An Efficient and Easily Parallelizable Algorithm for Pricing Weather Derivatives
An Efficient and Easily Parallelizable Algorithm for Pricing Weather Derivatives
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DOI：
10.1007/11666806_54
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发表时间：
2005-06
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通讯作者：
Yusaku Yamamoto
中科院分区：
文献类型：
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作者：
Yusaku Yamamoto
我们提出了一个快速和高度并行的算法来定价CDD天气衍生品，这是金融产品，对冲天气风险，由于高于平均温度在夏季。为了找到价格，我们需要计算其收益的期望值，即CDD天气指数。为此，我们推导出一个新的递推公式来计算CDD的概率密度函数。该公式由具有高斯分布的函数的多重卷积组成，并且可以用快速高斯变换有效地计算。此外，我们的算法具有很大程度的并行性，因为每个卷积可以独立计算。数值实验表明，我们的方法是10倍以上的速度比传统的蒙特卡罗方法时，计算各种CDD衍生物的价格在一个处理器上。此外，在具有8个节点的PC集群上的并行执行获得了高达6倍的加速比，允许在大约10秒内完成大多数衍生品的定价。
We present a fast and highly parallel algorithm for pricing CDD weather derivatives, which are financial products for hedging weather risks due to higher-than average temperature in summer. To find the price, we need to compute the expected value of its payoff, namely, the CDD weather index. To this end, we derive a new recurrence formula to compute the probability density function of the CDD. The formula consists of multiple convolutions of functions with a Gaussian distribution and can be computed efficiently with the fast Gauss transform. In addition, our algorithm has a large degree of parallelism because each convolution can be computed independently. Numerical experiments show that our method is more than 10 times faster than the conventional Monte Carlo method when computing the prices of various CDD derivatives on one processor. Moreover, parallel execution on a PC cluster with 8 nodes attains up to six times speedup, allowing the pricing of most of the derivatives to be completed in about 10 seconds.