A multi-factor jump-diffusion model for commodities
A multi-factor jump-diffusion model for commodities
复制标题
商品的多因素跳跃扩散模型
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Crosby
中科院分区：
文献类型：
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作者：
J. Crosby
在本文中，我们开发了一个无仲裁的商品衍生品定价模型。该模型生成的期货（或远期）商品价格与任何初始期限结构一致。该模型与商品价格的均值回归是一致的，也产生随机的便利收益。我们的模型是一个多因素跳跃扩散模型，其中一个规格允许长期期货合约的价格跳跃的幅度小于短期期货合约，据我们所知，这是一个功能，以前没有出现在文献中，尽管它是符合程式化的经验观察（特别是能源相关的商品）。我们的模型还考虑了随机利率。该模型为标准欧式期权提供半解析解，使期权价格通常在1/50秒内得到评估（取决于参数值和所需的精度）。这打开了校准模型参数的可能性，从期权的市场价格推导隐含参数。我们对原油期权进行了这样的校准，结果表明，允许长期期货合约比短期合约跳升更小的幅度，可以大大增强拟合。[2]这是前一份工作文件（克罗斯比2005年）“初级商品：一个简单的多因素跳跃-扩散模型”的精简和增强版。
In this paper we develop an arbitrage-free model for the pricing of commodity derivatives. The model generates futures (or forward) commodity prices consistent with any initial term structure. The model is consistent with mean reversion in commodity prices and also generates stochastic convenience yields. Our model is a multi-factor jump-diffusion model, one specification of which allows the prices of long-dated futures contracts to jump by smaller magnitudes than short-dated futures contracts, which, to our knowledge, is a feature that has not previously appeared in the literature, in spite of it being in line with stylised empirical observations (especially for energy-related commodities). Our model also allows for stochastic interest rates. The model produces semi-analytic solutions for standard European options, which enable option prices to be evaluated in typically about 1/50th of a second (depending upon parameter values and the required accuracy). This opens the possibility to calibrate the model parameters by deriving implied parameters from the market prices of options. We perform such a calibration on crude oil options and show that, allowing long-dated futures contracts to jump by smaller magnitudes than short-dated contracts, gives a greatly enhanced fit. †This is a condensed and enhanced version of a previous working paper (Crosby 2005) entitled “Commodities: a simple multi-factor jump-diffusion model”.