Interest Rate Derivatives
The best approach to valuing ore complex interest rate derivatives is to use a lattice, or possibly a Monte Carlo simulation, that is calibrated to the forward interest rate and volatility curves. The Black-Derman-Toy lognormal distribution model and the Hull-White mean-reverting normal distribution model are two popular choices. I have written about both of these models and also the Ho-Lee and Heath-Jarrow-Morton models. Copies of these articles, which I list below are available on request. More recently I wrote about using a closed-form solution to value interest rate floor with a 0% exercise price. That article is here.
Dwight Grant and Gautam Vora, “Extending the Universality of the Heath-Jarrow-Morton Model,” Review of Financial Economics 15 2 (2006) 129 – 157.
Dwight Grant and Gautam Vora, “Building Lattices: From Cox, Ross and Rubinstein to Heath, Jarrow and Morton,” Journal of Financial Education 31 (Spring 2005) 68 – 85.
Dwight Grant and Gautam Vora, “Analytical Implementation of the Ho and Lee Model of the Evolution of the Spot Interest Rate,” Global Finance Journal 14, 1 (May 2003) 19 – 47.
Dwight Grant and Gautam Vora, “The Hull and White Model of the Short Rate: An Alternative Analytical Representation,” Journal of Financial Research 25 (Winter 2002), 463 – 76.
Dwight Grant and Gautam Vora, “An Analytical Approximation of the Hull and White Model,” Journal of Derivatives (Winter 2001), 54 – 60.
Dwight Grant and Gautam Vora, “Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed,” Journal of Fixed Income 8 4 (March 1999), 85 – 98.