The pricing of marked-to-market contingent claims in a no-arbitrage economy

This paper assumes that the underlying asset prices are lognormally distributed, and derives necessary and su cient 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 ful lled, 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. The futures prices of contingent claims 1