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An Improved Convex Model for Efficient Estimation of Option Implied Surfaces
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.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Estimation of option implied surfaces that are consistent with observed market prices and stable over time is a fundamental problem in finance. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND) surface, while satisfying no-arbitrage constraints. Our developed framework considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized, which leads to an optimization model where it is possible to formulate the constraints as linear constraints, making the resulting large-scale optimization problem convex and the solution a global optimum. This is a major advantage of our method compared to most estimation algorithms described in the literature, which are typically cast as non-convex optimization problems with multiple local optima. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. The stability of our method is demonstrated through a time series study based on historical prices of S&P 500 index options.

Keyword [en]
Risk-neutral density surface; Non-parametric estimation; Optimization; No-arbitrage constraints; Implied volatility surface; Local volatility surface
National Category
Economics and Business
Identifiers
URN: urn:nbn:se:liu:diva-117101OAI: oai:DiVA.org:liu-117101DiVA: diva2:805716
Available from: 2015-04-16 Created: 2015-04-16 Last updated: 2015-04-21
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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1657
Keyword
Option implied information; Optimal decisions; Equity index derivatives; Stochastic programming; Local volatility surface; Real-world density
National Category
Economics and Business
Identifiers
urn:nbn:se:liu:diva-117106 (URN)10.3384/diss.diva-117106 (DOI)978-91-7519-081-5 (ISBN)
Public defence
2015-05-12, ACAS, Hus A, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-04-16 Created: 2015-04-16 Last updated: 2017-01-09Bibliographically approved

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Barkhagen, MathiasBlomvall, Jörgen

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