Stochastic Volatility Option Pricing

Ball, Clifford A.; Roma, Antonio

doi:10.2307/2331111

Cited by 233 publications

(122 citation statements)

References 26 publications

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“…Stochastic volatility models are a natural extension of the classical Black-Scholes model that have been introduced as a way to manage the skew and smiles observed in real market data (see for example Hull and White (1987), Scott (1987), Stein and Stein (1991), Ball and Roma (1994) and Heston (1993)). The study of these models have introduced new important mathematical and practical challenges, in particular related with the option pricing problem and the callibration of the corresponding parameters.…”

Section: Introductionmentioning

confidence: 99%

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

Alòs

2012

Finance Stoch

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By means of classical Itô's calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due by correlation and a term due to the volatility of the volatility. This decomposition allows us to develop …rst and second-order approximation formulas for option prices and implied volatilities in the Heston volatility framework, as well as to study their accuracy. Numerical examples are given.

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Section: Introductionmentioning

confidence: 99%

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

Alòs

2012

Finance Stoch

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“…Among these extensions, one of the most popular is to allow the volatility to be a stochastic process (see for example Hull and White (1987), Scott (1987), Stein and Stein (1991), Heston (1993) or Ball and Roma (1994), among others).…”

Section: Introductionmentioning

confidence: 99%

On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility

2006

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In this paper we use the Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process, as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

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“…Therefore, this result of S&S is no longer surprising. Ball and Roma (1994) found that the S&S misdiagnosis of stochastic volatility effects is due to using an "inappropriate" value for variance in the BS price. In context of our model, these arguments are not confirmed.…”

mentioning

confidence: 99%

Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension

Schöbel¹,

Zhu²

1999

Review of Finance

357

129

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Stochastic Volatility Option Pricing

Cited by 233 publications

References 26 publications

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility

Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension

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