Is there an informationally passive benchmark for option pricing incorporating maturity?

Abstract

Figlewski proposed testing the incremental contribution of the Black-Scholes model by comparing its performance against an “informationally passive” benchmark, which was defined to be an option pricing formula satisfying static no-arbitrage constraints. In this paper we extend Figlewski's analysis to include options of more than one maturity. Once maturity has been included in the model, any “informationally passive” call pricing function is consistent with some “active” model. In this sense, the notion of a passive model cannot be extended to pricing formulas incorporating option maturity. We derive the index dynamics of the active model implicit in Figlewski's implied G example. These dynamics are far more complicated than the dynamics of the Samuelson-Black-Scholes or Bachelier models. The main implication of our analysis is that an appropriate benchmark for assessing option pricing models should in fact have simple dynamics, such as those of Bachelier or the Black-Scholes models. This is despite the fact that the maturity extension of Figlewski's model gives as good a fit as the Black-Scholes model.

A Multi-Parameter Extension of Figlewski’s Option-Pricing Formula

“…We achieve this by generalizing the passive option-pricing model introduced by Figlewski [2002] and using the insights of Henderson et al [2007]. We achieve this by generalizing the passive option-pricing model introduced by Figlewski [2002] and using the insights of Henderson et al [2007].…”

“…constructing Suitable Pricing Functions Henderson et al [2007] point out that it is difficult to construct even single-parameter option-pricing functions that satisfy the no-arbitrage properties. To determine suitable call option functions, we follow their work.…”

“…Henderson et al [2007] point out that rather than attempting to determine suitable functions c = f(x) it is easier to look for the inverse function x = f −1 (c), where f −1 is a decreasing, convex function that satisfies f −1 (c) ≥ 1-c. A function satisfying these conditions is graphed in the left part of Exhibit 1. Henderson et al [2007] point out that rather than attempting to determine suitable functions c = f(x) it is easier to look for the inverse function x = f −1 (c), where f −1 is a decreasing, convex function that satisfies f −1 (c) ≥ 1-c. A function satisfying these conditions is graphed in the left part of Exhibit 1.…”

“…To incorporate the  f ( ) 1 0 = condition Henderson et al [2007] introduce To incorporate the  f ( ) 1 0 = condition Henderson et al [2007] introduce…”

A robust method to retrieve option implied risk neutral densities for defaultable assets

“…Although the likelihood of default is a critically important feature of numerous asset classes, most techniques developed to extract RNDs fail to adequately address it. Our study is based on the novel parametric implementation of the framework of Orosi (2011) who presented a multi-parameter extension of the models of Figlewski (2002) and Henderson, Hobson, and Kluge (2007). Recent empirical studies Orosi (2011, 2015a) support the use of this approach for its high empirical performance.…”