Information-Based Asset Pricing

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 corresponding 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 we assume are accessible to market participants. Each information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents "noise". The noise term is modelled by an independent Brownian bridge that spans the interval from the present to the time at which the value of the factor is revealed. 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. In the case where the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price process. Dividend growth is taken into account by introducing appropriate structure on the market factors. The prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European-style call option is of the Black–Scholes–Merton type. We consider the case where the rate at which information is revealed to the market is constant, and the case where the information rate varies in time. Option pricing formulae are obtained for both cases. The information-based framework generates a natural explanation for the origin of stochastic volatility in financial markets, without the need for specifying on an ad hoc basis the dynamics of the volatility.

Informed traders

“…Under B we find that the distribution of X T is the same as it is under Q, that {x t } and X T are independent, and that {x t } is a B-Brownian bridge (cf. Brody et al 2008a). To see these, recall that, since X T and {b tT }, and hence X T and {B t }, are independent, the probability law of {B t } conditional on X T remains that of a Brownian motion.…”

“…Our analysis is carried out within the information-based asset pricing framework of Brody, Hughston and Macrina (Macrina 2006;Brody et al 2007Brody et al , 2008aRutkowski & Yu 2007;Hughston & Macrina 2008). In this framework-hereafter referred to as the BHM frameworkthe price process of an asset is derived from the specification of (a) the future cash flows associated with the asset, and (b) the flow of information to market participants.…”

Lévy information and the aggregation of risk aversion

“…Examples include information flows concerning the market factors that determine dividends on stocks, defaults on bonds, or claims on insurance contracts. The approach that we are adopting is that of 'information-based asset pricing', as represented in Brody et al [6][7][8][9][10], Brody & Friedman [11], Filipovic et al [12], Hoyle [13], Hoyle et al [14], Hughston & Macrina [15,16], Macrina [17], Macrina & Parbhoo [18], and Rutkowski & Yu [19]. An important advantage of thinking of the filtration as being generated by information processes is that the treatment of informationally heterogeneous markets can then be pursued in a relatively straightforward way.…”

The sound of silence: equilibrium filtering and optimal censoring in financial markets

“…In particular, we derive closed-form exponential-decay solutions for the optimal time-varying censor in periods of silence; a new insight here is that penalization of silence is harshest at the beginning (see Section 3.1, Corollary 1 for details). These are the pleasing consequences of moving to continuous time: simplification of the natural equilibrium conditions (expressing indifference to disclosure: (1) in Section 2.3, (6) in Section 3.1.1, and (9) in Section 3.2) to a first-order differential equation (the filtering equation (5) of Section 3.1); a transparent narrative at the single-agent level; a rich joint asset price dynamic, via the repercussions on each other, of a stream of disclosures from the multiplicity of correlated agents. This paper is a sequel to our previous work, where such questions were pursued in a discrete two-period setting (in [29] and [17] for the case of one firm, and in [16] where further reality is added via a communication game with multiple competitors in an industry correlated by common operating conditions).…”