American Option Valuation under Continuous-Time Markov Chains
American Option Valuation under Continuous-Time Markov Chains
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DOI：
10.1239/aap/1435236980
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发表时间：
2015-06
影响因子：
1.2
通讯作者：
Björn Eriksson;M. Pistorius
中科院分区：
文献类型：
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作者：
Björn Eriksson;M. Pistorius
本文研究了连续时间马氏链驱动下美式期权价值的最优停止问题。在这种情况下，美式期权的价值函数被描述为变分不等式系统的唯一解（在分配意义上）。此外，连续和光滑的拟合原则不适用于这个离散的状态空间设置，一个新的明确的特征提供了最佳停止边界的发电机的底层马尔可夫链。在此基础上，给出了一个在马尔可夫链模型下美式期权定价的算法。通过应用于适当选择的马尔可夫链序列，该算法提供了一个近似的估值下的一类马尔可夫模型，包括扩散模型，指数Lévy模型，和随机微分方程驱动的Lévy过程的美式期权。一系列不同模型的数值实验表明，近似算法是灵活和准确的。还提供了收敛性的证明。
This paper is concerned with the solution of the optimal stopping problem associated to the value of American options driven by continuous-time Markov chains. The value-function of an American option in this setting is characterised as the unique solution (in a distributional sense) of a system of variational inequalities. Furthermore, with continuous and smooth fit principles not applicable in this discrete state-space setting, a novel explicit characterisation is provided of the optimal stopping boundary in terms of the generator of the underlying Markov chain. Subsequently, an algorithm is presented for the valuation of American options under Markov chain models. By application to a suitably chosen sequence of Markov chains, the algorithm provides an approximate valuation of an American option under a class of Markov models that includes diffusion models, exponential Lévy models, and stochastic differential equations driven by Lévy processes. Numerical experiments for a range of different models suggest that the approximation algorithm is flexible and accurate. A proof of convergence is also provided.