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Integral Equation Formulation for Interest Rate Options
Abstract
We address the pricing of American-style interest rate options under the assumption that interest rates obey a mean-reverting random walk as given by the Vasicek model, and consider caplets and floorlets which are the interest rate counterparts of calls and puts. We use a technique due to Kolodner (1956) and Kim (1990) to derive an expression involving integrals for the price of such an option close to expiry. We then evaluate this expression on the optimal exercise boundary to obtain and solve a pair of integral equations for the location of this exercise boundary, and solve these equations close to expiry.
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