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Abstract:
In project finance, sponsors and lenders set up a special purpose vehicle (SPV) that receives limited or no-recourse lending for the design, construction and management of a specific project with limited economic life. A network of nonfinancial contracts (NFCs) is set up in order to limit the managerial discretion of project sponsors, to make cash flows better verifiable for lenders, and to reduce the negative impact of unexpected events on project cash flows. Using a sample of more than 1,000 project finance loans worth about US$195 billion closed between 1998 and 2003, we study negotiation of financial packages between sponsors and lenders and their cost. We use a two-stage least squares methodology to model the joint determination of spread and leverage. Our results confirm the widespread adoption of a business practice in which sponsors tend first to set up the contractual network of the project finance transaction, and only later seek financing and negotiate the level of spread and the debt-to-equity ratio with a bank syndicate. In this negotiation process, we find that lenders: (1) rely on the network of contracts as a mechanism to control agency costs and project risks, (2) are reluctant to price the credit more cheaply if sponsors are involved as project counterparties in the relevant contracts, and finally (3) do not consider sponsor involvement as a contractual counterparty of the SPV when determining the level of leverage. Overall, the lack of NFCs increases loan cost some 19 bps, and the use of NFCs signed by counterparties other than project sponsors reduces loan cost by some 110 bps. Furthermore, the absence of NFCs is responsible for a drop of 1.1 bps in the debt-to-equity ratio used for deals. Further, results indicate that - in contrast to the level of the D/E ratio - country and industry risk do not influence the level of spread, which is instead driven by the negotiated leverage and by the existence of NFCs. Finally, our findings indicate that sponsors face a trade-off between higher financial leverage and lower interest rate levels during negotiation of loan terms with lenders.

project finance, contractual arrangements, long-term contracts, loan pricing, capital

Abstract:
In the setting of diffusion models for price evolution, we suggest an easily implementable approximate evaluation formula for measuring the errors in option pricing and hedging implied in volatility mis-specification. The main tool we use in this paper is a fundamental inequality for the L-2 norm of the solution, and the derivatives of the solution, of a partial differential equation (the so called "energy" inequality). This result allows us to give bounds to the errors implied in the use of approximate models for option valuation and hedging. When statistical or a-priori information is available on the "true" volatility, the error measure can be minimized w.r.t. the parameters of the approximating model. In this case the usual approximate hedging procedure, where hedging parameters are computed using an approximate model calibrated to observed prices (e.g. implied volatility), is sub optimal. The method suggested in this paper can help in conjugating statistical estimation of the volatility function derived from flexible but computationally cumbersome statistical models, with the use of analytically tractable approximate models calibrated using error estimates derived from energy inequalities. The performance of the new method is compared with the standard implied volatility hedging method in an example where the true model is a lognormal mixture while the approximating model is the standard lognormal model.

option pricing, hedging error bounds, optimal approximate hedging, energy inequality, parabolic PDE, model uncertainty, robustness, diffusion approximation, approximate hedging, mis-specified diffusion models

Abstract:
Index tracking requires building a portfolio of stocks (a replica) whose behaviour is as close as possible to that of a given stock index. Typically, much fewer stocks should appear in the replica than in the index, and there should be no low frequency (persistent) components in the tracking error. Unfortunately, the latter property is not satisfied by many commonly used methods for index tracking. These are based on the in-sample minimization of a loss function, but do not take into account the dynamic properties of the index components. Instead, we represent the index components with a dynamic factor model, and develop a procedure that, in a first step, builds a replica that is driven by the same persistent factors as the index. In a second step, it is also possible to refine the replica so that it minimizes a loss function, as in the traditional approach. Both Monte Carlo simulations and an application to the EuroStoxx50 index provide substantial support for our approach.

Index tracing, replica, stock index, factor models

Abstract:
In the setting of diffusion models for price evolution, we suggest an easily implementable approximate evaluation formula for measuring the errors in option pricing and hedging due to volatility misspecification. The main tool we use in this paper is a (suitably modified) classical inequality for the L(2) norm of the solution, and the derivatives of the solution, of a partial differential equation (the so-called "energy" inequality). This result allows us to give bounds on the errors implied by the use of approximate models for option valuation and hedging and can be used to justify formally some "folk" belief about the robustness of the Black and Scholes model. Surprisingly enough, the result can also be applied to improve pricing and hedging with an approximate model. When statistical or a priori information is available on the "true" volatility, the error measure given by the energy inequality can be minimized w.r.t. the parameters of the approximating model. The method suggested in this paper can help in conjugating statistical estimation of the volatility function derived from flexible but computationally cumbersome statistical models, with the use of analytically tractable approximate models calibrated using error estimates.