[A simple introduction to contingent claim valuation of risky assets in a discrete time, stochastic interest-rate economy is provided. Taking the term structure of interest rates as exogenous, closed-form solutions are derived for European options written on (i) Treasury bills, (ii) interest-rate forward contracts, (iii) interest-rate futures contracts, (iv) Treasury bonds, (v) interest-rate caps, (vi) stock options, (vii) equity forward contracts, (viii) equity futures contracts, (ix) Eurodollar liabilities, and (x) foreign exchange contracts.]

An algorithm is described that prices European average options. The algorithm is tested against Monte Carlo estimates and is shown to be accurate. The speed of the algorithm is comparable to the Black-Scholes algorithm. A closed-form solution is derived for European geometric average options.

This article provides a new methodology for pricing and hedging derivative securities involving credit risk. Two types of credit risks are considered. The first is where the asset underlying the derivative security may default. The second is where the writer of the derivative security may default. The authors apply the foreign currency analogy of R. Jarrow and S. Turnbull (1991) to decompose the dollar payoff from a risky security into a certain payoff and a 'spot exchange rate.' Arbitrage-free valuation techniques are then employed. This methodology can be applied to corporate debt and over the counter derivatives, such as swaps and caps.