Numerical Methods in Option Pricing

Introduction to numerical methods for the pricing and hedging of derivative securities.

1. Trees. Approximation of diffusions by binomial and trinomial trees. Option pricing: path independent, path dependent, early exercise.
2. Numerical PDE solutions by finite difference methods, including explicit, fully implicit and Crank-Nicholson. Convergence analysis: accuracy and stability. Solution methods for linear systems: direct and iterative PSOR for early-exercise linear complementarity problems.
3. Monte Carlo methods. Approximation of expectations: use of pseudo-random numbers, error analysis. Discretization methods for SDE simulation. Early exercise analysis via regression methods.
4. Transform methods: use of discrete Fourier transforms in option pricing.

When appropriate, we introduce and analyze the stochastic models to which we apply these numerical methods

Click here to close window.