State-price Process Research Articles

HETEROGENEITY IN RISK PREFERENCES LEADS TO STOCHASTIC VOLATILITY

This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are heterogeneous in risk-preferences.

Capital Ownership Under Market Incompleteness: Does it Matter?

The implications of a context with household heterogeneity and incomplete financial markets have been mostly studied under the assumption that households own the physical capital and undertake the intertemporal investment decision. Further, firms rent capital and labor from the households to maximize period profits. The present paper provides the conditions under which this assumption is still irrelevant when markets are incomplete. It is shown that, if firms choose the optimal investment to maximize their asset value, in the sense that they discount future cash flows with state price processes that are consistent with security prices, the equilibrium allocations are the same as in the standard setting with static firms. On the other hand, the firm valuation of future cash flows only coincides with the valuation of the unconstrained shareholders. Given this, value maximization might still lead to shareholder disagreement in the presence of effectively binding portfolio restrictions.

On the positive fundamental value of money with short-sale constraints

This paper is concerned with the pricing of money in a framework with restrictions on trading, under an extension of the standard-asset pricing theory that recognizes both tangible and intangible returns. It is argued that the underlying motivations for demanding money give content to its fundamental value and the bubble component. This approach is illustrated by analyzing the case where no short-sales are allowed, as two examples from the literature are made used to assert that money is a pure pricing bubble. Owing to this setup exhibits technically incomplete financial markets, the fundamental value of money is not uniquely defined over the set of generalized state-price processes. Then, these examples are shown to comprise an extreme case, as money is a pure store of value for the state-prices chosen (i.e., it is a pricing bubble). Instead, the fundamental value of money can be positive for other state-prices, representing the role of money in the trading process. Therefore, money should not be considered the equivalent of a pure pricing bubble.

The value of money in a dynamic equilibrium model

This paper studies the pricing of money in an infinite-horizon economy with heterogeneous agents, incomplete financial markets and arbitrary borrowing restrictions. Purchases of the consumption good are subject to a cash-in-advance constraint. Under general conditions I show that the price of money is equal to its fundamental value, where this value is defined over all state-price processes that are compatible with the existence of no-arbitrage opportunities. This equality implies that the cash-in-advance constraint is binding infinitely often for all agents in the economy. The analysis highlights certain differences in the determination of the price of money with respect to models with money in the utility function that bear on the optimal implementation of economic policies.

Pricing of New Assets in an Infinite‐Horizon Frictional Economy

This paper studies the pricing of new assets in an infinite‐horizon frictional economy. It uses results on state prices to establish conditions under which the valuation structure of the economy (defined as the collection of all state price processes) is unaffected by the introduction of new assets and conditions under which the new assets do not give rise to arbitrage.

Rational Bubbles under Diverse Information

This paper uses a set of post-extraction information trees to generally model diverse information and agent specific state price processes to define present and fundamental values. It shows that there can be no negative or finite bubbles and that, if agents are impatient and the aggregate endowment has a finite present value under some state price process of some agent, then there can be no bubble under this state price process for any asset with positive supply.

Rational Bubbles under Diverse Information

This paper uses a set of post-extraction information trees to generally model diverse information and agent specific state price processes to define present and fundamental values. It shows that there can be no negative or finite bubbles and that, if agents are impatient and the aggregate endowment has a finite present value under some state price process of some agent, then there can be no bubble under this state price process for any asset with positive supply.

Viable prices in financial markets with solvency constraints

We study the viability of a securities market model with continuous trading in which agents are required to remain solvent at all times and cannot add funds to their portfolio of securities in excess of an exogenous endowment. A financial security is characterized by its dividends and its usefulness as a collateral for borrowing. We show that viability, a notion introduced by Harrison and Kreps (1979), is equivalent to the existence of a pair of continuous linear functionals, defined on the consumption space and “risk-adjusted reserve” space, such that their sum represents a linear pricing rule for cash flows consistent with security prices. We also show that viability is equivalent to the existence of a state price process such that the adjusted total gains from securities are local martingales. In particular, one can construct a probability measure under which the discounted total gains of securities with the same collateral quality as the riskless asset are martingales. The discounted total gains of lower quality securities are submartingales. The state price process is always equal to the process of cash flow “shadow” price times an increasing process. Finally, we characterize the riskless rate and local risk premia on securities.