Option Valuation with Normal Mixture GARCH Models

Badescu, Alexandru; Kulperger, Reg; Lazar, Emese

doi:10.2202/1558-3708.1580

Cited by 36 publications

(22 citation statements)

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“…They find that the HAR models are better than the NGARCH model in predicting out-of-sample option prices probably because the former are based on realized volatility which is closer to the implied volatility of options. Badescu, Kulperger, and Lazar (2008) find that an asymmetric normal mixture GARCH model is better at predicting out-of-sample prices of S&P 500 call options than the standard NGARCH (1,1) option pricing model. Although researchers such as Singh, Ahmed and Pachori (2011) have studied the empirical performance of different models for pricing index options in India to the best of our knowledge there has been no study till date in respect of options on the rupee-dollar currency pair.…”

Section: Literature Reviewmentioning

confidence: 84%

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Bhat¹,

Arekar²

2016

IJEF

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Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models -the Black-Scholes-Merton Option Pricing Model (BSM) and Duan"s NGARCH option pricing model -for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the "volatility smile". This bias of the BSM results from its assumption of a constant volatility over the option"s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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Section: Literature Reviewmentioning

confidence: 84%

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Bhat¹,

Arekar²

2016

IJEF

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“…In fact, volatility is the only parameter that needs to be estimated and we could argue that in option markets, investors trade volatility. Second, volatility measurement is an important issue for policy makers, portfolio managers and financial market participants because it can be used as a measurement of risk, providing an important input for portfolio management, option pricing and market regulation (Poon and Granger, 2003;Badescu et al, 2008). Third, a related issue, which has become very clear during the 2007-2009 financial crisis, is that greater volatility in the financial markets raises important questions about the stability of the global financial system and its consequences on the real economy.…”

Section: Introductionmentioning

confidence: 99%

Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model

2010

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In this paper we model the return volatility of stocks traded in the Athens Stock Exchange using alternative GARCH models. We employ daily data for the period January 1998 to November 2008 allowing us to capture possible positive and negative effects that may be due to either contagion or idiosyncratic sources. The econometric analysis is based on the estimation of a class of five GARCH models under alternative assumptions with respect to the error distribution. The main findings of our analysis are: first, based on a battery of diagnostic tests it is shown that the normal mixture asymmetric GARCH (NM-AGARCH) models perform better in modeling the volatility of stock returns. Second, it is shown that with the use of the Kupiec's tests for in-sample and out-of-sample forecasting performance the evidence is mixed as the choice of the appropriate volatility model depends on the trading position under consideration. Third, at the 99% confidence interval the NM-AGARCH model with skewed Student-distribution outperforms all other competing models both for in-sample and out-of-sample forecasting performance. This increase in predictive performance for higher confidence intervals of the NM-AGARCH model with skewed Student-distribution makes this specification consistent with the requirements of the Basel II agreement. Copyright © 2010 John Wiley & Sons, Ltd.

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“…Stock-level leverage effects are not incompatible with our previous findings: once diversified away through index investing, leverage effects would therefore disappear, explaining the previously listed empirical results. Using the components of the SP500 index, we run the in-sample Hansen test and measure the percentage of stocks for which we find a statistically significant leverage effect 6 .…”

Section: Testing For Leverage Effects At a Stock Levelmentioning

confidence: 99%

“…The time varying volatility structure accounts for the potential changes in the level of risk in financial markets when the conditional distribution deals with the rare occurrence of extreme events, usually seen as jumps. Such an approach turned out to be both successful when applied in continuous -as in Bates (1996)'s extension of Heston (1993)'s work -and in discrete time models -as in Christoffersen et al (2006Christoffersen et al ( , 2010, Badescu et al (2008), Chorro et al (2010Chorro et al ( , 2012 or Guégan et al (2013). The estimation of such models is a complex matter as components in the volatility structure and in the conditional distribution can impact the model implied density in a very similar way.…”

Section: Introductionmentioning

confidence: 99%

“…This article aims to provide a reliable measure of it using 25 years of S&P 500 returns. Following Badescu et al (2008Badescu et al ( , 2011 and Chorro et al (2010Chorro et al ( , 2012, we combine two classical asymmetric GARCH specifications used in the financial literature, namely, the Exponential GARCH (EGARCH) introduced by Nelson (1991) and the Asymmetric Power ARCH model (APARCH) of Ding et al (1993), with two families of conditional distributions that are able to generate various levels of skewness and kurtosis: the Generalized Hyperbolic distribution as introduced by Barndorff-Nielsen (1977) and the mixture of two Gaussian distributions (see e.g. Behboodian, 1970).…”

Section: Introductionmentioning

confidence: 99%

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Testing for leverage effects in the returns of US equities

Chorro

Guégan

Ielpo

et al. 2018

Journal of Empirical Finance

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This article questions the empirical usefulness of leverage effects to describe the dynamics of equity returns. Relying on both in and out of sample tests we consistently find a weak contribution of leverage effects over the past 25 years of S&P 500 returns. The skewness in the conditional distribution of the returns's time series model is found to explain most of the returns' distribution's asymmetry. This conclusion holds both at the index level and for 70% of the individual stocks constituents of the equity index.

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Option Valuation with Normal Mixture GARCH Models

Cited by 36 publications

References 1 publication

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model

Testing for leverage effects in the returns of US equities

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