Evolutionary computation and the vega risk of American put options

Abstract

While European style options and American call options can be priced using analytical exact valuation models, closed-form solutions for the valuation of American puts have not yet been derived. The American put price as well as the corresponding greeks (e.g., delta, gamma, vega) can be calculated using numerical procedures or analytical approximations. We use a parallel implementation of the genetic programming approach and derive analytical approximations for determining the vega of an American put option because calculating vegas numerically requires even more computational effort than determining deltas or gammas. Applying our approximations to experimental data sets we can show that the genetically derived approximations outperform other approximations based on frequently used American put pricing formulas.

Natural Computing in Finance – A Review

“…The sensitivities are the so-called greeks for derivatives; duration and convexity for fixed income products. Keber [60] has used GP to calculate greeks of the American-type put options (see Section 3.5 for an explanation of derivative products).…”