derivative Models on Models, and a well known figure in the quantitative finance community.

The Black Scholes formula

And here's how it can be done in Excel.