# Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Feb
9

**A tractable LIBOR model with default risk**:a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework.

**Optimising a correlated asset calculation on MATLAB**:detailed example of applying vectorisation to speed up Matlab codes.

**Reading About the Financial Crisis: A 21-Book Review**: Professor Andrew W. Lo reviews a diverse set of 21 books on the crisis, 11 written by academics, and 10 written by journalists and one former Treasury Secretary. Are they helpful to understand the current crisis?

**A Forward Monte Carlo Method for American Options Pricing**: This study proposes a forward Monte Carlo method for the pricing of American options, and significantly improves in numerical efficiency and accuracy in contrast with the standard regression-based method of Longstaff and Schwartz(2001).

Dec
21

Like other conference, the last day of the 24th Australasian Finance & Banking Conference witnessed fewer attendance and less active discussion: people have left or eager to leave. Fortunately or unfortunately, my session was in the afternoon and had even fewer audiences.

That's the end of this conference, hopefully you have found some interesting articles as I did, enjoy them.

**Entropic Least-Squares Valuation of American Options Subject to Moment Constraints**: improvement of pricing accuracy of American options by incorporating a set of risk-neutral moment constraints into an entropic pricing framework.**Forecasting Equicorrelations**: We study the out-of-sample forecasting performance of several time-series models of equicorrelation, which is the average pairwise correlation between a number of assets.**Integrated Framework for Portfolio Risk Management**: Various risk measures are managed in a unique integrated framework for portfolio selection problems.**Information Asymmetry and Momentum Anomalies**: In this paper, we construct an information asymmetry factor (VECINF) based on the price discovery of large trades. VECINF is significantly negatively correlated with market excess return, indicating that market-wide information asymmetry is lower in bull markets.**Why Did Some Banks Perform Better During the Credit Crisis?**: thoughtful question and investigation.**Volatility, Correlation, and Spread ETFs as Factors**: Several methods for measuring factors have been investigated in previous literature, but an easy-to-implement general method is simply to specify a group of heterogeneous indexes or traded portfolios.That's the end of this conference, hopefully you have found some interesting articles as I did, enjoy them.

Oct
9

We know

In the paper "

Download the paper and accompanying Python codes at http://www2.visixion.com/dok/Fast_MCS_SVSI.pdf

**least-squares Monte Carlo simulation to price an American option**is time consuming because it involves optimal exercise decision on every step of a large number of simulation (in the least square case, to run a polynomial regression on cash flows and decide whether it is optimal to exercise or not). I once shared a simple Matlab file to illustrate the least squares Monte Carlo simulation. The situation becomes worse if we allow the presence of stochastic volatility and interest rate, typically my codes run quite a few minutes for 50,000 number of simulations.In the paper "

**Fast Monte Carlo Valuation of American Options under Stochastic Volatility and Interest Rates**" by Y. Hilpisch, the author demonstrates with Python script that the Least-Squares Monte Carlo (LSM) algorithm with control variates takes only less than one second to achieve satisfying accurateness. The overall statistics taken from the paper are as follows, AMAZING!Download the paper and accompanying Python codes at http://www2.visixion.com/dok/Fast_MCS_SVSI.pdf

May
20

This is a follow up post of my previous entry Nine Ways to Implement Binomial Tree Option Pricing because the latter covers European option only. Compared with pricing American option by Crank-Nicholson finite difference or American Options via least square Monte Carlo Simulation, Binomial tree is the easiest to implement, what you need to do is just adding a MAX expression on every node of your tree.

Here is a paper on the implementation of

Here is a paper on the implementation of

**binomial tree methods for the pricing of American option**' value and Greeks, matlab codes can be found in the paper or separately here.
Oct
6

Crank-Nicolson for a European put was introduced before, to better master this technique, i share another sample code using Crank-Nicholson finite difference for American option.

BLSPRICEFDAM Black-Scholes put and call pricing for American Options using the Crank-Nicholson finite difference solution of Black-Scholes Partial differential equation. Note that this function returns an approximate solution unlike the analytical solution (BLSPRICE)

SO is the current asset price, X is the exercise price, R is the risk-free interest rate, T is the time to maturity of the option in years, SIG is the standard deviation of the annualized continuously compounded rate of return of the asset (also known as volatility), and Q is the dividend rate of the asset. The default Q is 0. N denotes the number of discretization points in the stock price domain, and M denotes the number of discretization points in time domain used for the PDE solution.Try increasing either of M or N to achieve greater efficiency.

lecture notes can be downloaded at http://www.cs.cornell.edu/Info/Courses/Spring-98/CS522/home.html and matlab file http://www.cs.cornell.edu/Info/Courses/Spring-98/CS522/content/blspricefdam.m.

BLSPRICEFDAM Black-Scholes put and call pricing for American Options using the Crank-Nicholson finite difference solution of Black-Scholes Partial differential equation. Note that this function returns an approximate solution unlike the analytical solution (BLSPRICE)

SO is the current asset price, X is the exercise price, R is the risk-free interest rate, T is the time to maturity of the option in years, SIG is the standard deviation of the annualized continuously compounded rate of return of the asset (also known as volatility), and Q is the dividend rate of the asset. The default Q is 0. N denotes the number of discretization points in the stock price domain, and M denotes the number of discretization points in time domain used for the PDE solution.Try increasing either of M or N to achieve greater efficiency.

lecture notes can be downloaded at http://www.cs.cornell.edu/Info/Courses/Spring-98/CS522/home.html and matlab file http://www.cs.cornell.edu/Info/Courses/Spring-98/CS522/content/blspricefdam.m.