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摘要翻译：
几何L\'evy模型(GLM)是用于推导Black-Scholes公式的几何布朗运动模型(GBM)的自然推广。如果采用定价核心方法，这种模型的理论将大大简化。在一个维度上，一旦潜在的L\'evy过程被指定，GLM有四个参数：初始价格、利率、波动率和风险厌恶。定价核是一个折扣因子和一个风险厌恶鞅的乘积。对于GBM，风险规避参数是风险的市场价格。对于GLM来说，这种解释是不成立的：超额收益率是波动性和风险厌恶的非线性函数。结果表明，对于正波动性和风险厌恶，利率之上的超额收益率是正的，并且随着这些变量的增加而增加。就外汇而言，西格尔悖论意味着人们可以构造一个外汇模型，在这个模型中，对于汇率和反汇率，超额收益率都是正的。当波动率超过风险厌恶时，这一条件对任何外汇几何L\'Evy模型都成立。
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英文标题：
《General Theory of Geometric L\'evy Models for Dynamic Asset Pricing》
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作者：
Dorje C. Brody, Lane P. Hughston, Ewan Mackie
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最新提交年份：
2012
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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英文摘要：
The geometric L\'evy model (GLM) is a natural generalisation of the geometric Brownian motion model (GBM) used in the derivation of the Black-Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying L\'evy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility, and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. For a GLM, this interpretation is not valid: the excess rate of return is a nonlinear function of the volatility and the risk aversion. It is shown that for positive volatility and risk aversion the excess rate of return above the interest rate is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel's paradox implies that one can construct foreign exchange models for which the excess rate of return is positive both for the exchange rate and the inverse exchange rate. This condition is shown to hold for any geometric L\'evy model for foreign exchange in which volatility exceeds risk aversion.
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PDF链接：
https://arxiv.org/pdf/1111.2169
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