Relative entropy, distortion, the bootstrap and risk

Abstract

This thesis studies three related topics important to risk management. finance and insurance. The relative entropy bootstrap option pricing models are simulated pricing models where asset price movements are drawn from a set of historically observed movements. In particular, relative entropy is used to select the distribution that is closest to the empirical distribution and satisfies some prescribed moment conditions, such as the martingale constraint on the discounted asset price. A calibration algorithm for simulated pricing models is developed. The algorithm accommodates a set of options with different moneyness as well as across maturities. Finally. we establish the link between relative entropy and distortion. This connection gives a new perspective to the growing body of literature in which the Choquet integral is used to measure and price risks