Local volatility calibration during turbulent periods

Local volatility calibration during turbulent periods 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Quantitative Finance and Accounting Springer Journals

Local volatility calibration during turbulent periods

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Economics / Management Science; Finance/Investment/Banking; Accounting/Auditing; Econometrics; Operations Research/Decision Theory
ISSN
0924-865X
eISSN
1573-7179
D.O.I.
10.1007/s11156-013-0412-6
Publisher site
See Article on Publisher Site

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.

Journal

Review of Quantitative Finance and AccountingSpringer Journals

Published: Nov 6, 2013

References

  • Jump–diffusion processes: volatility smile fitting and numerical methods for option pricing
    Andersen, L; Andreasen, J
  • Using markov chains to estimate losses from a portfolio of mortgages
    Betancourt, L
  • News–good or bad–and its impact on volatility predictions over multiple horizons
    Chen, X; Ghysels, E
  • The importance of the loss function in option valuation
    Christoffersen, P; Jacobs, K
  • A joint analysis of the term structure of credit default swap spreads and the implied volatility surface
    Da Fonseca, J; Gottschalk, K
  • Riding on a smile
    Derman, E; Kani, I

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