Stochastic Volatility Inspired Parameterisation of the Local Volatility Model
Document ID: 2008-1259
Published on: 29th December 2008
Author: Graeme Lawson
The Local Volatility model can be viewed as a generalisation of the deterministic (time-varying deterministic volatility) model, such that the instantaneous volatility (or Local Volatility) function of the driving stochastic differential is a function of both the current asset price and time.
The purpose of this note is to introduce the SVI (Stochastic Volatility Inspired) parameterisation devised by Gatheral , whose purpose is to provide a mechanism for interpolating and extrapolating quoted implied volatility data to produce a continuous and smooth arbitrage free implied volatility surface. In this technical note, we show that the Stochastic Volatility Inspired method is a surprisingly good way to also create a Local Volatility function.
