Libor市场模型的Monte Carlo控制变量加速方法及并行实现

为了加速定价利率衍生产品的Monte Carlo模拟，对远期测度下Libor市场模型中的漂移项用确定性函数近似，构造了一个与原问题高度相关的控制变量. 然后将此控制变量算法移植到多核CPU和GPU的并行计算环境中，极大地提高了计算效率. 针对利率上限的数值结果表明选取的控制变量十分有效且稳健，多核CPU具有线性加速效果，GPU相对于单核CPU具有很大的计算优势，控制变量和并行计算结合得到的加速效果大致是两者的乘积. 结合控制变量和并行计算的方法可以为其他利率衍生产品如利率下限，互换期权的定价提供有效思路.

Accelerating Monte Carlo simulation of Libor market model via control variates and parallelization

In order to accelerate the Monte Carlo simulation for pricing interest rate derivatives, an efficient control variate was constructed by approximating the drift of Libor market model by a deterministic function under forward measure. Then the control variate Monte Carlo simulation was transplanted to the paralleling computing environment including multi-core CPUs and GPU, resulting in further efficiency enhancement. The numerical results for caps show that the constructed control variate is very efficient and robust; multi-core CPU has a linear acceleration effect while GPU has a great computational advantage compared to single CPU and the method of combining control variate and parallel computing enjoys a speed-up factor about of the product of the two methods. The combined method can also be applied to pricing other interest rate derivatives such as floors and swaptions.