Coherent risk measure for derivatives under Black-Scholes economy with regime switching

Abstract

PURPOSE – The purpose of this paper is to provide a scenario-based risk measure for a portfolio of European-style derivative securities over a fixed time horizon under the regime switching Black-Scholes economy.

DESIGN/METHDOLOGY/APPROACH – The risk measure is constructed by using the risk-neutral probability, the physical probability and a family of subjective probability measures. The subjective probabilities can be interpreted as risk managers or regulators' risk preferences and/or subjective beliefs.

FINDINGS – The authors provide closed form expressions for the European option and barrier option.

RESEARCH LIMITATIONS/IMPLICATIONS – The results are difficult to apply to a portfolio with many different kinds of options.

PRACTCAL IMPLICATIONS – The results provide some insights on risk management of portfolios with derivatives.

ORIGINALITY/VALUE – The paper presents a scenario-based risk measure for a portfolio of European-style derivative securities over a fixed time horizon under the regime switching Black-Scholes economy. Risk management is the most important task for almost all financial industries, although it cannot be claimed that the method and results of this paper solve the problem, it is believed to provide some insights to the problem, albeit theoretical. For vanilla European options and barrier options, the authors obtained a closed form expression for the risk measure. The idea of this paper can be applied to some other exotic options. For portfolios containing different kinds of derivatives, the results of this paper provide some guideline and insights.