In this paper, we consider the pricing problem of forward start options in the presence of stochastic volatility and regime-switching. By making use of the measure transform technique, with the underlying price as a new numeraire, a closed-form pricing formula is derived in which the only unknown term is the so-called forward characteristic function of the underlying price. The analytical expression of the forward characteristic function under the new measure is subsequently obtained in two steps; the first step treats the regime-switching Heston model as a time-dependent Heston model with the information of the Markov chain beingassumed to be given in advance, while the second step takes the expectation with respect to the Markov chain. Finally, the influence of introducing regime-switching into the Heston model is investigated to show the difference in terms of forward start option pricing between the two models.

在本文中，我们考虑了存在随机波动和制度转换的情况下的远期启动期权的定价问题。通过使用度量转换技术，以基础价格作为新的数字，得出了一个封闭形式的定价公式，其中唯一未知的术语是基础价格的所谓前向特征函数。随后分两步获得新度量下的前向特征函数的解析表达式：第一步将政权转换的Heston模型视为与时间相关的Heston模型，并假定事先提供了马尔可夫链的信息，而第二步则采用了对Markov链的期望。最后，