Abstract
In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiples strikes, outperforming the state-of-the-art method we compare with. Further, the a priori knowledge of SWIFT parameters makes possible a reliable and practical implementation of the presented calibration method. A wide set of stress, speed and convergence numerical experiments is carried out, with deep in-the-money, at-the-money and deep out-of-the-money options for very short and very long maturities.
Highlights
We extend the SWIFT method to the calibration problem by deriving the option price gradient; We implement and test the speeding-up techniques mentioned in [1] based on multiple strike valuation; We propose a novel method for calibrating the Heston model with a set of options with certain fixed strikes that can be later used for arbitrary strikes by interpolation; We develop and implement speeding up techniques for the option price gradient
The SWIFT method is used to calibrate a Heston model with European call options price data at different strikes and maturities, and it will be compared to the pricing and calibration method based on expression (8) proposed by [5], which, for the sake of readability, will be called Cui pricer (CP)
Stress tests: the CP and SWIFT methods will be tested with several combinations of extreme strikes (ATM and deep ITM and OTM) as well as with long-term and short-term maturities, to detect any possible limitation or numerical issue in a wide usage range; Speed
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The Heston model is a well-known stochastic volatility (SV) model for driving the dynamics of the assets. In order to use the Heston model, we need to calibrate its five parameters to real-market data. The goal of calibrating a model using market data is to estimate the model parameters in such a way that, when it is used for option valuation with an appropriate option valuation method, it yields prices similar to the real market ones
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