A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics

56 Pages Posted: 14 Dec 2003

See all articles by Alexey Medvedev

Alexey Medvedev

Lombard Odier & Cie

O. Scaillet

Swiss Finance Institute - University of Geneva

Date Written: September 2003

Abstract

In this paper we develop approximating formulas for European options prices based on short term asymptotics, i.e. when time-to-maturity tends to zero. The analysis is performed in a general setting where stochastic volatility and jumps drive the dynamics of stock returns. In a numerical study we show that the closed form approximation is accurate for a broad range of option parameters typically encountered in practice. An empirical application illustrates its use in calibrating observed smiles of S&P 500 index options, and in getting new insight into the dependence of the volatility of volatility and jump size distribution on the spot volatility. We test the consistency of the calibration by showing that the shape of the volatility of volatility inferred from option prices agrees with its estimate from the time series of spot volatilities inferred from the same observed option prices.

Keywords: Option pricing, stochastic volatility, asymptotic approximation, jump-diffusion

JEL Classification: G12

Suggested Citation

Medvedev, Alexey and Scaillet, Olivier, A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics (September 2003). Available at SSRN: https://ssrn.com/abstract=477441 or http://dx.doi.org/10.2139/ssrn.477441

Alexey Medvedev (Contact Author)

Lombard Odier & Cie ( email )

Avenue des Morgines 6
Petit-Lancy
Switzerland

Olivier Scaillet

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland

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