On the Non-Existence of Redundant Options

In a seminal paper, Ross (Q J Econ 90:75–89, 1976) shows that if security markets are resolving, then there exist (non-redundant) options that generate complete security markets. Complementing his work, Aliprantis and Tourky (2002) show that if security markets are strongly resolving and the number of primitive securities is less than half the number of states, then every option is non-redundant. Our paper extends Aliprantis and Tourky’s result to the case when their condition on the number of primitive securities is not imposed. Specifically, we show that if there exists no binary payoff vector in the asset span, then for each portfolio there exists a set of exercise prices of full measure such that any option on the portfolio with an exercise price in this set is non-redundant. Since the condition that there exists no binary payoff vector in the asset span holds generically, redundant options are thus rare. I am grateful to an anonymous referee for very helpful comments. Research support from the School of Business at The George Washington University is gratefully acknowledged     

Dynamic versus one-period completeness in event-tree security markets

We show that in event-tree security markets dynamic completeness does not coincide with one-period completeness unless the law of one price is explicitely assumed. We do so by means of a simple example of a dynamically complete market with an incomplete one-period sub-market.     

Collective fineness of stock prices and efficiency of financial markets

Recent literature exploring the efficiency properties of options has examined the conditions under which incomplete financial markets would be equivalent to the Arrow-Debreu model. A usual assumption made in establishing such an equivalence is that some security price is ‘fine’ on the state space. This assumption is relaxed. Under more realistic assumptions it is shown that any portfolio is fine and options written on it can bring about complete markets.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

Differential mortality and social security

Abstract This paper studies the normative problem of redistribution between individuals who differ in their lifespans. We discuss aspects related to the objective function and argue that aversion to multiperiod inequality should be taken into account. Then, we study the properties of the social optimum both with full information and with asymmetric information. We highlight the role of aversion to multiperiod inequality and show that it has substantial consequences on the design of Social Security schemes. In particular, we show that for a low (resp. high) aversion to multiperiod inequality, a negative (resp. positive) implicit tax rate on continued activity is desirable.     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

Market clearing, utility functions, and securities prices

Summary. We prove the existence of equilibrium in a continuous-time finance model; our results include the case of dynamically incomplete markets as well as dynamically complete markets. In addition, we derive explicitly the stochastic process describing securities prices. The price process depends on the risk-aversion characteristics of the utility function, as well as on the presence of additional sources of wealth (including endowments and other securities). With a single stock, zero endowment in the terminal period, and Constant Relative Risk Aversion (CRRA) utility, the price process is geometric Brownian motion; in essentially any other situation, the price process is not a geometric Brownian motion.JEL Classification Numbers: D52.This paper is part of my Dissertation (UC Berkeley). I am very grateful to my advisor Professor Robert M. Anderson. I also would like to thank Steve Evans, Roger Purves, Jacob Sagi, Chris Shannon and the participants of the 2002 NBER General Equilibrium Conference at the University of Minnesota (Minneapolis) for very helpful discussions and comments. This work was supported by Grant SES-9710424 from the National Science Foundation.     

Non-existence and inefficiency of equilibria with American options

Summary We analyze two examples of economies with incomplete financial markets. In the first model we consider a stock and an American put option on the stock. Although there is only one commodity and asset payoffs therefore do not depend on spot prices, we derive robust non-existence of equilibria. In the second model we consider an economy where a stock is the only asset available for trade. We show that it is impossible to complete the market by introducing American put options and that equilibria are inefficient. This example is also robust.We wish to thank Jonathan Berk, Virginia France, Flavio Menezes and a referee of this journal for useful comments. This research was partially funded by the National Science Foundation (SES-8821723).     

On the recoverability of intertemporal preferences

In the absence of futures markets, a consumer's complete set of intertemporal demand functions may not be revealed. Under mild regularity conditions, the multiperiod utility function that generates the observable demand functions is shown to be unique in the class of additively separable and stationary functions.     

Pricing rules and Arrow–Debreu ambiguous valuation

This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow–Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow–Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.     

Hedging exchange rate risk: The multiperiod case

We analyse production and hedging in a multiperiod framework for a risk-averse exporting firm facing a random exchange rate. We extend the separation theorem to this multiperiod model. Our study shows that unbiased currency forward markets in all periods do not imply standard full hedging. Under some conditions, the firm tends to overhedge compared to the one-period hedging models.     

Market structure and multiperiod hedging

This paper develops a multiperiod hedging model for a competitive risk-averse international firm. We study the optimal sequential hedging strategy and analyze the impact of the structure of available risk sharing markets on the firm's export decision. As a main result, we find that the number of risk sharing markets critically affects the export level while the timing of these markets is inconsequential.     

Debt and deficit fluctuations and the structure of bond markets

We analyse the implications of optimal taxation for the stochastic behaviour of debt. We show that when a government pursues an optimal fiscal policy under complete markets, the value of debt has the same or less persistence than other variables in the economy and it declines in response to shocks that cause the deficit to increase. By contrast, under incomplete markets debt shows more persistence than other variables and it increases in response to shocks that cause a higher deficit. Data for US government debt reveals diametrically opposite results from those of complete markets and is much more supportive of bond market incompleteness.     

Long‐Term Contracts,Irreversibility, and Uncertainty

Long‐term contracting implies contracting based on expected future demand. In this paper, I develop a multiperiod procurement model where, once the actual level of demand is realized, the irreversible initial provision level may be supplemented by additional provisions. This paper shows that, with the possibility of additional upward adjustments, the first‐period provision level will be lower than when no additional adjustments are possible. This reduction in first‐period provision level is higher under complete contracting than under incomplete contracting, and because of the reduction in information rents it yields a higher expected utility to the principal but lower total welfare.     

Equilibrium with arbitrary market structure

Summary. Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The complete market predicted by this theory is clearly unrealistic, and Radner [10] formulated and proved existence of equilibrium in a multiperiod model with incomplete markets.In this paper the Radner result is extended. Radner assumed a specific structure of markets, independence of preferences, indifference of preferences, and total and transitive preferences. All of these assumptions are dropped here. We - like Radner - keep assumptions implying compactness.Received: 17 April 2003, Revised: 26 March 2004, JEL Classification Numbers: D52, D40.     

Incomplete markets: transverse financial structures

Summary. In a multiperiod economy with incomplete markets and assets with payoff depending on the price history (e.g., asset and derivatives), we show that in order to get endowment generic existence of an equilibrium it is not needed to alter settlement features such as when payments are made and when the asset is traded. This is non-trivial as each such characteristic introduces a non-generic subclass of financial instruments. We show essentially that expiry date payments are the only payments that one needs perturbing (if at all). For previous periods - the P&L discovery map - is the one relevant for wealth transfers. This map transfers wealth between one period and the next by associating to each portfolio next period potential profit and losses as a function of the revealed information at the node. All present values involved can in general - because of backward induction pricing structure - be appropriately controlled via expiry payoffs only. This enables us to extend two-period work and introduce Transverse Financial Structures for multiperiod economies, where one cannot identify the payoffs of financial instruments to the P&L discovery map (in other words we introduce some financial ingeneering for Transverse Financial Structures). We capitalize on that difference using unexploited “maturity payout degrees of freedom” and rolling back the uncertainty tree. As an application of this approach we prove a conjecture by Magill and Quinzii that commodity forward contracts lead to endowment generic existence of an equilibrium in a multiperiod set-up. Received: June 25, 1999; revised version: April 4, 2001     

Does the impact of private education on growth differ at different levels of credit market development?

Using an overlapping generations model, we show that the impact of private financing of education on growth depends on credit market development, being positive when credit markets are adequately developed but negative if sufficiently low levels of credit market development occur alongside relatively high private financing intensities. Employing cross-country data, we find that reduced-form growth relationships are statistically significant and robust under various controls and samples. We also lay out conditions under which economies with missing credit markets are dynamically efficient and outperform, in terms of growth, economies with complete credit markets. The latter may explain large cross-country differences in savings and growth, while facilitating the evaluation of policies on financing education.     

Derivative securities and cash market stability

This study investigates the effect of introducing interest-rate futures and options on the price variances in related financial cash markets. Standard research approaches to this issue relate cash-price stability before the introduction of futures and options trading to cash-price stability after trading in the derivative security begins. However, controlling for the additional factors that may also effect cash markets is difficult. The approach employed here to deal with this obstacle is motivated by recent theoretical research relating cash and futures markets, but hitherto not operationalized to empirically test for a relationship between the markets. Varying-parameter models of (1) the demand for short-term Treasury securities, (2) the demand for large time-deposits, and (3) the supply of large time-deposits are specified such that changes in the parameters imply changes in the volatility of the cash price. These parameters are modelled as functions of the trading volume of interest-rate futures and options, thereby enabling a direct test of the hypothesis that trading volume in these derivative securities influences the behaviour of cash-market participants, and therefore, cash-price volatility. We find no convincing evidence that the level of activity in interest-rate futures and options has a significant effect on these cash markets.     

THE GREAT RECESSION, “RAINY DAY” FUNDS,AND COUNTERCYCLICAL FISCAL POLICY IN LATIN AMERICA

We examine the fiscal policy options that were available to Latin American countries at the onset of the current global economic crisis, concluding that most of the major countries in the region possessed the fiscal space (as measured by credible fiscal sustainability and debt headroom) to run prudent countercyclical fiscal deficits. For those countries, the appropriate policy response involved a constrained fiscal expansion focused on productive public spending and financed by drawing on the “rainy day” funds—in the form of large stocks of foreign exchange reserves—that they accumulated in prior years, rather than by market borrowing. (JEL E62, E63, F34)     

Valuation of American CAC 40 index and wildcard options

American options traded on the CAC 40 index are cash settled. However, the stocks underlying the CAC 40 index are traded in a particular “forward” market. In this market, settlements take place periodically on a given date as in the UK. At that date, all transactions accomplished before are settled. The settlement procedure differs from that in countries where settlements appear as fixed number of business days after the transaction as in the US. The characteristics of the distributions to the index underlying stocks might justify a specific model for the valuation of these options. Besides, the organization of the Paris Bourse gives market participants the possibility to exercise their positions during the 45 min following the close of the stock exchange. They face each day as an exercise risk that must be accounted for. This article applies to existing models for the valuation of CAC 40 options, and this type of risk is identified as a wildcard option. This option is implicit in the values of index calls and puts. The magnitude of wildcard options in a multiperiod setting is studied empirically using a new dataset by adapting the model in Fleming and Whaley [J. Finance XLIX (1994) 215.] to the French market.