发帖
雷达卡
摘要翻译：
在股票和外汇市场中，标的资产的风险中性动态通常用带跳跃的随机波动率模型来表示。在本文中，我们考虑了这类模型的一个稠密子类，并给出了一系列第一代奇异衍生物的价格的解析可处理公式。我们给出了vanilla期权价格和远期期权价格的Fourier变换的闭式公式，以及大罢工时隐含波动率微笑斜率的公式。给出了方差互换价格的一个简单的显式逼近公式。波动率互换和其他波动率衍生品的价格是显函数的一维积分。给出了双无接触期权的Laplace变换（成熟时）和双敲除看涨和看跌期权的Fourier-Laplace变换（罢工时和成熟时）的解析表达式。后一公式的证明是基于推广的矩阵Wiener-Hopf分解结果。我们还提供了收敛性结果。
---
英文标题：
《Exotic derivatives under stochastic volatility models with jumps》
---
作者：
Aleksandar Mijatovi\'c and Martijn Pistorius
---
最新提交年份：
2010
---
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
--
---
英文摘要：
In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed form formulae for the Fourier transforms of vanilla and forward starting option prices as well as a formula for the slope of the implied volatility smile for large strikes. A simple explicit approximation formula for the variance swap price is given. The prices of volatility swaps and other volatility derivatives are given as a one-dimensional integral of an explicit function. Analytically tractable formulae for the Laplace transform (in maturity) of the double-no-touch options and the Fourier-Laplace transform (in strike and maturity) of the double knock-out call and put options are obtained. The proof of the latter formulae is based on extended matrix Wiener-Hopf factorisation results. We also provide convergence results.
---
PDF链接：
https://arxiv.org/pdf/0912.2595
京公网安备 11010802022788号
