# Computation of second order price sensitivities in depressed markets

## TL;DR

This paper derives explicit formulas for second order price sensitivities in financial markets under crisis conditions, addressing a gap in risk management tools beyond first order sensitivities.

## Contribution

It provides the first explicit computation of second order price sensitivities in depressed markets, extending existing models beyond the Black-Scholes framework.

## Key findings

- Explicit formulas for second order sensitivities derived
- Improved accuracy of hedging strategies during crises
- Addresses a gap in risk management tools for depressed markets

## Abstract

Risk management in financial derivative markets requires inevitably the calculation of the different price sensitivities. The literature contains an abundant amount of research works that have studied the computation of these important values. Most of these works consider the well-known Black and Scholes model where the volatility is assumed to be constant. Moreover, to our best knowledge, they compute only the first order price sensitivities. Some works that attempt to extend to markets affected by financial crisis appeared recently. However, none of these papers deal with the calculation of the price sensitivities of second order. Providing second derivatives for the underlying price sensitivities is an important issue in financial risk management because the investor can determine whether or not each source of risk is increasing at an increasing rate. In this paper, we work on the computation of second order prices sensitivities for a market under crisis. The underlying second order price sensitivities are derived explicitly. The obtained formulas are expected to improve on the accuracy of the hedging strategies during a financial crunch.