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The Pricing of Marked-to-Market Contingent Claims in a No-Arbitrage Economy
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Stephen E. Satchell, Richard C. Stapleton and Marti G. Subrahmanyam
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Abstract
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This paper assumes that the underlying asset prices are lognormally distributed, and
derives necessary and sufficient conditions for the valuation of options using a
Black-Scholes type methodology. It is shown that the price of a futures-style,
marked-to-market option is given by Black's formula if the pricing kernel is
lognormally distributed. Assuming that this condition is fulfilled, it is then
shown that the Black-Scholes formula prices a spot-settled contingent claim, if the
interest-rate accumulation factor is lognormally distributed. Otherwise, the Black-Scholes
formula holds if the product of the pricing kernel and the interest-rate
accumulation factor is lognormally distributed.
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Keywords
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FUTURES; FORWARDS; OPTIONS; ARBITRAGE; PRICING KERNEL; MARTINGALE;
BLACK-SCHOLES MODEL; RISK-NEUTRAL DISTRIBUTION.
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Contact Details
Stephen E. Satchell
Trinity College
Cambridge CB2 1TQ
UK
Richard C. Stapleton
The Management School
Lancaster University
Bailrigg
Lancaster LA1 4YW
UK
Marti G. Subrahmanyam
Stern School of Business
New York University
Salomon Center
40 West Fourth Street
New York NY 10012-1118
USA
E-mail: msubrahm@stern.nyu.edu
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We acknowledge with thanks helpful comments on previous versions of this paper
by participants at the European Finance Association, the Universities of
Michigan, North Carolina and Texas and the Australian Graduate School of Management.
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