Effective Markovian projection: application to CMS spread options and mid-curve swaptions
提出有效马尔可夫投影技术，将复杂随机波动率模型简化为易处理模型，用于定价CMS价差期权和中期互换期权，并给出三种数值方法和基于Johnson分布矩匹配的闭式定价公式。
Pricing of interest rate derivatives, such as CMS spread or mid-curve options, depends on the modelling of the underlying single rates. For flexibility and realism, these rates are often described in the framework of stochastic volatility models. In this paper we allow rates to be modelled within a class of general stochastic volatility models, which includes the SABR, ZABR, free SABR and Heston models. We provide a versatile technique called Effective Markovian Projection, which allows a tractable model to be found that mimics the distribution of the more complex models used to price multi-rate derivatives. Three different numerical approaches are outlined and applied to relevant examples from practice. Finally, a new method that involves moment-matching of Johnson distributions is applied to facilitate closed-form pricing formulas.