Explaining the volatility smile: non-parametric versus parametric option models

Explaining the volatility smile: non-parametric versus parametric option models We employ a “non-parametric” pricing approach of European options to explain the volatility smile. In contrast to “parametric” models that assume that the underlying state variable(s) follows a stochastic process that adheres to a strict functional form, “non-parametric” models directly fit the end distribution of the underlying state variable(s) with statistical distributions that are not represented by parametric functions. We derive an approximation formula which prices S&P 500 index options in closed form which corresponds to the lower bound recently proposed by Lin et al. (Rev Quant Financ Account 38(1):109–129, 2012). Our model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models. Although a quantitative comparison with other non-parametric models is more difficult, there are indications that our model is also more consistent with the data than these models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Quantitative Finance and Accounting Springer Journals

Explaining the volatility smile: non-parametric versus parametric option models

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Finance; Corporate Finance; Accounting/Auditing; Econometrics; Operation Research/Decision Theory
ISSN
0924-865X
eISSN
1573-7179
D.O.I.
10.1007/s11156-014-0491-z
Publisher site
See Article on Publisher Site

Abstract

We employ a “non-parametric” pricing approach of European options to explain the volatility smile. In contrast to “parametric” models that assume that the underlying state variable(s) follows a stochastic process that adheres to a strict functional form, “non-parametric” models directly fit the end distribution of the underlying state variable(s) with statistical distributions that are not represented by parametric functions. We derive an approximation formula which prices S&P 500 index options in closed form which corresponds to the lower bound recently proposed by Lin et al. (Rev Quant Financ Account 38(1):109–129, 2012). Our model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models. Although a quantitative comparison with other non-parametric models is more difficult, there are indications that our model is also more consistent with the data than these models.

Journal

Review of Quantitative Finance and AccountingSpringer Journals

Published: Jan 1, 2015

References

  • Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options
    Bates, D
  • Empirical option pricing: a retrospection
    Bates, DS
  • The valuation of option contracts and a test of market efficiency
    Black, F; Scholes, M
  • The pricing of contingent claims in discrete time
    Brennan, Michael

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