英文标题：
《Additive energy forward curves in a Heath-Jarrow-Morton framework》
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作者：
Fred Espen Benth, Marco Piccirilli, Tiziano Vargiolu
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最新提交年份：
2018
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英文摘要：
  One of the peculiarities of power and gas markets is the delivery mechanism of forward contracts. The seller of a futures contract commits to deliver, say, power, over a certain period, while the classical forward is a financial agreement settled on a maturity date. Our purpose is to design a Heath-Jarrow-Morton framework for an additive, mean-reverting, multicommodity market consisting of forward contracts of any delivery period. The main assumption is that forward prices can be represented as affine functions of a universal source of randomness. This allows us to completely characterize the models which prevent arbitrage opportunities: this boils down to finding a density between a risk-neutral measure $\\mathbb{Q}$, such that the prices of traded assets like forward contracts are true $\\mathbb{Q}$-martingales, and the real world probability measure $\\mathbb{P}$, under which forward prices are mean-reverting. The Girsanov kernel for such a transformation turns out to be stochastic and unbounded in the diffusion part, while in the jump part the Girsanov kernel must be deterministic and bounded: thus, in this respect, we prove two results on the martingale property of stochastic exponentials. The first allows to validate measure changes made of two components: an Esscher-type density and a Girsanov transform with stochastic and unbounded kernel. The second uses a different approach and works for the case of continuous density. We apply this framework to two models: a generalized Lucia-Schwartz model and a cross-commodity cointegrated market.
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中文摘要：
电力和天然气市场的一个特点是远期合约的交付机制。期货合约的卖方承诺在一定期限内交付（比如说）权力，而传统的远期合约是在到期日结算的金融协议。我们的目的是设计一个Heath-Jarrow-Morton框架，用于由任何交货期的远期合约组成的加性、均值回复、多商品市场。主要假设是，远期价格可以表示为普遍随机性来源的仿射函数。这使我们能够完整地描述防止套利机会的模型：这归结为在风险中性度量$\\mathbb{Q}$$之间找到一个密度，这样像远期合约这样的交易资产的价格是真实的$\\mathbb{Q}$-鞅，而现实世界的概率度量$\\mathbb{P}$，在此情况下远期价格是均值回复。这种变换的Girsanov核在扩散部分是随机无界的，而在跳跃部分，Girsanov核必须是确定性有界的：因此，在这方面，我们证明了随机指数鞅性质的两个结果。第一种方法允许验证由两个组件所做的度量更改：Esscher型密度和具有随机无界核的Girsanov变换。第二种方法使用不同的方法，适用于连续密度的情况。我们将此框架应用于两个模型：广义Lucia Schwartz模型和跨商品协整市场。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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