On the pricing and hedging of options for highly volatile periods

TL;DR

This paper extends the Black-Scholes model to account for increasing volatility during financial crises, providing new pricing formulas and hedging strategies for options in highly volatile periods.

Contribution

It introduces a model capturing rising volatility during crises and derives explicit pricing and hedging solutions for such market conditions.

Findings

Derived a closed-form option pricing formula for increasing volatility scenarios.

Provided explicit hedging strategies tailored for volatile crisis periods.

Enhanced accuracy of option valuation during financial crises.

Abstract

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time. We consider a market suffering from a financial crisis. We provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during financial crisis more precise.