The Pricing of Markedâ€toâ€Market Contingent Claims in a Noâ€Arbitrage Economy

This paper assumes that the underlying asset prices are lognormally distributed, and derives necessary and sufficient conditions for the valuation of options using a Blackâ€Scholes type methodology. It is shown that the price of a futuresâ€style, markedâ€toâ€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 Blackâ€Scholes for Mula prices a spotâ€settled contingent claim, if the interestâ€rate accumulation factor is lognormally distributed. Otherwise, the Blackâ€Scholes for Mula holds if the product of the pricing kernel and the interestâ€rate accumulation factor is lognormally distributed.