Quantitative Finance I

Syllabus

• Interest-rate risk and the dynamics of the yield curve.
• Monte Carlo simulation of interest rate swaps.
• Hull-White and Heath-Jarrow-Morton models.
• The Black-Scholes model; the Black-Scholes equation and its numerical solution.
• Numerical methods: finite difference methods and Monte Carlo simulation.
• The market price of risk in stock, bond and derivative markets.
• Hedging and speculative strategies.
• Monte Carlo simulation with multiple risk factors; the Hua He model and Cholesky factorization.
• Risk-neutral measure, forward measure, and martingale pricing of derivatives.
• Trading correlation and volatility; exotic options.
• Markov processes, martingales, Markov chains and birth-death processes.
• Financing corporate investment processes, debt dynamics and real options.
• The input-output model of the credit-money system: the PKM and Polak models.
• Profit, loss and psychology.