Despite the use of VaR as a means to control risk, using VaR can have the opposite effect. VaR is used by bank and insurance regulators more than any other risk measure. A value-at-risk (VaR) constraint on the probability that future firm equity value will be less than a floor, when the floor is...

Despite the use of VaR as a means to control risk, using VaR can have the opposite effect. VaR is used by bank and insurance regulators more than any other risk measure. A value-at-risk (VaR) constraint on the probability that future firm equity value will be less than a floor, when the floor is...

The standard put-call parity result does not include equalities based on buy-and-hold strategies for options on the minimum or maximum of two risky assets and for quantity-adjusting options. This article generalizes put-call parity to these contracts. International put-call parity relations and...

Quantity-adjusting option and forward contracts deliver a payoff on a variable quantity of underlying. This article explains the use, pricing, and hedging of such contracts. The pricing of product options is also derived. Product options include quantity-adjusting options as a special case and...

A new model for capital budgeting is derived from a manager's optimizing behavior that, unlike the capital asset pricing model (CAPM), prices total risk. Manager risk preferences are characterized by a constraint on the probability of ruin, otherwise known as a Value-at-Risk or Telser...

Var is perhaps the most commonly used measure of risk by financial institutions. At many of these the head of risk management gets a daily report on firm-wide Var as well disaggregated Var across the firm's businesses. Often chief risk manager (CRM) is a top level officer in many financial...

We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneously in a fashion consistent with the priority of debt claims and the limited liability of equity. We first show, via a fixed-point argument, that...

Applying the approach used by Eisenberg (2007) to derive the marginal price of risk for an expected value maximizing manager who has a Var constraint, I derive the marginal price of risk given a Cvar (Acerbi and Tasche, 2001), also known as an expected shortfall constraint. Despite the criticism...

We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneously in a fashion consistent with the priority of debt claims and the limited liability of equity. We first show, via a fixed-point argument, that...