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

Abstract

This paper assumes that the underlying asset prices are lognormally distributed and drives 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, market-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.