The Complexities of Financial Risk Management and Systemic Risks

Risk-management systems in financial institutions have come under increasing scrutiny in light of the current financial crisis, resulting in calls for improvements and an increased role for regulators. Yet such objectives miss the intricacy at the heart of the risk-management process. This article outlines the complexity inherent in any modern risk-management system, which arises because there are shortcuts in the theoretical models that risk managers need to be aware of, as well as the difficulties in sensible calibration of model parameters. The author suggests that prudential regulation of such systems should focus on failures within the financial firm and in the market interactions between firms and reviews possible strategies that can improve the performance of risk management and microprudential regulatory practice.

Taxation and Transaction Costs in a General Equilibrium Asset Economy

Most financial asset pricing models assume frictionless, competitive markets that imply the absence of arbitrage opportunities. Given the absence of arbitrage opportunities and complete asset markets, there exists a unique martingale measure that implies martingale pricing formulae and replicating asset portfolios. In incomplete markets, or markets with transaction costs, these results must be modified to admit non-unique measures and the possibility of imperfectly replicating portfolios. Similar difficulties arise in markets with taxation. Some theoretical research has argued that some taxation functions will imply arbitrage opportunities and the non-existence of a competitive asset economy. In this paper, we construct a multi-period, discrete time/state general equilibrium model of asset markets with transaction costs and taxes. The transaction cost technology and the tax system are quite general, so that we can include most discrete time/state models with transaction costs and taxation. We show that a competitive equilibrium exists. Our results require careful modeling of the government budget constraints to rule out tax arbitrage possibilities.Taxation, Transaction Costs, General Equilibrium, Asset Economy

OPTION PRICING WITH V. G. MARTINGALE COMPONENTS

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. An exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means. low variances, and high kurtosis.Option, pricing, Variance Gamma, martingale

Market distortions and corporate governance.

This paper studies corporate governance when a firm operates in imperfect markets. We derive firms' decisions from utility maximisation by individuals. This reduces the usual monopoly distortion. Corporate governance can effect the equilibrium in the product (or input) markets. This enables us to endogenise the objective function of the firm. If the firm cannot commit not to change its constitution, we find a Coase-like result where all market power is lost in the limit. We present a more abstract model of governance in the presence of market distortions and discuss its implications for the governance of universities.corporate governance, stakeholder, strategic delegation, economics of universities.

A Large Trader in Bubbles and Crashes: an Application to Currency Attacks

Abreu and Brunnermeier (2003) study stock market bubbles and crashes in a dynamic model with a continuum of rational small traders. We introduce a large trader into their model and apply it to currency attacks. In an attack against a fixed exchange rate regime with a gradually overvaluing currency, traders lack common knowledge about the time when the overvaluation starts. Meanwhile, they need to coordinate to break a peg. In such a setup, both the inability of traders to synchronize their attack and their incentive to time the collapse of the regime lead to the persistent overvaluation of the currency. We find that the presence of a large trader with perfect information will accelerate the collapse of the regime and alleviate currency overvaluation. However, if a large trader has incomplete information, the presence of a large trader may accelerate or delay the collapse of the regime ex post, depending on the size of his wealth and the precision of his information. More specifically, we find that a large trader with both a large amount of wealth and very noisy information can greatly delay the collapse of the regime ex post. Moreover, we find that the presence of a large trader with incomplete information can greatly increase the unpredictability about the time when the regime collapses, implying the difficulty for traders to time the collapse.Large Trader, Bubbles and Crashes, Currency Attack

CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and for which the family of Hermite polynomials serves as an orthonormal basis. Basis pricing synthesizes claim valuation and basis investment provides static hedging opportunities. For claims written as functions of a single asset price we infer from observed option prices the implicit prices of basis elements and use these to construct the implied equivalent martingale measure density with respect to the reference measure, which in this case is the Black-Scholes geometric Brownian motion model. Data on S&P 500 options from the Wall Street Journal are used to illustrate the calculations involved. On this illustrative data set the equivalent martingale measure deviates from the Black-Scholes model by relatively discounting the larger price movements with a compensating premia placed on the smaller movements.Contingent claims, options, Hilbert space, Hermite, S & P 500 index

A General Equilibrium Financial Asset Economy with Transaction Costs and Trading Constraints

This paper presents a unified framework for examining the general equilibrium effects of transactions costs and trading constraints on security market trades and prices. The model uses a discrete time/state framework and Kuhn-Tucker theory to characterize the optimal decisions of consumers and financial intermediaries. Transaction costs and constraints give rise to regions of no trade and to bid-ask spreads: their existence frustrate the derivation of standard results in arbitrage-based pricing. Nevertheless, we are able to obtain as dual characterizations of our primal problems, one-sided arbitrage pricing results and a personalized martingale representation of asset pricing. These pricing results are identical to those derived by Jouini and Kallal (1995) using arbitrage arguments. The paper's framework incorporates a number of specialized existing models and results, proves new results and discusses new directions for research. In particular, we include characterizations of intermediaries who hold optimal portfolios; brokers who do not hold portfolios, and consumer-specific transactions costs and trading constraints. Furthermore we show that in the special case of equiproportional transaction costs and a sufficient number of assets, there is an analogue of the arbitrage pricing result for European derivatives where prices are interpreted as mid-prices between the bid-ask spread. We discuss the effects of non-convex transaction technologies on prices and trades.Financial Markets, Transaction Costs, Trading Constraints, Asset Pricing, General Equilibrium, Incomplete Markets

Externalities, Monopoly and the Objective Function of the Firm

This paper provides a theory of general equilibrium with externalities and/or monopoly. We assume that the firm's decisions are based on the preferences of shareholders and/or other stakeholders. Under these assumptions, a firm will produce fewer negative externalities than the comparable profit maximizing firm. In the absence of externalities, equilibrium with a monopoly will be Pareto efficient if the firm can price discriminate. The equilibrium can be implemented by a 2-part tariff.Externality, general equilibrium, 2-part tariff, objective function of the firm.

Takeovers and Cooperatives

If consumers wholly or partially control a firm with market power they will charge less than the profit maximising price. Starting at the usual monopoly price, a small price reduction will have a second order e¤ect on profits but a first order effect on consumer surplus. Despite this desirable static result, it has been argued that cooperatives are vulnerable to take-over by outsiders who will run them as for-profit businesses. This paper studies takeovers of cooperatives. We argue that cooperatives are in fact quite stable due to the Grossman-Hart problem of free riding during takeovers.corporate governance, co-operative, take-over, free-rider

The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices.Multinomial, option, pricing, Brownian, Poisson