Risk Measures for Derivative Securities under Multiplicative Binomial Model

Abstract

This paper proposes a model for measuring risks of derivatives in the context of a multiplicative binomial framework. Our model is scenario-based and involves the risk-neutral probability (Bbb Q-measure), the physical probability (Bbb P-measure) and a family of subjective probability measures. Each subjective probability is assigned as a distorting Bbb P-measure in order to provide regulators/traders with the flexibility of adjusting risk measures according to their risk preferences. Our model is easy to implement and satisfies the four coherent properties introduced by Artzner et~al. (1999). In practice, it is more realistic to incorporate the uncertainty of the Bbb P- measure. By adopting the idea of Bayesian statistics, we provide confidence intervals at a given probability level for our risk measures under the uncertainty of the Bbb P-measure. Our model can also be applied to deal with American options and the presence of transaction costs. (This is a joint work with my supervisor Dr. Yang)