On option pricing in illiquid markets with jumps

TL;DR

This paper develops a novel option pricing and hedging model for illiquid markets that incorporates both price impact and jump processes, addressing a gap in existing financial models.

Contribution

It introduces the first model combining illiquidity effects with jump processes for option pricing and hedging, filling a significant research gap.

Findings

Provides a new framework for option valuation in illiquid markets with jumps.

Demonstrates the impact of jumps and illiquidity on hedging strategies.

Offers insights into more realistic market modeling under extreme conditions.

Abstract

One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets. Since most markets are illquid, this assumption might be too restrictive. Thus, taking into account the price impact in option pricing is an important issue. This issue has been dealt with, to some extent, for illiquid markets by assuming a continuous process, mainly based on the Brownian motion. However, the recent financial crisis and its effects on the global stock markets have propagated the urgent need for more realistic models where the stochastic process describing the price trajectories involves random jumps. Nonetheless, works related to markets with jumps are scant compared to the continuous ones. In addition, these previous studies do not deal with illiquid markets. The contribution of this paper is to tackle the pricing problem for options in illiquid markets with jumps as well as the hedging strategy within this context, which is the first of its kind to the best knowledge.