From Local Volatility to Local Levy Models
Quantitative Finance, Vol. 4, No. 5, October 2004
17 Pages Posted: 15 Jan 2007
We define the class of local Levy processes. These are Levy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded option prices of all strikes and maturities. The local Levy processes generalize the class of local volatility models. Closed forms for local speed functions for a variety of cases are also presented. Numerical methods for recovery are also described.
Keywords: Hunt Processes, Persistent Skewness, Convolution Transforms
JEL Classification: G10, G12, G13
Suggested Citation: Suggested Citation