• Summary
• Related Documents
  • Active Bibliography
  • Co-citation
• Version History

Abstract:

This paper shows that the binomial option pricing model, suitably parameterized, is a special case of the explicit finite difference method. To prepare for writing the sequel volume of my new book Derivatives: A PowerPlus Picture Book, I recently reviewed the work on trinomial option pricing since Boyle’s 1988 JFQA paper. I found myself attracted to the Kamrad and Ritchken (1991) trinomial model because it seemed to be the “natural ” generalization of the binomial model described by Cox, Ross and Rubinstein (1979). In that model, as is quite well known, the underlying asset price moves by return x over each period of elapsed time h, where x equals either u or d, while cash earns return r for sure. The resulting corresponding binomial tree is designed to emulate continuoustime risk-neutral geometric Brownian motion with annualized logarithmic mean µ ≡ log(r/d) – σ 2 and variance σ 2, where r is the annualized riskless return (discrete) and d is the annualized payout return (discrete) of the asset. The idea is to choose a parameterization for (r, u, d, and p) in terms of (r, µ and σ) so that

Citations