nach oben

Review of Quantitative Finance and Accounting

Erschienen in:

01.02.2013 | Original Research

Option pricing under non-normality: a comparative analysis

verfasst von: Sharif Mozumder, Ghulam Sorwar, Kevin Dowd

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 2/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, 1973), the Gram–Charlier (GC) approach of Backus et al. (1997), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, 1993), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, 2000) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, 2002) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio.

Vorheriger Artikel International equity flows, marginal conditional stochastic dominance and diversification

Nächster Artikel Returns transmission, value at risk, and diversification benefits in international REITs: evidence from the financial crisis

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

The reader will note that here the volatility υ_t is not only time-varying, but is also roughly speaking to be interpreted as the square of the BS volatility σ.

Further details on these processes can be found in Cont and Tankov (2004) and Kyprianou (2006).

We have also re-run our results for other Wednesdays with different data sets and find our results robust.

Note that maximum likelihood is not possible for all the Lévy processes because their densities do not always exist. Hence, for consistency, we compute RMSE’s numerically using the mean square error (MSE) function appearing in the Jacobian and then apply finite difference scheme with the same perturbation to compute the partials. This enables us to obtain the MLE even if closed form densities don’t exist. We prefer to use the RMSE because it provides ‘prospective estimates’ which are more appropriate for options, which are forward looking. By contrast MLE provides us with ‘retrospective estimates’ based on, e.g., historical stock prices. An alternative approach which may have been used, but is left as the basis for future study is Bayesian Markov Chain Monte Carlo (MCMC) approach. A recent application of the MCMC approach can be found in the forthcoming paper by Hachicha et al. (2011).

Alles L, Murray L (2010) Non-normality and risk in developing Asian markets. Rev Pac Basin Financ Mark Policies 13(4):583–605CrossRef

Arora RK, Das H, Jain PK (2009) Stock returns and volatility: evidence from select emerging markets. Rev Pac Basin Financ Mark Policies 12(4):567–592CrossRef

Backus D, Foresi S, Li K, Wu L (1997) Accounting for biases in Black–Scholes. Working paper, New York University

Bakshi G, Cao C, Chen Z (1997) Empirical performance of alternative option pricing models. J Finance 52:2003–2049CrossRef

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

Britten-Jones M, Schaefer S (1999) Non-linear value at risk. Eur Finance Rev 2:161–187CrossRef

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

Carr P, Geman H, Madan DB, Yor M (2002) The affine structure of asset returns: an empirical investigation. J Bus 75:305–332CrossRef

Chan JR, Mao WH, Lee CF (2007) The jump behavior of foreign exchange market: analysis of Thai Baht. Rev Pac Basin Financ Mark Policies 10(2):265–288CrossRef

Chen RR, Lee CF, Lee HH (2009) Empirical performance of the constant elasticity variance option pricing model. Rev Pac Basin Financ Mark Policies 12(2):177–217CrossRef

Christoffersen PF (2003) Elements of financial risk management. Academic Press, San Diego

Cont R, Tankov P (2004) Financial modelling with jump processes. Chapman & Hall/CRC Financial Mathematics Series, London

Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53:385–407CrossRef

Dowd K (2005) Measuring market risk. Wiley, New York

Duffy DJ (2006) Finite difference methods in financial engineering: a partial differential equation approach. Wiley, New York

Fusai G, Roncoroni A (2008) Implementing models in quantitative finance: methods and cases. Springer Finance, Berlin

Geman H (2002) Pure jump Lévy processes for asset price modelling. J Bank Finance 26:1297–1316CrossRef

Hachicha A, Hachicha F, Masmoudi A (2011) A comparative study of two models with MCMC alogorithm. Rev Quant Finance Account (forthcoming)

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

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

Hull JC, White A (1988) The pricing of options on assets with stochastic volatility. J Finance 42:281–300CrossRef

Jondeau E, Poon SH, Rockinger M (2007) Financial modelling under non-gaussian distributions. Springer Finance, Berlin

Kou S (2002) A jump diffusion model for option pricing. Manag Sci 48:1086–1101CrossRef

Kyprianou A (2006) Introductory lectures on fluctuations of Lévy processes with applications. Springer, Berlin

Psychoyios D, Dotsis G, Markellos RN (2010) A jump diffusion model for VIX volatility options and futures. Rev Quant Financ Acc 35:245–269CrossRef

Sapp TRA (2009) Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter. Rev Quant Financ Acc 33:303–326CrossRef

Titel: Option pricing under non-normality: a comparative analysis
verfasst von: Sharif Mozumder
Ghulam Sorwar
Kevin Dowd
Publikationsdatum: 01.02.2013
Verlag: Springer US
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 2/2013
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-011-0271-y

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2013

Effects of the Boxing Day tsunami on the world capital markets

Information content of credit ratings in pricing of future earnings

Returns transmission, value at risk, and diversification benefits in international REITs: evidence from the financial crisis

Do investors still benefit from culturally home-biased diversification? An empirical study of China, Hong Kong, and Taiwan

International equity flows, marginal conditional stochastic dominance and diversification

How crosslisting affects merger and acquisition activity