Implied volatility. Existence, uniqueness and properties. Asymptotic behavior. Local volatility. Stochastic volatility. Heston's model. Model calibration. Additional topics at the instructor's discretion.
· Gatheral. The volatility surface. Wiley.
· Fouque, Papanicolaou, Sircar and Solna. Multiscale Stochastic Volatility for Equity, Interest Rate and Credit Derivatives. Cambridge.
· Musiela and Rutkowski. Martingale Methods in Financial Modeling. Springer.
· Hull, J. (2014). Options, Futures and Other Derivatives. Pearson. 9th Edition.
· Björk. Arbitrage Theory in Continuous Time. Oxford Finance.
· Shreve. Stochastic Calculus for Finance Vol 2. Springer.
· Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer.
· Etheridge. A Course in Financial Calculus. Cambridge.