Options pricing and risk measures under regime-switching models

Abstract

As a more realistic reflection of the underlying economy, regime switching models have been widely applied to a variety of finance-related fields. The main characteristic of the model is that some parameters, such as the volatility of the underlying risky asset and risk-free interest rate, can be modulated by the market mood which is often modeled by a Markov chain. This talk focuses on the applications of regime switching models in option pricing and risk measurement. In option pricing, European geometric Asian options are considered, firstly with fixed strike price and then with floating strike price. In risk measurement, we deliberate on the coherent risk measures for derivatives, such as vanilla European options and barrier option, under Black-Scholes economy and mean-reverting lognormal setting, respectively. In this talk, the market mood process is modeled by a continuous-time Markov chain with finite states. In valuation of Asian option prices, Taylor expansion allows us to derive an explicit approximate formula to value both fixed strike and floating strike Asian options under regime switching models. In absence of regime switching, a closed-form pricing formula to floating strike Asian options is presented. In all cases, to assess the accuracy of the resulting prices, Markov chain Monte Carlo simulations have been used as benchmarks. All these simulations show that the proposed solution is fairly accurate for various levels of each parameter. In constructing risk measure, we consider 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, the mean-reverting lognormal process and the regime switching mean-reverting lognormal process, respectively. The risk measure is constructed by using the risk-neutral probability (Q-measure), the physical probability (P-measure) and a family of subjective probability measures. The subjective probabilities can be interpreted as risk managers or regulators’ risk preferences and/or subjective beliefs. We provide closed form expressions for the barrier option under Black-Scholes models and European options under both Black-Scholes models and mean-reverting lognormal process. These results provide some insights on risk management of portfolios with derivatives. on Thursday, May 19, 2011 10:30 a.m. – 11:30 a.m. at Room 524, Meng Wah Complex (behind the Chong Yuet Ming Amenities Centre) All interested are welcome