Risk and Derivative Price

We consider an asset market traded three types of assets: the risk–free asset, the market portfolio and derivatives written on the market portfolio return. We determine a sufficient condition to guarantee that noise risk monotonically changes their derivatives. The condition is that Arrow–Pratt absolute risk aversion is decreasing and convex.Derivative price, Noise risk, Nonlineality, Risk aversion

Dependent Background Risks and Asset Prices

Dependent background risks which have functional forms are introduced into Lucas economies. This paper determines the conditions on preferences to guarantee the monotonicity of asset prices, when dependent background risks satisfy the monotonicity and the single crossing conditions.Asset Price, Dependent Background Risk, Monotonicity, Single Crossing Condition.

A Note on Sufficient Conditions of Cross Risk Vulnerability

This note gives sufficient conditions of cross risk vulnerability introduced by Malevergne and Rey (2005), which is the equivalent condition to guarantee that an unfair non-monetary background risk makes decision makers more risk averse. The sufficient conditions determined by this note expand the results for univariate utility function into bivariate utility functions.Background risk, cross risk vulnerabiilty, risk aversion.

The Monotonicity of Asset Prices with Changes in Risk

The goal of this paper is the examination of the conditions on preferences to guarantee the monotonicity of asset prices, when their returns change in the sense of first- and second-order stochastic dominances.Asset Price; Comparative Statics; First-order Stochastic Dominance; Second-order Stochastic Dominance.

A Risk–Neutral Characterization of Optimism and Pessimism, and its Applications

This note gives a simple, but useful characterization of optimism and pessimism represented by a convex and concave shift of probability weighting functions, and applies it to two comparative static analysis.Optimism, pessimism, rank dependent expected utility, risk–neutral decision weight.

Comparative Risk Aversion under Background Risks Revisited

This note determines a sufficient condition on (von Neumann-Morgenstern) utility functions to preserve (reserve) comparative risk aversion under general background risks. Our condition is weaker than the one determined by Nachman (1982, Journal of Economic Theory). Nachmanfs condition requires the monotonicity in the global sense, in other hand our condition only requires it in the local sense. And this generalization may make the condition on utility functions to hold the desirable property consisitent with the recent empirical observation.Background risk, comparative risk aversion, single crossing condition.

The Comparative Statics on Asset Prices Based on Bull and Bear Market Measure

For single-period complete financial asset markets with representative investors, we introduce a bull market measure for uncertain state occurrence and its associated ordering between representative investors in markets based on their marginal rate of substitution between equilibrium consumption allocations among possible states. These concepts combine and generalize the likelihood-ratio-dominance relation between probability prospects of state occurrence and the Arrow-Pratt ordering of risk aversion in expected utility settings. By analyzing the comparative statics for bull market effects on equilibrium asset prices, we derive some monotone properties of the risk-free rate and discounted prices of dividend-monotone assets.Bull and Bear Market Measure, Comparative Statics, Equilibrium Asset Price, Dividend-Monotone Asset, Total Positivity of Order 2

The Comparative Statics of Equilibrium Derivative Prices

We examine the conditions for preferences and risks that guarantee monotonicity of equilibrium derivative prices. In a Lucas economy with a derivative, we derive the equilibrium derivative price under expectation with respect to risk-neutral probability, and analyze comparative statics on the equilibrium derivative price based on the risk-neutral probability.Equilibrium Derivative Price, First-order Stochastic Dominance, Noise Risk, Risk-Neutral Probability.