Analytical pricing of the smile in a forward LIBOR market model
提出一类解析可解的扩散过程来建模远期LIBOR利率，能精确复制市场给定的caplet波动率，并展示隐含波动率曲线。
We introduce a general class of analytically tractable diffusions for modelling forward LIBOR rates under their canonical measure. The class, which is based on assuming a smooth functional dependence at expiry between a forward rate and an associated Brownian motion, is highly tractable. It implies explicit dynamics, known marginal and transition densities and explicit caplet prices at any time. As an example, we analyse the dynamics given by a linear combination of geometric Brownian motions with perfectly correlated (decorrelated) returns. We finally construct a specific model in the class that reproduces exactly the market caplet volatilities given in input. Examples of the implied-volatility curves produced by the considered models are also shown.