Gamma过程及其扩展的精确模拟定价

Lancelot F. James, Dohyun Kim, Zhiyuan Zhang
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引用次数: 3

摘要

在金融衍生品定价公式没有解析解的情况下,基础状态变量的精确路径模拟对于模拟金融衍生品的价格或其敏感性具有重要的实际意义。然而,通常情况下,大多数非平凡随机波动(SV)模型所固有的复杂依赖结构给精确模拟带来了困难。在本文中,我们提出了一个非平凡的SV模型,它与著名的Heston SV模型在承认精确路径模拟的意义上相似,如broaddie和Kaya所研究的那样。该模型的瞬时波动过程由Gamma过程驱动。研究了模型的扩展,包括独立瞬时波动过程的叠加。数值结果表明,该模型在拟合实物期权数据方面优于Heston模型和其他两种L 'evy驱动的SV模型。强调了精确模拟某些依赖路径的衍生品价格的能力。此外,这是第一个可以在这种定价环境中精确应用无限活动波动过程的实例。
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Exact simulation pricing with Gamma processes and their extensions
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other L\'evy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.
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