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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.
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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