Local volatility calibration during turbulent periods

Konstantinos Skindilias () and Chia Lo

Review of Quantitative Finance and Accounting, 2015, vol. 44, issue 3, 425-444

Abstract: We propose a methodology to calibrate the local volatility function under a continuous time setting. For this purpose, we used the Markov chain approximation method built on the well-established idea of local consistency. The chain was designed to approximate jump–diffusions coupled with a local volatility function. We found that this method outperforms traditional numerical algorithms that require time discretization. Furthermore, we showed that a local volatility jump–diffusion model outperformed the in- and out-of-sample pricing that the market practitioners benchmark, namely the Practitioners Black–Scholes, in turbulent periods during which at-the-money implied volatilities have risen substantially. Hedging experiments show a moderate portfolio risk under the local volatility jump–diffusion case. As in previous literature concerning local volatility estimation, we represent the local volatility function using a space-time cubic spline. Copyright Springer Science+Business Media New York 2015

Keywords: Markov chain approximation; Local volatility; Jump–diffusions; Cubic splines; Option pricing; Hedging; C65; G13 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11156-013-0412-6

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