Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures

Understand

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk.

• Focusing for the first time on the context where risk is measured according to convex risk measures, we establish that the problem reduces to solving independently the writer and the buyer's hedging problem with zero initial capital.
• By further imposing that the risk measures decompose in a way that satisfies a Markovian property, we provide dynamic programming equations that can be used to solve the hedging problems for both the case of European and American options.
• All of our results are general enough to accommodate situations where the risk is measured according to a worst-case risk measure as is typically done in robust optimization.