A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model

Abstract

Approximation accuracy, Option pricing, Partial differential equation, Singular perturbation, Stochastic volatility,

Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment

“…For the case of ρ = 0, the errors of the approximation method are about 2% for all strikes. [17] reported the result that the difference rates of this method for plain vanilla European call OTM options are also relatively high. Our result agrees with that evidence.…”

“…Fouque et al [4] argues the method for option pricing in detail. The accuracy of the approximation is examined in Yamamoto and Takahashi [17]. In this paper, it is shown that the first order stochastic volatility term is linearly related to the instantaneous correlation between asset value and volatility state.…”

An Asymptotic Expansion for Forward–Backward SDEs: A Malliavin Calculus Approach

“…Especially, Fujii and Takahashi [9] derived an approximation formula for dynamic optimal portfolio in an incomplete market with stochastic volatility, and confirmed its validity through numerical experiment. This paper presents a new analytical approximation method for the FBSDEs based on a Picard-type iteration and an asymptotic expansion (for the asymptotic expansion approach, see Takahashi and Yamada [33] [34] and related previous works [30] [24][31] [35] [29] for example). Also, our method can be regarded as an extension of the representation theorem of BSDEs by Ma and Zhang [23].…”

A new improvement scheme for approximation methods of probability density functions

“…For other approximation methods in mathematical finance/financial engineering see for example, Bayer and Laurence [3], Ben Arous and Laurence [4], Gatheral, Hsu, Laurence, Ouyang, and Wang [14], Fouque, Papanicolaou and Sircar [13], Henry-Labordere [25], Kusuoka and Osajima [23], Osajima [34], Siopacha and Teichmann [40], and [10], [11], [12], [18], [55], [60], [61].…”