Local Volatility Calibration with the Markov Chain Approximation

Lo, Chia Chun and Skindilias, Konstantinos (2011) Local Volatility Calibration with the Markov Chain Approximation. Centre for EMEA Banking, Finance and Economics Working Paper Series, 2011 (29). pp. 1-11.

Abstract

We propose a method for calibrating the local volatility surface that relaxes the computational complexity associated with many models and prices options consistently with the volatility skew. We achieve this under a continuous time semi-closed form solution based on the Markov chain approximation of Kushner (1990). The continuous time Markov chain setting can accommodate a diffusion or a jump-diffusion. We show that under both cases without the use of any regularisation we can accurately price out-of-sample options.

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