First semester

Calibration of Stochastic Processes

Objectives

– Know the standard methods for discretizing stochastic differential equations;
– Know how to use estimation techniques for stochastic volatility models (Heston) and jump models (Merton);
– Mastery of Monte Carlo pricing and variance reduction techniques.

Course outline

1. Review of models: Black-Scholes model, implied volatility, Orstein Uhlenbeck model, Heston stochastic volatility model, Merton jump models…
2. Pricing/hedging methods and Monte Carlo calculation of Greeks
3. Process discretization (Euler-Maruyama scheme & Milshtein scheme)
4. Variance reduction techniques for pricing

Prerequisites

Inferential statistics, Markov chain, Bayesian calculus, stochastic calculus