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Introduction

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A Time Series Approach to Option Pricing

Abstract

An equity option is a financial asset that gives its buyer the right (but not the obligation) to buy or sell a certain quantity of stocks or financial instruments on or before specified dates at a predefined price. To a certain extent, an option is similar to an equity future, except for the fact that the buyer has no commitment to buy or sell anything at the due date. Actually, options fall into two main classes (see e.g. Hull, Options, futures and other derivatives, 8th edn. Prentice Hall, Boston, 2011): vanilla and exotic that differ in exercise styles and payoff values. As their respective names make it rather clear, vanilla options are standard financial assets with a simple type of guaranty whereas exotic ones have more complex financial structures (e.g. a Barrier option structured such that the underlying stock has to reach a certain level to be active or inactive). To avoid specific technical and numerical problems, in this book we will focus on the vanilla type as it has been used in the academic literature as a benchmark for comparing empirical performances of pricing models. Basically, we wish to help readers to understand the value that the time series methodologies presented in this book can add to this well known basis before turning to securities with a more complex payoff.

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Notes

  1. 1.

    The authors attribute to Robert C. Merton the key financial intuition of their seminal paper: the no-arbitrage principle.

References

  • Aît-Sahalia Y, Lo A (1998) Nonparametric estimation of state-price densities implicit in financial asset prices. J Financ 53:499–547

    Article  Google Scholar 

  • Aît-Sahalia Y, Lo A (2000) Nonparametric risk management and implied risk aversion. J Econ 94:9–51

    Article  Google Scholar 

  • Badescu A, Elliott RJ, Ortega JP (2014) Quadratic hedging schemes for non-Gaussian GARCH models. J Econ Dyn Control 42:13–32

    Article  Google Scholar 

  • Barone-Adesi G, Engle RF, Mancini LA (2008) GARCH option pricing model in incomplete markets. Rev Financ Stud 21(3):1223–1258

    Article  Google Scholar 

  • Bates DS (1991) The crash of ’87 was it expected? The evidence from options markets. J Financ 46:1009–1044

    Article  Google Scholar 

  • Bates DS (1996) Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Rev Financ Stud 9(1):69–107

    Article  Google Scholar 

  • Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:637–659

    Article  Google Scholar 

  • Carr P, Madan D (1999) Option valuation using the fast Fourier transform. J Comput Financ 2(4):61–73

    Google Scholar 

  • Chorro C, Guégan D, Ielpo F (2010) Martingalized historical approach for option pricing. Financ Res Lett 7(1):24–28

    Article  Google Scholar 

  • Chorro C, Guégan D, Ielpo F (2012) Option pricing for GARCH type models with generalized hyperbolic innovations. Quant Financ 12(7):1079–1094

    Article  Google Scholar 

  • Christoffersen P, Heston SL, Jacobs K (2006) Option valuation with conditional skewness. J Econ 131:253–284

    Article  Google Scholar 

  • Christoffersen P, Heston SL, Jacobs K (2013) Capturing option anomalies with a variance-dependent pricing kernel. Rev Financ Stud 26(8):1963–2006

    Article  Google Scholar 

  • Duan JC (1995) The GARCH option pricing model. Math Financ 5:13–32

    Article  Google Scholar 

  • Duffie D, Kan R (1996) A yield-factor model of interest rates. Math Financ 6(4):379–406

    Article  Google Scholar 

  • Elliott R, Madan D (1998) A discrete time equivalent martingale measure. Math Financ 2(8):127–152

    Article  Google Scholar 

  • Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987–1007

    Article  Google Scholar 

  • Engle RF, Bollerslev T (1986) Modelling the persistence of conditional variances. Econ Rev 94:405–420

    Article  Google Scholar 

  • Gouriéroux C, Monfort A (2007) Econometric specification of stochastic discount factor models. J Econ 136(2):509–530

    Article  Google Scholar 

  • Heston SL (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud 6(2):327–343

    Article  Google Scholar 

  • Heston SL, Nandi S (2000) A closed-form GARCH option valuation. Rev Financ Stud 13:585–625

    Article  Google Scholar 

  • Hull JC (2011) Options, futures and other derivatives, 8th edn. Prentice Hall, Boston

    Google Scholar 

  • Jackwerth J (2000) Recovering risk aversion from option prices and realized returns. Rev Financ Stud 13:433–451

    Article  Google Scholar 

  • Mercuri L (2008) Option pricing in a garch model with tempered stable innovations. Financ Res Lett 5(3):172–182.

    Article  Google Scholar 

  • Monfort A, Pegoraro F (2012) Asset pricing with second-order esscher transforms. J Bank Financ 36(6):1678–1687

    Article  Google Scholar 

  • Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32:122–136

    Article  Google Scholar 

  • Rubinstein M (1985) Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. J Financ 40:455–480

    Article  Google Scholar 

  • Siu TK, Tong H, Yang H (2004) On pricing derivatives under GARCH models: a dynamic Gerber-Shiu approach. N Am Actuarial J 8:17–31

    Google Scholar 

  • Walker JS (1996) Fast Fourier transforms, 2nd edn. CRC, Boca Raton

    Google Scholar 

Download references

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Chorro, C., Guégan, D., Ielpo, F. (2015). Introduction. In: A Time Series Approach to Option Pricing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45037-6_1

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  • DOI: https://doi.org/10.1007/978-3-662-45037-6_1

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