Stochastic Expansion for the Pricing of Call Options with Discrete Dividends
37 Pages Posted: 7 Oct 2010
Date Written: October 5, 2010
Abstract
In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. the fixed part of the dividends. Using Cameron-Martin transformations, we provide explicit representations of the correction terms as Greeks in the Black-Scholes model. The use of Malliavin calculus enables us to provide tight error estimates for our approximations. Numerical experiments show that the current approach yields very accurate results, in particular compared to known approximations of [BGS03,VW09], and quicker than the iterated integration procedure of [HHL03] or than the binomial tree method of [VN06].
Keywords: equity option, discrete dividend, stochastic approximation, analytic formula
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Smart Expansion and Fast Calibration for Jump Diffusion
By Eric Benhamou, Emmanuel Gobet, ...
-
By Eric Benhamou, Emmanuel Gobet, ...
-
Closed Forms for European Options in a Local Volatility Model
By Eric Benhamou, Emmanuel Gobet, ...
-
Analytical Formulas for Local Volatility Model with Stochastic Rates
By Eric Benhamou, Emmanuel Gobet, ...
-
New Approximations in Local Volatility Models
By Emmanuel Gobet and Ali Suleiman
-
Asymptotic and Non Asymptotic Approximations for Option Valuation
By Romain Bompis and Emmanuel Gobet
-
High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models
By Bertram Düring and Michel Fournie