Coherent risk measures for derivatives under Black-Scholes Economy

Abstract

This paper proposes a risk measure for a portfolio of European-style derivative securities over a fixed time horizon under the Black–Scholes economy. The proposed risk measure is scenario-based along the same line as [3]. The risk measure is constructed by using the risk-neutral probability (-measure), the physical probability (-measure) and a family of subjective probability measures. The subjective probabilities are introduced by using Girsanov's theorem. In this way, we provide risk managers or regulators with the flexibility of adjusting the risk measure according to their risk preferences and subjective beliefs. The advantages of the proposed measure are that it is easy to implement and that it satisfies the four desirable properties introduced in [3], which make it a coherent risk measure. Finally, we incorporate the presence of transaction costs into our framework.