Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model
Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model
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DOI：
10.1080/07362990701420118
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发表时间：
2007-06
影响因子：
1.3
通讯作者：
R. Elliott;T. Siu;Leunglung Chan;J. Lau
中科院分区：
文献类型：
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作者：
R. Elliott;T. Siu;Leunglung Chan;J. Lau
摘要本文研究了标的资产的动态行为由马尔可夫调制跳扩散模型驱动的期权定价问题。我们假设市场利率、标的风险资产的漂移和波动率随着时间的推移而变化，根据经济的状态，这是由一个连续时间马尔可夫链建模。测度过程被定义为Poisson随机测度的广义混合过程，并包含一般的过程类，例如广义Gamma过程，它包括加权Gamma过程和逆高斯过程.测量过程的另一个有趣的特征是跳跃时间和跳跃大小通常可以相关。这里考虑的模型可以为市场从业者提供灵活性，以模拟相关风险资产的动态。在不完全市场环境下，我们利用广义状态转换Esscher变换来确定一个等价的鞅测度。导出了欧式期权价格所满足的耦合偏微分积分方程组。我们还推导出了美式看跌期权到欧式看跌期权和提前执行溢价的分解结果。该模型的仿真结果已经提出和讨论。
Abstract We consider the pricing of options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump-diffusion model. We suppose that the market interest rate, the drift and the volatility of the underlying risky asset switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The measure process is defined to be a generalized mixture of Poisson random measure and encompasses a general class of processes, for example, a generalized gamma process, which includes the weighted gamma process and the inverse Gaussian process. Another interesting feature of the measure process is that jump times and jump sizes can be correlated in general. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the underlying risky asset. We employ the generalized regime-switching Esscher transform to determine an equivalent martingale measure in the incomplete market setting. A system of coupled partial-differential-integral equations satisfied by the European option prices is derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Simulation results of the model have been presented and discussed.