Pricing and Hedging of Derivative Contracts
In this class we will cover basic ideas and their related methods to price and hedge derivative contracts. The material in this class is most useful if the students have a minimum knowledge of derivative pricing (familiarity with the concepts and main ideas of hedging, as taught in an introduction to Finance class) as well as to be comfortable with using basic calculus and basic statistics. Simple programming will be used too.
The program is divided in two related parts:
Part A: General Valuation of Derivatives
- Review of Basic Binomial Formula for risk-neutral probability, risk-neutral variation, Delta, and pricing of derivatives. American vs European options.
- Numerical Implementation of Binomial Formula.
- Black-Scholes as Limit of Binomial. Lognormal change of probability, risk neutral density.
- Derivation of Fundamental p.d.e. for the pricing a derivative. Linear vs Non-linear pde’s (ie. European vs American options).
- (Numerical) Solution methods for p.d.e’s. coming from a derivative contract.
- Exotic and path dependent derivatives. Monte Carlo valuation. Numerical Techniques.
Part B: Derivatives on Volatility, VIX and others.
- Derivatives on Volatility: Variance Swaps
- VIX and Variance Swaps.
- Stochastic Volatility, and derivatives on VIX.