An Actuarial Mathematics Approach to Option Pricing

We derive and test a new option pricing method based on statistics. We show how such a method allows to a) analytically price options with risk measures - such as Value-at-Risk or Expected Shortfall - on assets with stochastic volatility; and b) build several new structural models for the credit spread. We discuss how the method entails a new put-call parity relation, and how the option price is affected by the issuer’s credit spread. Finally, we discuss several extensions to the formalism developed here, such as to assets with interdependencies, and to any model for the asset’s returns distribution.