英文标题：
《An Option Pricing Model with Memory》
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作者：
Flavia Sancier and Salah Mohammed
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最新提交年份：
2017
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英文摘要：
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential equation. A model with full memory is obtained via approximation through a stock price model in which the continuous path dependence does not go up to the present: there is a memory gap. A strong solution is obtained by closing the gap. Fair option prices are obtained through an equivalent (local) martingale measure via Girsanov\'s Theorem and therefore are given in terms of a conditional expectation. The models maintain the completeness of the market and have no arbitrage opportunities.
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中文摘要：
我们得到了漂移项和波动项是股票价格连续历史函数的股票价格模型的期权定价公式。也就是说，股票动力学遵循一个非线性随机泛函微分方程。通过一个股票价格模型的近似，得到了一个具有完全记忆的模型，在该模型中，连续路径依赖性不会上升到现在：存在记忆缺口。通过闭合间隙可获得强解。公平期权价格通过Girsanov定理通过等价（局部）鞅测度获得，因此以条件期望的形式给出。这些模型保持了市场的完整性，没有套利机会。
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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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