About subordinated generalizations of 3 classical models of option pricing

TL;DR

This paper explores subordinated versions of classical option pricing models driven by inverse subordinators, demonstrating convergence of the binomial model to the subordinated Black-Scholes model and applying it to option pricing.

Contribution

It introduces a subordinated Cox-Ross-Rubinstein model and proves its convergence to the subordinated Black-Scholes model, extending classical models to markets with stagnation periods.

Findings

Binomial model converges to subordinated Black-Scholes model

Option prices computed via binomial trees are validated

Numerical results compare different pricing methods

Abstract

In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of stagnation are observed. We introduce the subordinated Cox-Ross-Rubinstein model and prove that the price of the underlying in that model converges in distribution and in Skorokhod space to the price of underlying in the subordinated Black-Scholes model defined in [31]. Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.