Two-Asset Double Barrier Options

In this paper, we explore the pricing of two-asset double barrier options. These options feature two double barriers, each corresponding to one of the two underlying assets within a specific time subinterval. They are useful for reducing premiums, hedging, and aligning with investor expectations regarding asset prices. However, pricing these options is challenging due to the assumed correlation between the two asset prices. We derive the non-crossing probability of two-dimensional Brownian motion for non-overlapping double boundaries and use it to establish analytic pricing formulas for two-asset non-overlapping double barrier options. Furthermore, we present a semi-analytic method for pricing a two-asset overlapping double barrier option. Through numerical experiments, we examine the characteristics of option prices and demonstrate the efficiency of the semi-analytic method.