Real World Pricing of Long Term Contracts

Platen, Eckhard

doi:10.2139/ssrn.1767522

Cited by 4 publications

(2 citation statements)

References 152 publications

(132 reference statements)

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“…The portfolio value at time t is given by 30) Optimal Decisions in the Equity Index Derivatives Markets Using Option Implied Information where h j t is the number of units invested in the jth primary security account at time t. We let V + denote the set of all strictly positive, finite, self-financing portfolios with initial capital x > 0. We use the following definition, formulated by Platen (2009), for the numéraire portfolio, also called the growth optimal portfolio (GOP).…”

Section: Pricing Of European-style Derivatives Under the Benchmark Apmentioning

confidence: 99%

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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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Section: Pricing Of European-style Derivatives Under the Benchmark Apmentioning

confidence: 99%

“…As formulated in Platen (2009), the fair price of the contingent claim, H T , is by the Law of the Minimal Price given by the real world pricing formula:…”

Section: )mentioning

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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Recovering the real-world density and liquidity premia from option data

Barkhagen

Blomvall

Platen

2016

Quantitative Finance

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In this paper we develop a methodology for simultaneous recovery of the real-world probability density and liquidity premia from observed S&P 500 index option prices. Assuming the existence of a numéraire 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 identification of liquidity premia embedded in option price data. We identify and estimate two separate liquidity premia embedded in S&P 500 index options that are consistent with previous findings in the literature.

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A dynamic portfolio approach to asset markets and monetary policy

Platen¹,

Semmler²

2012

Advances in Statistics, Probability and Actuarial Science

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Real World Pricing of Long Term Contracts

Cited by 4 publications

References 152 publications

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

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

Recovering the real-world density and liquidity premia from option data

A dynamic portfolio approach to asset markets and monetary policy

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