Explaining the Volatility Surface: A Closed-Form Solution to Option Pricing in a Fractional Jump-Diffusion Market
23 Pages Posted: 6 Mar 2012 Last revised: 26 Oct 2012
Date Written: June 8, 2012
Abstract
This paper prices European options in a framework that captures both non-normality of returns and serial correlation within financial time series. The underlying security dynamics are driven by a jump-diffusion process where the diffusion part is fractional Brownian motion while jumps exhibit a double-exponential distribution. These model characteristics suffice to overcome most of the evident drawbacks of the classical Black-Scholes setting, while the parsimony of my model still ensures analytical tractability.
Due to market incompleteness, I suggest an equilibrium model à la Brennan (1979). I derive a closed-from solution to the problem, which contains the Black-Scholes pricing formulae and the formulae of Kou (2002) as limit cases.
As an intuitive illustration of the model's power, I choose the phenomenon of volatility surfaces: I show that the derived formulae are able to reflect observable patterns of real market data as the model entails a smile over moneyness as well as a non-flat term structure of implied Black-Scholes volatilities.
Keywords: closed-form solution, equilibrium model, fractional Brownian motion, jump-diffusion
JEL Classification: G12, G13
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
A Jump Diffusion Model for Option Pricing
By Steven Kou
-
Option Pricing Under a Double Exponential Jump Diffusion Model
By Steven Kou and Hui Wang
-
A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes
-
The Term Structure of Simple Forward Rates with Jump Risk
By Paul Glasserman and Steven Kou
-
A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes
By Roger Lord, Fang Fang, ...
-
From Local Volatility to Local Levy Models
By Peter Carr, Hélyette Geman, ...
-
Interest Rate Option Pricing with Poisson-Gaussian Forward Rate Curve Processes
-
By Liming Feng and Vadim Linetsky
-
By Liming Feng and Vadim Linetsky
