FIRST-ORDER ASYMPTOTICS OF PATH-DEPENDENT DERIVATIVES IN MULTISCALE STOCHASTIC VOLATILITY ENVIRONMENT

YURI F. SAPORITO

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FIRST-ORDER ASYMPTOTICS OF PATH-DEPENDENT DERIVATIVES IN MULTISCALE STOCHASTIC VOLATILITY ENVIRONMENT

机译：多尺度随机波动率环境下依赖衍生物的一阶渐近态

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In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire’s functional It? calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent derivatives as well. Under general conditions, the first-order condition is represented by a conditional expectation that could be numerically evaluated. Moreover, if the path-dependence is not too severe, we are able to find path-dependent closed-form solutions equivalent to the first-order approximation of path-independent options derived in Fouque et al. Additionally, we exemplify the results with Asian options and options on quadratic variation.

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《International journal of theoretical and applied finance》 |2018年第3期|共22页
作者
YURI F. SAPORITO;
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作者单位

1Escola de Matemática Aplicada (EMAp) Funda??o Getulio Vargas Praia de Botafogo 190 Rio de Janeiro RJ 22250-900 Brazil;

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正文语种 eng
中图分类财政、金融;
关键词
Functional It? calculus; multiscale stochastic volatility; path dependence;

机译：功能吗？微积分;多尺度随机波动;路径依赖;

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FIRST-ORDER ASYMPTOTICS OF PATH-DEPENDENT DERIVATIVES IN MULTISCALE STOCHASTIC VOLATILITY ENVIRONMENT

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