Numerical Studies of the Implied Volatility Expansions up to Third Order under the Gatheral Model

• The Gatheral double stochastic volatility model is a three-factor model with mean-reverting stochastic volatility that reverts to a stochastic long-run mean. Our previous paper investigated the performance of the first and second-order implied volatilities expansions under this model. Moreover, a simple partial calibration method has been proposed. This paper reviews and extends previous results to the third-order implied volatility expansions under the same model. Using Monte-Carlo simulation as the benchmark method, extensive numerical studies are conducted to investigate the accuracy and properties of the third-order expansion. 

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Financial Market

Mean Reversion Volatility

Gatheral Model

Implied Volatility Expansions

Monte-Carlo Simulation

European Option

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publikations- och innehållstyp

vet (ämneskategori)

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