Three-point volatility smile classificationEvidence from the Warsow Stock Exchange during volatile summer 2011

  1. García Machado, Juan José
  2. Rybczynski, Jaroslaw
Revista:
Investigaciones europeas de dirección y economía de la empresa

ISSN: 1135-2523

Año de publicación: 2015

Volumen: 21

Número: 1

Páginas: 17-25

Tipo: Artículo

DOI: 10.1016/J.IEDEE.2013.09.005 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Investigaciones europeas de dirección y economía de la empresa

Resumen

Este artículo analiza el comportamiento de la sonrisa de la volatilidad en la Bolsa de Varsovia (WSE) durante el volátil verano de 2011, derivada de las opciones más líquidas sobre el índice polaco WIG20, cuyas series expiraron en septiembre de 2011. En ese período, el índice había caído aproximadamente un 20% en tan sólo dos semanas. Mediante interpolación lineal construimos 355 curvas de sonrisas para poder estudiar una posible clasificación o tipología de las mismas. Proponemos 17 tipos de sonrisas, las cuales representan todos los casos posibles de tres monetizaciones de patrones gráficos. Esta clasificación se basa en la relación valores superiores/iguales/inferiores de la volatilidad implícita para cada uno de los tres puntos. Además, se distingue la convexidad de cada una. Destacamos que las sonrisas completas, las sonrisas asimétricas y las inclinadas hacia arriba son de forma convexa, mientras que las invertidas y las inclinadas hacia abajo son funciones cóncavas.

Referencias bibliográficas

  • Bates D. The crash of 87: Was it expected? The evidence from options markets. Journal of Finance 1991, 46(3):1009-1044.
  • Black F., Scholes M. The valuation of option contracts and a test of market efficiency. Journal of Finance 1972, 27:399-417.
  • Black F., Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 1973, 81(May/June (3)):637-659.
  • Bollen N.P.B., Whaley R.E. Does net buying pressure affect the shape of the implied volatility functions?. Journal of Finance 2004, 59:711-753.
  • Bookstaber R. Option pricing and investment strategies 1991, Probus Publishing, Chicago. 3rd ed.
  • Brenner M., Subrahmanyam M.G. A simple formula to compute the implied standard deviation. Financial Analysts Journal 1988, 44(September/October (5)):80-83.
  • Carverhill A.P., Cheuk T.H.F., Dyrting S. The rice of the smirk: Returns to delta and vega neutral portfolios of S&P 500 futures options. Discussion Paper, EFA 2002. Berlin Meetings 2002.
  • Chang E.C., Ren J., Shi Q. Effects of the volatility smile on exchange settlement practices: The Hong Kong case. Journal of Banking and Finance 2009, 33:98-112.
  • Clewlow L., Xu X. A review of option pricing with stochastic volatility. FORC Preprint, 92/35 1992, University of Warwick.
  • Clewlow L., Xu X. The dynamics of stochastic volatility. Working paper 1993, Financial Options Research Centre, University of Warwick.
  • CME Options and Alternatives Chicago Mercantile Exchange. Chicago 1988.
  • Constantinides G.M. Transaction costs and the volatility implied by options prices. Working Paper 1997, University of Chicago.
  • Covring V., Low B.S. The quality of volatility traded on the over-the-counter currency market: A multiple horizons study. Journal of Futures Markets 2003, 23(March (3)):261-285.
  • Cox J., Ross S.A., Rubinstein M. Option pricing: A simplified approach. Journal of Financial Economics 1979, 7(September (3)):229-263.
  • Culumovic L., Welch R.L. A reexamination of constant-variance American call mispricing. Advances in Futures and Options Research 1994, 7(1):177-221.
  • Das S.R., Sundaram R. Of smiles and smirks: A term-structure perspective. Journal of Finance and Quantitative Analysis 1999, 34(2):211-241.
  • Deuskar P., Gupta A., Subrahmanyam M.G. Liquidity effects in OTC markets: Premium or discount?. Journal of Financial Markets 2011, 14(1):127-160.
  • Dumas B., Fleming J., Whaley R. Implied volatility functions: Empirical tests. Journal of Finance 1998, 53(6):2059-2106.
  • Duque J.L.C., Paxson D. Implied volatility and dynamic hedging. Review of Futures Markets 1994, 13(2):381-421.
  • Duque J.L.C., Teixeira Lopes P. Maturity and volatility effects on UK smiles or dying smiling. Portuguese Economic Journal 2003, 2:173-193.
  • Ederington L., Guan W. Why are those options smiling?. Journal of Derivatives 2002, 10:9-34.
  • Engle R.F., Mustafa C. Implied ARCH models from options prices. Journal of Econometrics 1992, 52(April/May (1 & 2)):289-311.
  • Engström M. Do Swedes smile? On implied volatility functions. Journal of Multinational Financial Management 2002, 12:285-304.
  • Galai D. A survey of empirical tests of option pricing models. Option pricing: Theory and applications 1983, 45-80. Lexington, Massachusetts. B. Menachem (Ed.).
  • Gemmill G. Did option traders anticipate the crash? Evidence from volatility smiles in U.K. with U.S. comparisons. Journal of Futures Markets 1996, 16(8):881-897.
  • Gemmill G., Kamiyama N. International transmission of option volatility and skewness: When you're smiling does the whole world smile?. Proceedings of the 24th Annual Meeting of European Finance Association 1997.
  • Gerald C.F., Wheatley P.O. Applied numerical analysis 1994, Reading, Addison Wesley. 4th ed.
  • Geske R., Johnson H.E. The American put option valued analytically. Journal of Finance 1984, 39(December (5)):1511-1524.
  • Geske R., Roll R. On valuing American call options with the Black-Scholes European formula. Journal of Finance 1984, 39(2):443-455.
  • Gkamas D., Paxson D. Which stochastic volatility model for option pricing? Working Paper 1999, Manchester Business School.
  • Grossman S., Zhou Z. Equilibrium analysis of portfolio insurance. Journal of Finance 1996, 51(4):1379-1403.
  • Heynen R. An empirical investigation of observed smile patterns. Working paper 1994, Tinbergen Institute, Erasmus University, Rotterdam.
  • Heynen R., Kemna A., Vorst T. Analysis of the term structure of implied volatilities. Journal of Financial and Quantitative Analysis 1994, 29(March (1)):31-56.
  • Hull J.C. Options, futures, and other derivatives 2012, Prentice Hall, Pearson Education, New Jersey. 8th ed.
  • Hull J.C., White A. The pricing of options on assets with stochastic volatilities. Journal of Finance 1987, 42(2):281-300.
  • Jarrow R., Li H., Zhao F. Interest rate caps 'smile' too! But can the LIBOR market models capture it?. Journal of Finance 2007, 62(1):345-382.
  • Kritzman M. What practitioners need to know about estimating volatility: Part I. Financial Analysts Journal 1991, 47(July/August (4)):22-25.
  • Kuo I-D. Pricing and hedging volatility smile under multifactor interest rate models. Review of Quantitative Finance and Accounting 2011, 36:83-104.
  • León A., Rubio G. Smiling under stochastic volatility. Spanish Economic Review 2004, 6:53-75.
  • Lim G.C., Martin G.M., Martin V.L. Pricing currency options in tranquil markets: Modelling volatility frowns. Monash Econometrics and Business Statistics Working Papers 2002, Monash University, Department of Econometrics and Business Statistics.
  • Low C. The fear and exuberance from implied volatility of S&P 100 index options. Discussion Paper, AFA 2001. New Orleans Meetings 2000.
  • Macbeth J.D., Merville L.J. An empirical examination of the Black-Scholes call option pricing model. Journal of Finance 1979, 34(December (5)):1173-1186.
  • McKenzie S., Gerace D., Subedar Z. An empirical investigation of the Black-Scholes model: Evidence from the Australian Stock Exchange. Australasian Accounting Business and Finance Journal 2007, 1(December (4)):71-82.
  • Marks R.J. Introduction to Shannon sampling and interpolation theory 1991, Springer-Verlag, New York.
  • Mayhew S. Implied volatility. Financial Analysts Journal 1995, 51(July/August (4)):8-20.
  • Pan J. The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics 2002, 63:3-50.
  • Peña I., Serna G., Rubio G. Why do we smile? On the determinants of the implied volatility function. Journal of Banking and Finance 1999, 23:1151-1179.
  • Peña I., Serna G., Rubio G. Smiles, bid-ask spreads and option pricing. European Financial Management 2001, 7:351-374.
  • Rompolis L., Tzavalis E. Risk premium effects on implied volatility regressions. Journal of Financial Research 2010, 33(3):125-152.
  • Rubinstein M. Nonparametric tests of alternative option pricing model using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. Journal of Finance 1985, 40(June (2)):455-480.
  • Shastri K., Tandon K. An empirical test of a valuation model for American options on futures contracts. Journal of Financial and Quantitative Analysis 1986, 21(December (4)):377-392.
  • Sheikh A. Transaction data tests of S&P 100 call option pricing. Journal of Financial and Quantitative Analysis 1991, 26(December (4)):727-752.
  • Szu W.M., Wang M.C., Yang W.R. The determinants of exchange settlement practices and the implication of volatility smile: Evidence from the Taiwan Futures Exchange. International Review of Economics and Finance 2011, 20:826-838.
  • Wong W.K., Tu A.H. Market imperfections and the information content of implied and realized volatility. Pacific-Basin Finance Journal 2009, 17:58-79.
  • Xu X., Taylor S. The term structure of volatility implied by foreign exchange options. Journal of Financial and Quantitative Analysis 1994, 29(March (1)):57-74.
Fuente de los datos: Dialnet