英文标题：
《Expansion formulas for European quanto options in a local volatility
FX-LIBOR model》
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作者：
Julien Hok, Philip Ngare, Antonis Papapantoleon
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最新提交年份：
2018
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英文摘要：
We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in fixed income and FX markets into account, we consider local volatility models for both the LIBOR and the FX rate. Because of the structure of the local volatility function, a closed form solution for quanto option prices does not exist. Using expansions around a proxy related to log-normal dynamics, we derive approximation formulas of Black--Scholes type for the price, that have the benefit of giving very rapid numerical procedures. Our expansion formulas have the major advantage that they allow for an accurate estimation of the error, using Malliavin calculus, which is directly related to the maturity of the option, the payoff, and the level and curvature of the local volatility function. These expansions also illustrate the impact of the quanto drift adjustment, while the numerical experiments show an excellent accuracy.
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中文摘要：
我们开发了一种扩展方法，用于以伦敦银行同业拆借利率（外币）为基础的欧洲quanto期权定价。我们推导了在国内远期措施下国外LIBOR利率体系的动力学，然后考虑quanto期权的价格。为了考虑固定收益和外汇市场中观察到的倾斜/微笑效应，我们考虑了伦敦银行同业拆借利率和外汇利率的局部波动模型。由于局部波动函数的结构，不存在quanto期权价格的封闭式解。利用对数正态动力学相关代理的展开式，我们导出了价格的Black-Scholes型近似公式，这有助于给出非常快速的数值过程。我们的扩展公式的主要优点是，它们允许使用Malliavin演算精确估计误差，这与期权的成熟度、回报以及局部波动率函数的水平和曲率直接相关。这些展开式也说明了量子漂移调整的影响，而数值实验显示了极好的精度。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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