LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

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CAM Stochastic Volatility Model for Option Pricing

Mathematical Problems in Engineering ◽

10.1155/2016/5496945 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8

Author(s):

Wanwan Huang ◽

Brian Ewald ◽

Giray Ökten

Keyword(s):

Monte Carlo ◽

Characteristic Function ◽

Stochastic Volatility ◽

Stochastic Volatility Model ◽

The Other ◽

Stochastic Volatility Models ◽

Control Variate ◽

Volatility Models ◽

Volatility Model ◽

Cam Model

The coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks) of the model. We also derive an approximation for the characteristic function of the model.

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Bayesian Analysis of Stochastic Volatility Models with Levy Jumps : Application to Risk Analysis

Finance and Economics Discussion Series ◽

10.17016/feds.2009.40 ◽

2009 ◽

Vol 2009 (40) ◽

pp. 1-45

Author(s):

Pawel J. Szerszen ◽

Keyword(s):

Risk Analysis ◽

Bayesian Analysis ◽

Stochastic Volatility ◽

Stochastic Volatility Models ◽

Volatility Models ◽

Lévy Jumps

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CLOSED-FORM APPROXIMATION OF PERPETUAL TIMER OPTION PRICES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024914500265 ◽

2014 ◽

Vol 17 (04) ◽

pp. 1450026 ◽

Cited By ~ 6

Author(s):

MINQIANG LI ◽

FABIO MERCURIO

Keyword(s):

Asymptotic Expansion ◽

Closed Form ◽

Stochastic Volatility ◽

Option Prices ◽

Stochastic Volatility Models ◽

Volatility Models ◽

Expansion Technique ◽

Black Scholes ◽

Approximation Formulas ◽

Closed Form Approximation

We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand Black–Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate, especially when the volatility of variance is not large.

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