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arXiv 1801.07044q-fin.CP
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真实世界测量下的量化：长期合同的快速准确估值

Quantization Under the Real-world Measure: Fast and Accurate Valuation of Long-dated Contracts

Ralph Rudd, Thomas A. McWalter, Joerg Kienitz, Eckhard Platen

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摘要：

本文提供了一种方法，快速和准确的定价的长期合同，出现的建筑砌块的保险和养老基金协议。它应用递归边际量化（RMQ）和联合递归边际量化（JRMQ）算法在传统风险中性方法的框架之外，在真实世界的概率测度下，使用基准方法对期权进行定价。基准方法进行了审查，并提出了现实世界的定价定理，并适用于各种长期索赔，以获得较便宜的价格比传统的风险中性估值。增长最优投资组合（GOP），基准方法的中心目标，使用时间依赖的常数方差弹性模型（TCEV）建模。推导了欧式期权的解析价格，并利用RMQ算法对GOP上的欧式期权进行了高效、准确的定价。然后将TCEV模型与$3/2$随机短期利率模型相结合，并使用RMQ对零息债券和零息债券期权进行定价，突出了对风险中性定价的偏离。

英文摘要：

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional risk-neutral methods by pricing options under the real-world probability measure, using the benchmark approach. The benchmark approach is reviewed, and the real-world pricing theorem is presented and applied to various long-dated claims to obtain less expensive prices than suggested by traditional risk-neutral valuation. The growth-optimal portfolio (GOP), the central object of the benchmark approach, is modelled using the time-dependent constant elasticity of variance model (TCEV). Analytic European option prices are derived and the RMQ algorithm is used to efficiently and accurately price Bermudan options on the GOP. The TCEV model is then combined with a $3/2$ stochastic short-rate model and RMQ is used to price zero-coupon bonds and zero-coupon bond options, highlighting the departure from risk-neutral pricing.

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