An application of the Malliavin calculus for calculating the precise and approximate prices of options with stochastic volatility

DOI10.1090/tpms/1012zbMath1377.91160OpenAlexW2745601398MaRDI QIDQ5351667

S. V. Kuchuk-Yatsenko, Ye. Yu. Munchak, Yuliya S. Mishura

Publication date: 30 August 2017

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tpms/1012

zbMATH Keywords

stochastic volatilityMalliavin calculusoption pricingBlack-Scholes model

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Derivative securities (option pricing, hedging, etc.) (91G20) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (2)

Fractional Cox-Ingersoll-Ross process with small Hurst indices ⋮ Stochastic representation and path properties of a fractional Cox–Ingersoll–Ross process

Cites Work

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• Pricing the European call option in the model with stochastic volatility driven by Ornstein-Uhlenbeck process. Exact formulas
• Option pricing in the model with stochastic volatility driven by Ornstein-Uhlenbeck process. Simulation
• European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process
• On changes of measure in stochastic volatility models
• Stochastic calculus with anticipating integrands
• Stochastic evolution equations with random generators
• Exact and approximate solutions for options with time-dependent stochastic volatility
• Stochastic calculus for finance. II: Continuous-time models.
• Applications of Malliavin calculus to Monte Carlo methods in finance
• The mathematics of arbitrage
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Rate of convergence of option prices by using the method of pseudomoments
• A Theory of the Term Structure of Interest Rates
• Rate of convergence of option prices for approximations of the geometric Ornstein–Uhlenbeck process by Bernoulli jumps of prices on assets
• Fubini-type theorem for anticipating integrals
• A generalized clark representation formula, with application to optimal portfolios
• The Malliavin Calculus and Related Topics
• Stochastic Volatility: Origins and Overview
• Multi-Product Economic Order Quantity Analysis Under Minimum Inventory Valuation Constraints^*
• Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type
• Malliavin Calculus with Applications to Stochastic Partial Differential Equations
• An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach
• Option pricing under stochastic volatility: the exponential Ornstein–Uhlenbeck model

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