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Recovering the Real-World Density and Liquidity Premia from Option Data
Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
Quantitative Finance Research Centre, University of Technology, Sydney, Australia.
2016 (English)In: Quantitative finance (Print), ISSN 1469-7688, E-ISSN 1469-7696, Vol. 16, no 7, 1147-1164 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we develop a methodology for simultaneous recovery of the real-world probability density and liquidity premia from observed S&P500 index option prices. Assuming the existence of a numeraire portfolio for the US equity market, fair prices of derivatives under the benchmark approach can be obtained directly under the real-world measure. Under this modeling framework there exists a direct link between observed call option prices on the index and the real-world density for the underlying index. We use a novel method for estimation of option implied volatility surfaces of high quality which enables the subsequent analysis. We show that the real-world density that we recover is consistent with the observed realized dynamics of the underlying index. This admits the identication of liquidity premia embedded in option price data. We identify and estimate two separate liquidity premia embedded in S&P500 index options that are consistent with previous findings in the literature.

Place, publisher, year, edition, pages
Taylor & Francis, 2016. Vol. 16, no 7, 1147-1164 p.
Keyword [en]
Real-world density; Liquidity premia; Local volatility model; No-nparametric estimation; Simulated Maximum Likelihood
National Category
Economics and Business
URN: urn:nbn:se:liu:diva-117104DOI: 10.1080/14697688.2015.1128117ISI: 000379836500011OAI: diva2:805724
Available from: 2015-04-16 Created: 2015-04-16 Last updated: 2016-08-20Bibliographically approved
In thesis
1. Optimal Decisions in the Equity Index Derivatives Markets Using Option Implied Information
Open this publication in new window or tab >>Optimal Decisions in the Equity Index Derivatives Markets Using Option Implied Information
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 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 results with the performance of commonly used models for the underlying index. The results show that option prices contain a premium in the tails of the distribution. By removing the estimated premia from the tails, the resulting density predicts future realizations of the underlying index very well.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 103 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1657
Option implied information; Optimal decisions; Equity index derivatives; Stochastic programming; Local volatility surface; Real-world density
National Category
Economics and Business
urn:nbn:se:liu:diva-117106 (URN)10.3384/diss.diva-117106 (DOI)978-91-7519-081-5 (print) (ISBN)
Public defence
2015-05-12, ACAS, Hus A, Campus Valla, Linköping, 10:15 (English)
Available from: 2015-04-16 Created: 2015-04-16 Last updated: 2015-04-21Bibliographically approved

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