MFE

Rational valuation of derivative securities

1. Use put-call parity to determine the relationship between prices of European put and call options and to identify arbitrage opportunities.
2. Calculate the value of European and American options using the binomial model.
3. Calculate the value of European and American options using the Black-Scholes option-pricing model.
4. Interpret the option Greeks.
5. Explain the cash flow characteristics of the following exotic options: Asian, barrier, compound, gap, and exchange.
6. Explain what it means to say that stock prices follow a diffusion process.
7. Apply Itô's lemma in the one-dimensional case.
8. Apply option pricing concepts to actuarial problems such as equity-linked insurance.

Interest rate models

1. Evaluate features of the Vasicek and Cox-Ingersoll-Ross bond price models.
2. Explain why the time-zero yield curve in the Vasicek and Cox-Ingersoll-Ross bond price models cannot be exogenously prescribed.
3. Construct a Black-Derman-Toy binomial model matching a given time-zero yield curve and a set of volatilities.

Risk management techniques

1. Explain and demonstrate how to control risk using the method of delta-hedging.