Adaptive mixture for a controlled smile: the LT model
构建了一个无套利权益资产模型，允许远期波动率曲面存在不确定性并随时间平稳变化，通过对数正态混合表达即期和远期分布，可校准于cliquet和香草期权，用于观察和控制波动率曲面演化。
We build here an arbitrage-free model for an equity-type asset that allows the forward volatility surface to be uncertain today and change profiles over time with some stationarity. Sport and forward distributions are both expressed in the same format through convenient lognormal mixtures ensuring consisten recombinations. The underlying spot process is botained as the product of a lognormal and a jump variable that can be easily simulated. Closed-form solutions are dervied for standard and forward-start European options. The model addresses the drawbacks of local volatilitites and is very tractable with respect to jump-discussion and stochastic vol models. It allows to callibrate, as needed, on both cliquet and vanilla options and offers a convenient framework to observe and control volatility surface evolution.