Chapter

OPTION PRICING IN A SINGLE-PERIOD MODEL

Ser-Huang Poon and Richard Stapleton

in Asset Pricing in Discrete Time

Published in print January 2005 | ISBN: 9780199271443
Published online July 2005 | e-ISBN: 9780191602559 | DOI: http://dx.doi.org/10.1093/0199271445.003.0003
OPTION PRICING IN A SINGLE-PERIOD MODEL

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‘Option Pricing in a Single-Period Model’ uses the one-period complete markets model to derive forward prices of European-style options relates them to the forward price of the underlying asset. The authors show that the value of the option depends upon the shape of the pricing kernel, and, in particular, on the shape of the asset-specific pricing kernel, ψ(xj). The analysis starts at a general level and then concentrates on an important special case, where the underlying cash flow is lognormal. They establish in this case that a risk-neutral valuation relationship (RNVR) exists between the option price and the price of the underlying asset if the asset-specific pricing kernel, ψ(xj), has the property of constant elasticity. This establishes the well known Black–Scholes equation for the value of an option.

Keywords: asset-specific pricing kernel; Black–Scholes; constant elasticity; European-style options; lognormal; pricing kernel; risk-neutral valuation relationship (RNVR)

Chapter.  6576 words.  Illustrated.

Subjects: Financial Markets

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