A model with a stochastic interest rate process correlated to a stochastic volatility process is needed to accurately price long-dated contingent claims. Such a model should also price claims efficiently in order to allow for fast calibration. This dissertation explores the approximations for the characteristic function of the Heston-Hull & White model introduced by Grzelak and Oosterlee (2011). Fourier-Cosine expansion pricing is then used to price contingent claims under this model, which is implemented in MATLAB (Fang and Oosterlee, 2008). We find that the model is efficient, accurate and has a relatively simple calibration procedure. In back-tests, it is determined that the Heston-Hull & White model produces better hedging profit and loss results than a Heston (1993) or a Black and Scholes (1973) model.
为了准确地为长期或有债权定价，需要一个随机利率过程与随机波动过程相关联的模型。这样的模型还应该有效地为索赔定价，以便进行快速校准。本文探讨了Grzelak和Oosterlee(2011)提出的Heston-Hull & White模型特征函数的近似。然后使用傅里叶-余弦展开定价来为该模型下的或有债权定价，该模型在MATLAB中实现(Fang和Oosterlee, 2008)。我们发现，该模型是有效的，准确的，并有一个相对简单的校准过程。在回测中，确定了Heston- hull & White模型比Heston(1993)或Black and Scholes(1973)模型产生更好的对冲损益结果。
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