Jussi Keppo

Optimal Bank Capital with Costly Recapitalization

We study optimal bank capital choice as a dynamic trade-off between the opportunity cost of equity, the loss of franchise value following a regulatory minimum capital violation, and the cost of recapitalization. We introduce a recapitalization delay that results in a strictly positive probability of capital adequacy violation. We calibrate the model to bank accounting return data and evaluate the models ability to explain observed bank capital ratios. Differences in return volatility explain a significant fraction of the cross-sectional variation in bank capital ratios. Differences in the level of capital market imperfections across banks constitute a secondary explanation.

Managing electricity market price risk

Abstract This paper introduces an application of financial risk management methods to the deregulated electricity markets. A framework for the Monte Carlo performance simulation of a power portfolio is presented. The optimal portfolio selection problem is addressed and a numerical method is implemented. Numerical results of simulation and optimization are presented in the Nordic electricity market. The results suggest that the risk management methods of the paper can be applied to the everyday electricity market practice.

Pricing of Electricity Swing Options

Electricity is one of the most important commodities for both consumers and producers, and it is subject to sharp variations in supply and demand, sometimes within a single day. But it is also one of the most difficult commodities on which to trade derivatives, because electricity is virtually unstorable. This has given rise to contracts such as the “swing option,” which sets minimum and maximum values for both the amount of power to be purchased in each period and also the cumulative amount of electricity purchased over the life of the contract. A swing option thus entails complex timing options with regard to fulfillment of the required minimum cumulative quantity purchased, and price-related options that let the holder buy more when the market price is above the options strike price, all constrained by the limits on maximum instantaneous and cumulative consumption. In this article, Keppo describes the decision process and presents a swing option valuation model based on simple electricity forwards and options. The use of the approach is illustrated with a couple of examples based on Nord Pool electricity prices.

Real options and a large producer: the case of electricity markets

In this paper we extend the real option theory to consider the situation of a large producer and we employ the model to electricity markets. This is important because many producers in these markets affect the market supply and, therefore, also the electricity price. This production price effect influences not only on the assets that the energy company owns but also on its investment opportunities. We show that this productions price effect has to be considered in the investment analysis if the company is not able to hedge the price effect in the financial markets and if there is no competition on the investment opportunity.

The impact of delivery lags on irreversible investment under uncertainty

Abstract We consider the valuation and rational exercise of irreversible investment opportunities in the presence of revenue uncertainty and delivery lags. In order to capture supply side market imperfections in the markets for investment goods, we assume that the lag depends on the revenue process faced by the investor. We show that such imperfections have a pronounced decelerating impact on rational investment demand as they may increase the value of waiting in excess of the exercise payoff even for projects which otherwise would be perceived as highly remunerative. We also consider the comparative static properties of the optimal investment policy and its value, and demonstrate that typically increased uncertainty decreases the investment incentives by increasing the value of waiting.

Risk, Financing and the Optimal Number of Suppliers

Should firms in developed economies work with more or fewer suppliers than firms in developing economies? More generally, how does the number of suppliers for a firm depend on the firm’s economic environment? To answer these questions we identify several economic and business factors that might affect the number of suppliers (and that separate developed and developing economies): supply risk, fixed costs of working with suppliers, and access to financing (particularly trade-credit financing).

A GAME MODEL OF IRREVERSIBLE INVESTMENT UNDER UNCERTAINTY

Most of the literature on real options considers the optimal decision of a firm in isolation from competitors. In reality, however, the actions of competing firms often affect each others investment opportunities. We develop a game model where many firms compete for a single investment opportunity. When one of the firms triggers the investment the opportunity is completely lost for the other firms. The value of the project for the firms is assumed to follow a geometric Brownian motion. The model combines game theory and the theory of irreversible investment under uncertainty. We characterize the resulting Nash equilibrium under different assumptions on the information that the firms have about each others valuations for the project. As an example, we present a case of building a telecommunications network.

Optimal Consumption and Portfolio Decisions with Partially Observed Real Prices

We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the basket price and (ii) when he receives only noisy observations on the basket price. We derive the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases. The compositions of the funds in the two cases are the same, but in general the investors allocations of his wealth into these funds will differ. However, in the particular case when the investor has constant relative risk-aversion (CRRA) utility, his optimal investment allocations into these funds are also the same in both cases.

Bonus Caps, Deferrals and Bankers' Risk-Taking

Regulators restrict bankers’ risk-taking by bonus caps or deferrals. We derive a structural model to analyze these compensation regulations and show that for a risk-neutral banker subject to positive switching costs of reducing bank risk, a bonus deferral is impotent while a sufficiently tight bonus cap reduces risk-taking. The model suggests that a bonus cap that equals fixed salary (as in the EU) reduces risk on average by 13% under conservatively calibrated positive switching costs. Further, the bonus cap would have considerably reduced risk-taking incentives in most US banks that did poorly during the global financial crisis. We also show that the bonus deferral is effective if the banker is risk-averse and the switching costs are not too high.

Hydropower with Financial Information

The paper considers a single utility companys long‐ and medium‐term hydropower planning. The uncertainties are from the electricity forward curve and a random inflow. A simple and intuitive parameterization is given for the optimal production strategy. The accuracy of the parameterization is analysed by comparing its expected cash flows with the corresponding upper bound. In a test case the proposed method is compared with the realized production strategy of a Norwegian hydropower producer during winters 1997–2003. The parameterization gives earnings that are within 2.6% from the theoretical upper bound. Further, the results illustrate that during some years, part of the realized production strategy can be explained with the method, suggesting that during these years the forward curve information has already been incorporated in the production planning. However, even during the years when the correlation between the proposed strategy and the realized production is low, the strategy would have increased the realized earnings. This suggests that the information from the derivative markets would improve the production strategy. *We thank Stein‐Erik Fleten, Audun Botterud, and seminar participants at the Norwegian University of Science and Technology for helpful comments. Driva Kraftverk is gratefully acknowledged for providing the data.