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Asset Pricing in Discrete TimeA Complete Markets Approach$
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Ser-Huang Poon and Richard Stapleton

Print publication date: 2005

Print ISBN-13: 9780199271443

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0199271445.001.0001

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OPTION PRICING IN A SINGLE-PERIOD MODEL

OPTION PRICING IN A SINGLE-PERIOD MODEL

Chapter:
(p.39) 3 OPTION PRICING IN A SINGLE-PERIOD MODEL
Source:
Asset Pricing in Discrete Time
Author(s):

Ser-Huang Poon (Contributor Webpage)

Richard Stapleton (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271445.003.0003

‘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)

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