Range-Curtailing for Options with Discrete Dividend Payments under General Diffusions

Abstract

Lattice methods are often employed to price contingent claims with discrete dividends under the lognormal diffusion, but they are inclined to suffer from large decreases in execution speed as the number of dividends increases. Heteroskedastic assumptions for the stock price dynamics in between ex-dividend dates exacerbate these difficulties, and the option pricing problem with discrete dividends has thus been limited to the lognormal framework. This article proposes strategies to speed up lattice-based approximations under these general diffusions. A range-curtailing technique that bypasses superfluous computations of numerous subtrees at unrealistic stock prices is considered for European, American, and barrier options. The effect of discrete dividends on the premature exercise of American options is also studied. A benchmark method based on numerical integration is described to validate results obtained in the heteroskedastic framework. TOPICS: Options, statistical methods