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Interest rate derivative pricing under the CIR model and LFM

机译:CIR模型和LFM下的利率衍生产品定价

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Short-term interest rate models and forward rate models have been widely used for interest rate derivative pricing, while their performances are usually measured by comparing model implied volatilities with market volatilities. In this paper, we first calibrate LFM (lognormal forward-LIBOR model) and CIR short rate model to market caps data, and find that the LFM is closer to real market. Then we study the pricing problem of caps and European options on coupon bearing bonds under the LFM, resorting to PDE method and Monte Carlo method. We show some numerical experiments and find that these derivative prices under the LFM are lower than that under the CIR model. In addition, we investigate these problems under the two-factor LFM which is similar to two-factor short rate models, and get some approximate analytic solutions.
机译:短期利率模型和远期利率模型已广泛用于利率衍生产品定价,而它们的表现通常是通过比较模型隐含波动率和市场波动率来衡量的。在本文中,我们首先根据市值数据对LFM(对数正向前向LIBOR模型)和CIR短期利率模型进行校准,发现LFM更接近于实际市场。然后,我们采用PDE方法和Monte Carlo方法研究了LFM下附息票债券的上限和欧式期权的定价问题。我们显示了一些数值实验,发现在LFM下这些衍生价格低于在CIR模型下。此外,我们在类似于两因素短期利率模型的两因素LFM下研究了这些问题,并获得了一些近似解析解。

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