Improved Implementation of Local Volatility and Its Application to S&amp;P 500 Index Options

Orosi, Greg

doi:10.3905/jod.2010.17.3.053

Cited by 15 publications

(9 citation statements)

References 32 publications

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“…Performance compared with other spline-based models Orosi (2010) has previously shown that local volatility spline-based models have superior empirical performance compared wtth the benchmark models considered in this study. In our experience, implied volatility and local volatility thin-plate spline-based models have similar performance for the purpose of interpolation if the number of parameters of both models is comparable.…”

Section: Loocv Option Pricing Errormentioning

confidence: 86%

Empirical performance of a spline-based implied volatility surface

Orosi

2012

J Deriv Hedge Funds

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. His research areas include computational finance and applications, numerical methods applied to derivative pricing, empirical performance of option pricing models, and nonparametric modeling.Correspondence: Greg Orosi, Department of Mathematics and Statistics, American University of Sharjah, Office: Nab 254, P.O. Box 26666, Sharjah, UAE E-mail: gorosi@ucalgary.edu ABSTRACT Since the crash of 1987, it has been observed by option market participants that implied volatilities for out-of-the-money options are higher than predicted by the constant volatility Black-Scholes (1973) model. Option prices also exhibit dependence on time to expiry. The collection of these implied volatilities across strike and maturity is known as the implied volatility surface (IVS). We propose a nonparametric spline-based representation of the IVS and evaluate its empirical performance. Our findings indicate that the proposed model significantly outperforms the best performing implied volatility model reported in the current literature for the purpose of pricing European-style S&P500 index options. We further contribute to the empirical finance literature by choosing a proper model evaluation criterion. By measuring the leave-one-out cross-validation model pricing error of the thin-plate spline-based model, we demonstrate that this superior performance is not the result of overfitting. Although we have previously shown that splinebased models have superior empirical performance, the models considered in this study have advantages over the previously considered models.

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Section: Loocv Option Pricing Errormentioning

confidence: 86%

Empirical performance of a spline-based implied volatility surface

Orosi

2012

J Deriv Hedge Funds

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“…The PBS has been extensively used in the literature as a benchmark model when evaluating the performance in terms of out-of-sample pricing for competing models (see e.g. Dumas et al, 1998;Christoffersen and Jacobs, 2003;Christoffersen et al, 2009;Orosi, 2010). The model parameters of the PBS can be estimated with the help of ordinary least squares and since the implied volatility function is linear in the model parameters the resulting optimization problem is convex.…”

Section: Estimation Methods Described In the Literaturementioning

confidence: 99%

Optimal Decisions in the Equity Index Derivatives Markets Using Option Implied Information

Barkhagen¹

2015

Linköping Studies in Science and Technology. Dissertations

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This dissertation is centered around two comprehensive themes: the extraction of information embedded in equity index option prices, and how to use this information in order to be able to make optimal decisions in the equity index option markets. These problems are important for decision makers in the equity index options markets, since they are continuously faced with making decisions under uncertainty given observed market prices. The methods developed in this dissertation provide robust tools that can be used by practitioners in order to improve the quality of the decisions that they make.In order to be able to extract information embedded in option prices, the dissertation develops two different methods for estimation of stable option implied surfaces which are consistent with observed market prices. This is a difficult and ill-posed inverse problem which is complicated by the fact that observed option prices contain a large amount of noise stemming from market micro structure effects. Producing estimated surfaces that are stable over time is important since otherwise risk measurement of derivatives portfolios, pricing of exotic options and calculation of hedge parameters will be prone to include significant errors. The first method that we develop leads to an optimization problem which is formulated as a convex quadratic program with linear constraints which can be solved very efficiently. The second estimation method that we develop in the dissertation makes it possible to produce local volatility surfaces of high quality, which are consistent with market prices and stable over time. The high quality of the surfaces estimated with the second method is the crucial input to the research which has resulted in the last three papers of the dissertation.The stability of the estimated local volatility surfaces makes it possible to build a realistic dynamic model for the equity index derivatives market. This model forms the basis for the stochastic programming (SP) model for option hedging that we develop in the dissertation. We show that the SP model, which uses i Optimal Decisions in the Equity Index Derivatives Markets Using Option Implied Information generated scenarios for the squared local volatility surface as input, outperforms the traditional hedging methods that are described in the literature. Apart from having an accurate view of the variance of relevant risk factors, it is when building a dynamic model also important to have a good estimate of the expected values, and thereby risk premia, of those factors. We use a result from recently published research which lets us recover the real-world density from only a cross-section of observed option prices via a local volatility model. The recovered real-world densities are then used in order to identify and estimate liquidity premia that are embedded in option prices.We also use the recovered real-world densities in order to test how well the option market predicts the realized statistical characteristics of the underlying index. We compare the resu...

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“…This dataset is identical to the one used in our previous study to evaluate the empirical performance of spline-based, local volatility models (Orosi [2010]). This dataset is identical to the one used in our previous study to evaluate the empirical performance of spline-based, local volatility models (Orosi [2010]).…”

Section: Datamentioning

confidence: 99%