Option Pricing in the Moderate Deviations Regime
20 Pages Posted: 5 Apr 2016
Date Written: April 5, 2016
Abstract
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher order small-time moderate deviation estimates of call prices and implied volatility are obtained. The expansions involve only simple expressions of the model parameters, and we show in detail how to calculate them for generic local and stochastic volatility models. Some numerical examples for the Heston model illustrate the accuracy of our results.
Keywords: density expansions in small time, option pricing in small time, moderate deviations
JEL Classification: G13
Suggested Citation: Suggested Citation