La estimación diaria de la prima de riesgo de la volatilidad

  1. Rubio Irigoyen, Gonzalo
  2. Fiorentini, Gabriele
  3. León Valle, Angel
Journal:
Revista española de financiación y contabilidad

ISSN: 0210-2412

Year of publication: 1999

Issue: 100

Pages: 89-110

Type: Article

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Abstract

This paper examines the stochastic volatility option pricing model suggested by Heston (1993). We estimate the parameters of the stochastic variance process assumed by the model usging the so called indirect inference technique, while daily volatility is estimated by sing the so called indirect inference technique, while daily volatility is estimated by using an aproximation to the diffusion process based on a NAGARCH (1,1). This procedure allows us to daily estimate the volatility risk premiun embbedeb in option prices. The volatility risk premium out to be negative whic implies that investors vill pay (rather than requiring) a risk premium for the risk associated with changing wolatility. We also observe that, in our sampled period, the Black-Scholes model tends to undeprice option prices, while Heston's model underprices at-the-money an in-the-money options, but it overprices otu-of-the money options. Volver al índice de artículos

Bibliographic References

  • AIT-SAHALIA, Y., and A. Lo [1998]: «Nonparametric estimation of state-price densities implicit in financial asset prices», Journal of Finance, 53, pp.499-547.
  • BACKUS, D.; FORESI, S.; LI, K., and Wu, L. [1997]: «Accounting for biases in BlackScholes», Working Paper, Stern School of Business, New York University.
  • BAKSHI, G.; CAO, C., and CHEN, Z. [1997]: «Empirical performance of alternative option pricing models», Journal of Finance, 52, pp. 2003-2049.
  • BATES, D. [1996]: «Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options», Review of Financial Studies, 9, pp. 69-107.
  • BLACK, F. [1976]: «The pricing of commodity contracts», Journal of Financial Economics, 3, pp. 167-179.
  • BLACK, F., and SCHOLES, M. [1973]: «The pricing of options and corporate liabilities», Journal of Political Economy, 81, pp. 637-659.
  • CHRISS, N. [1995]: How to grow a smiling tree, Harvard University, Department of Mathematics Working paper.
  • CORRADO, C., and Su, T. [1996]: «Skewness and kurtosis in S&P 500 index returns implied by option prices», Journal of Financial Research, 19, pp. 175-192.
  • Cox, J., and Ross, S. [1976]: «The valuation of options for alternative stochastic processes», Journal of Financial Economics, 3, pp. 145-160.
  • DAS, S., and SUNDARAM, R. [1998]: «Of smiles and smirks: A term-structure perspective», próxima publicación en el Journal of Financial and Quantitative Analysis.
  • DERMAN, E., and KANI, I. [1994]: «Riding on a smile», Risk, 7, pp. 32-39.
  • DERMAN, E.; KANI, I., and CHRISS, N. [1996]: «Implied trinomial trees of the volatility smile», Journal of Derivatives, 3, pp. 7-22.
  • DUMAS, B.; FLEMING, J., and WHALEY, R. [1998]: «Implied volatility functions: empirical tests», Journal of Finance, 53, pp. 2059-2106.
  • DUPIRE, B. [1994]: «Pricing with a smile», Risk 7, pp. 18-20.
  • EBERLEIN, E.; KELLER, U., and PRAUSE, K. [1998]: «New insights into smile, mispricing, and value at risk: The hyperbolic model», Journal of Business, 71, pp. 371-405.
  • FIORENTINI, G.; LEÓN, A., and RUBIO, G. [1998]: Short-term options with stochastic volatility: Estimation and empirical performance, Instituto Valenciano de Investigaciones Económicas, Otoño.
  • GOURIÉROUX, C.; MONFORT, A., and RENAULT, E. [1993]: «Indirect inference», Journal of Applied Econometrics, 8, pp. 85-118.
  • GUO, D. [1998]: «The risk premium of volatility implicit in currency options», Journal of Business & Economic Statistics, 16, pp. 498-507.
  • HESTON, S. [1993]: «A closed-form solution for options with stochastic volatility with applications to bond and currency options», Review of Financial Studies, 6, pp. 327-344.
  • HULL, J., and WHITE, A. [1987]: «The pricing of options on assets with stochastic volatilities», Journal of Finance, 42, pp. 281-300.
  • JACKWERTH, J. C. [1996]: Implied binomial trees: generalizations and empirical tests, University of California at Berkeley, Working paper RPF-262.
  • JACKWERTH, J. C., and RUBINSTEIN, M. [1996]: «Recovering probability distributions from option prices», Journal of Finance, 51, pp. 1611-1631.
  • LEÓN, A., and MORA, J. [1998]: «Modelling conditional heteroskedasticity: application to the IBEX-35 stock return index», forthcoming in the Spanish Economic Review.
  • LEÓN, A., and RUBIO, G. [1999]: Smiling under stochastic volatility, Documento de trabajo, Universidad de Alicante y Universidad del País Vasco.
  • NANDI, S. [1998]: «How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market», Journal of Banking and Finance, 22, pp. 589-610.
  • NOWMAN, K. [1997]: «Gaussian estimation of single-factor continuous time models of the term structure of interest rates», Journal of Finance, 52, pp. 1695-1706.
  • PEÑA, I.; SERNA, G., and RUBIO, G. [1999]: «Why do we smile? On the determinants of the implied volatility function», Journal of Banking and Finance, 23, pp. 1151-1179.
  • ROSENBERG, J. [1998]: «Pricing multivariate contingent claims using estimated risk-neutral density functions», Journal of International Money and Finance, 17, pp. 229-247.
  • RUBINSTEIN, M. [1994]: «Implied binomial trees», Journal of Finance, 49, pp. 771-818.
  • STEIN, E., and STEIN, J. [1991]: «Stock price distributions with stochastic volatility: an analytical approach», Review of Financial Studies, 4, pp. 727-752.
  • TAYLOR, S., and Xu, X. [1994]: «The magnitude of implied volatility smiles: theory and empirical evidence for exhange rates», The Review of Futures Markets, 13, pp. 355-380.
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