Paper #1346

Title:

Calibration of stochastic volatility models via second order approximation: the Heston model case

Authors:

Elisa Alòs, Rafael De Santiago and Josep Vives

Date:

October 2012

Abstract:

Using a suitable Hull and White type formula we develop a methodology to obtain a second order approximation to the implied volatility for very short maturities. Using this approximation we accurately calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short maturities so accurate is that we also take into account the term-structure for large maturities. We may say that calibration is not "memoryless", in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla options that can then be used to price exotic derivatives. The methodology is simple, accurate, fast, and it requires a minimal computational cost.

JEL codes:

G13

Area of Research:

Statistics, Econometrics and Quantitative Methods

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