Regime Switching Levy模型下的局部风险最小套期保值策略

Locally Risk Minimizing Hedging Strategy Under a Regime Switching Levy Model

本文假定风险资产的价格满足马尔可夫调制的几何Levy过程,其中市场利率、风险资产的平均回报率、波动率以及跳跃强度和幅度都依赖于市场的经济状态,这些经济状态由一连续时间马尔可夫链描述.由于该模型下的市场是不完备的,在本文中我们首先采用局部风险最小化方法获得了欧式未定权益的最优套期保值策略.接着,本文给出了一个具体的例子,得到了马尔科夫调制的几何布朗运动模型下的最优套期保值策略的数值结果.最后将该最优套期保值策略与Black-Scholes模型下Delta套期保值策略进行了比较,证实了不确定因素-马氏链的存在给风险管理者的投资决策带来了影响.

In this paper, we suppose that the risky asset follows a Markov-modulated Geometric L@vy process, the market interest rate, the appreciation rate and the volatility rate of the risky asset, and the intensity and magnitude of the jump depend on the states of the economy which are described by a continuous-time Markov chain. Since the market which we considered is incomplete, we find an optimal hedging strategy for a European contingent claim by employing the local risk minimization method. Then we also provide an example and obtain the numerical result of an optimal risk hedging strategy for a European call option under a Markov-modulated Geometry Brownian motion. Finally, this optimal risk hedging strategy and the Delta hedging strategy under the Black-Scholes model are compared in this paper, and prove that the uncertain factors of Markov chain will bring the impact on the investment decision of risk manager.