Under a no-arbitrage assumption, the futures price converges to the spot price at the maturity of the futures contract, where the basis equals zero. Assuming that the basis process follows a modified Brownian bridge process with a zero basis at maturity, we derive the closed-form solutions of...

This article provides a closed-form valuation formula for the Black-Scholes options subject to interest rate risk and credit risk. Not only does our model allow for the possible default of the option issuer prior to the option's maturity, but also considers the correlations among the option...