Understanding the Implied Volatility Surface for Options on a Diversified Index |
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Authors: | David?Heath Email author" target="_blank">Eckhard?PlatenEmail author |
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Institution: | (1) Department of Mathematical Sciences, School of Finance and Economics, University of Technology Sydney, Broadway, NSW 2007, Australia |
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Abstract: | This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the
implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal
portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a
time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral
martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale.
However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which
includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options
that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed
model and their Black-Scholes counterparts.
Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20
JEL Classification: G10, G13 |
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Keywords: | index derivatives minimal market model random scaling growth optimal portfolio fair pricing binary options |
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