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arXiv · 0704.1976

Information-Based Asset Pricing

Dorje C. Brody·Lane P. Hughston·Andrea Macrina
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Abstract

A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such "X-factor" we associate a market information process, the values of which are accessible to market agents. Each information process is a sum of two terms; one contains true information about the value of the market factor; the other represents "noise". The noise term is modelled by an independent Brownian bridge. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of an asset is given by the expectation of the discounted cash flows in the risk-neutral measure, conditional on the information provided by the market filtration. When the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price, and the prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European call option is of the Black-Scholes-Merton type. The information-based framework also generates a natural explanation for the origin of stochastic volatility.

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Dorje C. Brody, Lane P. Hughston, Andrea Macrina. 2007-04-16. Information-Based Asset Pricing. https://arxiv.org/abs/0704.1976

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