或有债权函数生成的投资组合及其在期权定价中的应用

arXiv - QuantFin - Pricing of Securities Pub Date : 2023-08-26 DOI:arxiv-2308.13717

Ricardo T. Fernholz, Robert Fernholz

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引用次数: 0

摘要

在由严格正连续半鞅表示的股票市场中，或有债权函数是给定终端值的股票价格和时间的正C^{2,1}函数。如果某一或有索求函数满足某一抛物线微分方程，则该或有索求函数将生成具有复制该或有索求函数的价值过程的投资组合。抛物型微分方程是布莱克-斯科尔斯方程的一般形式。

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Portfolios Generated by Contingent Claim Functions, with Applications to Option Pricing

In a market of stocks represented by strictly positive continuous semimartingales, a contingent claim function is a positive C^{2, 1} function of the stock prices and time with a given terminal value. If a contingent claim function satisfies a certain parabolic differential equation, it will generate a portfolio with value process that replicates the contingent claim function. This parabolic differential equation is a general form of the Black-Scholes equation.

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arXiv - QuantFin - Pricing of Securities

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