The work of Black and Scholes [2] and Merton [4] suggests that analysis of hedged positions in a continuous time random walk model yields powerful insights into the valuation of financial securities. The present paper extends this methodology in a straightforward fashion to foreign exchange transactions. By adopting the device of hedging in a secondary market for forward currency contracts against a long position in spot currency, a simple statement of boundary conditions for the forward position can be detailed. This allows a direct solution of the continuous time valuation problem that yields the interest rate parity theory.

This paper develops a new distribution theory for common stock returns. The model is composed of a calendar time diffusion process and a jump process where the magnitudes of the jumps may be autocorrelated. Empirical tests are performed on a month of transactions returns for twenty New York Stock Exchange securities. The data analysis supports the validity of the proposed theory.