The Pricing of Marked†to†Market Contingent Claims in a No†Arbitrage Economy

Stephen E. Satchell, Richard C. Stapleton and Marti G. Subrahmanyam
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Stephen E. Satchell: Trinity College, Trinity Street, 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, 40th West Fourth Street, New York NY 10012–1118, USA; E†mail: msubrahm@stern.nyu.edu

Australian Journal of Management, 1997, vol. 22, issue 1, 1-20

Abstract: 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 for Mula if the pricing kernel is lognormally distributed. Assuming that this condition is fulfilled, it is then shown that the Black†Scholes for Mula prices a spot†settled contingent claim, if the interest†rate accumulation factor is lognormally distributed. Otherwise, the Black†Scholes for Mula holds if the product of the pricing kernel and the interest†rate accumulation factor is lognormally distributed.

Keywords: FUTURES; FORWARDS; OPTIONS; ARBITRAGE; PRICING KERNEL; MARTINGALE; BLACK†SCHOLES MODEL; RISK†NEUTRAL DISTRIBUTION (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:sae:ausman:v:22:y:1997:i:1:p:1-20

DOI: 10.1177/031289629702200101

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