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This paper presents a new approximation formula for pricing swaptions and caps/floors under the Libor Market Model of interest rates (LMM) with the local and affine-type stochastic volatility. In particular, two approximation methods are applied in pricing, one of which is so called "Drift-freezing" that fixes parts of the underlying stochastic processes at their initial values. Another approximation is based on an asymptotic expansion approach. An advantage of the authors' method is that those approximations can be applied in a unified manner to a general class of local-stochastic volatility models of interest rates.
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