Narrow Results

We consider a general discrete-time dynamic financial market with three assets: a riskless bond, a security and a derivative. The market is incomplete (a priori) and at equilibrium. We assume also that the agents of the economy have short-sales constraints on the stock and that the payoff at the expiry of the derivative asset is a monotone function of the underlying security price. The derivative price process is not identified ex ante. This leads the agents to act as if there were no market for this asset at the intermediary dates. Using some nice properties of the pricing probabilities, which are admissible at the equilibrium, we prove that it suffices to consider the subset of the risk-neutral probabilities that overestimate the low values of the security and underestimate its high values with respect to the true probability. This approach greatly reduces the interval of admissible prices for the derivative asset with respect to no-arbitrage, as showed numerically.

We consider a model of the economy that splits investors into two groups. One group (the reference traders) trades an underlying asset according to the difference in realized returns between that asset and some evolving consensus estimate of those returns; the other group (hedgers) hedge options, namely straddles, on the underlying asset. We consider the cases when hedgers are long the straddle and when the hedgers are short the straddle. We numerically simulate the terminal distribution of the underlying asset price and find that hedgers that are long the straddle tend to push the underlying toward the strike, while hedgers that are short the straddle cause the underlying security to have a bimodal terminal probability distribution with a local minimum at the strike.

Results in He–Leland (1993) are extended and properties of the risk-premium process in an equilibrium are examined in a pure exchange economy with a representative agent: for example, (i) the risk-premium process is characterized by using a martingale representation of the reciprocal of a terminal marginal utility, (ii) it is expressed as a (conditional) expected value including the relative risk aversion coefficient of a terminal utility and the Jacobian matrix process of the state variables, and, (iii) a "mean-reverting" property relates to the monotonic decreasing property of the relative risk aversion coefficient.

The continuous-time version of Kyle [(1985) Continuous auctions and insider trading, Econometrica53 (6), 1315–1335.] developed by Back [(1992) Insider trading in continuous time, The Review of Financial Studies5 (3), 387–409.] is studied here. In Back’s model, there is asymmetric information in the market in the sense that there is an insider having information on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First, we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular, we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium.

We study a mean-field game framework in which agents expend costly effort in order to transition into a state where they receive cash flows. As more agents transition into the cash flow receiving state, the magnitude of all remaining cash flows decreases, introducing an element of competition whereby agents are rewarded for transitioning earlier. An equilibrium is reached if the optimal expenditure of effort produces a transition intensity which is equal to the flow rate at which the continuous population enters the receiving state. We give closed-form expressions which yield equilibrium when the cash flow horizon is infinite or exponentially distributed. When the cash flow horizon is finite, we implement an algorithm which yields equilibrium if it converges. We show that in some cases, a higher cost of effort results in the agents placing greater value on the potential cash flows in equilibrium. We also present cases where the algorithm fails to converge to an equilibrium.

We examine the impact of pandemics on equilibrium in an integrated epidemic-economy model with production. Two types of technologies are considered: a neo-classical technology and one capturing the notion of time-to-produce. The impact of a shelter-in-place policy with and without layoffs is studied. The paper documents adjustments in interest rate, market price of risk, stock market and real wage as the epidemic propagates. It shows the qualitative effects of a shelter-in-place policy in the model are consistent with the patterns displayed by the stock market and real wage during the COVID-19 outbreak. Puzzles emerging from the analysis are outlined.

We develop an equilibrium model for market impact of trades when investors with private signals execute via a trading desk. Fat tails in the signal distribution lead to a power law for price impact, while the impact is logarithmic for lighter tails. Moreover, the tail distribution of the equilibrium trade volume obeys a power law. The spread decreases with the degree of noise trading and increases with the number of insiders. In case of a monopolistic insider, the last slice traded against the limit order book is priced at the fundamental value of the asset reminiscent of the Kyle models in continuous time. However, competition among insiders leads to aggressive trading, hence vanishing profit in the limit. The model also predicts that the order book flattens as the amount of noise trading increases converging to a model with proportional transactions costs with non-vanishing spread.

In a recent article [4], we have developed a market model where an insider trades using future information on the value of the underlying, through these trades it creates an effect on the drift of the underlying model. We find points of partial equilibria. That is, when the filtration is fixed the chosen portfolio is optimal, leads to finite utility of the insider and prices are semimartingales in their own filtration. In this article, we treat two explicit examples in detail. The first is an insider which has a medium term effect on the price. The second is an insider which has a long term effect on the price with memory effects. These examples were quoted in [4] but no details were given.

Utility indifference pricing is an effective method for investors to construct a strategy in an incomplete market. In fact, if an investor can trade a random endowment under the criteria shown by utility indifference pricing, they can devise financial contracts that are optimized according to their preferences. However, because it does not have the direct implication of equilibrium, the value of the random endowment given by indifference pricing is not necessarily the same as the market price. In this study, we attempt to derive the equilibrium of random endowment under the framework of indifference pricing. However, letting the utility function be of exponential type means that any trade involving random endowment will not appear in equilibrium. Thus, we show that non-zero trade in equilibrium appears by introducing uncertainty in a model, which is one of the sources of market incompleteness.