SIAM Journal on Financial Mathematics, Volume 12, Issue 2, Page 672-689, January 2021.
We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function $G$ of the European contract satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. We present examples of Markov processes where the function $G$ that prices the variance swap can be computed explicitly. In general, the solutions $G$ are not contained in the logarithmic family previously obtained in the special case where the Markov process is a Lévy process.

中文翻译：

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时变马尔可夫过程的定价差异交换

SIAM 金融数学杂志，第 12 卷，第 2 期，第 672-689 页，2021 年 1 月。
我们证明，当标的物是指数马尔可夫过程时，方差掉期率（公平罢工）等于联合终端欧式合约的价格，由任意连续随机时钟随时间变化，与驱动马尔可夫具有任意相关性过程，前提是欧洲合约的收益函数 $G$ 满足一个普通的积分微分方程，该方程仅取决于马尔可夫过程的动力学，而不取决于时钟。我们展示了马尔可夫过程的例子，其中可以显式计算对方差交换定价的函数 $G$。通常，解$G$ 不包含在先前在马尔可夫过程是Lévy 过程的特殊情况下获得的对数族中。