Development of a First LIBOR Market Simulation for Valuation (Pricing) of Complex Interest Rate Derivatives

Funded by ValuePrice AG, 2009-2010

Coordinator: Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)

Researchers:

1. Martin Rainer (Institute of Applied Mathematics, Middle East Technical University, Ankara)
2. Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)

Feature Specification for the Project

1. Mathematical Finance
1. Process
• multidimensional log-normal process for correlated primary rates (forward rates)
• extendability for stochastic volatilities
• simulation for a (market-)given number of primary rates
• Cholesky decorrelation of the process
• change of measure corresponding to the relevant event dates
• computation of drift vectors, volatility vectors, and correlation matrices
2. Calibration
• implied volatilities of primary rates (caps for forward rates)
• implied volatilities of secondary rates (swaptions for swap rates)
• calibration of correlations via historical method
• calibration of correlations via volatilies of secondary rates
• parametrized form of correlations
3. Monte Carlo Simulation
• modular Monte Carlo simulation of a given multidimensional stochastic process
4. Process Evaluation
• Primary Rates: interpolation method for relevant event dates
• Discount Factors: computation from simulated forward rates
• Payoff: valuation for a given (possibly path-dependent) payoff
2. Scientific Computing
1. Programming
• modular structuring of components according to their functionality
• object-oriented programming or at least prepared for it bt structuring
• performance: efficient algorithm design
2. Implementation
• programming language: MATLAB

Keywords: option pricing models, fixed-rate mortgage contract, default option, prepayment option, mortgage insurance, numerical solutions to partial differential equations