英文标题：
《Asian option as a fixed-point》
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作者：
Adriana Ocejo
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最新提交年份：
2018
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英文摘要：
We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a regime-switching geometric Brownian motion with coefficients that depend on a Markov chain. The typical approach to finding the value of a financial option is to solve an associated system of coupled partial differential equations. Alternatively, we propose an iterative procedure that converges to the value of this contract with geometric rate using a classical fixed-point theorem.
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中文摘要：
我们将金融合约亚式期权的价格描述为非线性算子的不动点。近年来，人们有兴趣将制度变化纳入描述基础资产价格（即利率和波动性）演变的参数中，以模拟经济中的突发外生事件。亚洲期权尤其有趣，因为回报取决于综合资产价格。我们研究了具有算术平均的浮动和固定行使亚洲看涨期权的情况，当资产遵循区域切换几何布朗运动，其系数依赖于马尔可夫链。寻找金融期权价值的典型方法是求解相关的耦合偏微分方程组。或者，我们提出了一个迭代过程，使用经典的不动点定理，以几何速率收敛到这个契约的值。
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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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