Relative Guarantees

Many real-world financial contracts have some sort of minimum rate of return guarantee included. One class of these guarantees is so-called relative guarantees, i.e., guarantees where the minimum guaranteed rate of return is given as a function of the stochastic return on a reference portfolio. These guarantees are the topic of this paper. We analyse a wide range of different functional specifications for the minimum guaranteed rate of return, hereunder both so-called maturity and multi-period guarantees. Several closed form solutions are presented.     

Pricing American exchange options in a jump‐diffusion model

A way to estimate the value of an American exchange option when the underlying assets follow jump‐diffusion processes is presented. The estimate is based on combining a European exchange option and a Bermudan exchange option with two exercise dates by using Richardson extrapolation as proposed by R. Geske and H. Johnson (1984). Closed‐form solutions for the values of European and Bermudan exchange options are derived. Several numerical examples are presented, illustrating that the early exercise feature may have a significant economic value. The results presented should have potential for pricing over‐the‐counter options and in particular for pricing real options. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:257–273, 2007     

Effects of Transport Regulation on the Oil Market: Does Market Power Matter?

Instruments used to regulate the consumption of oil in the transport sector include fuel taxes, biofuel requirements, and fuel‐efficiency standards. However, the effects that these have on oil consumption and price vary. If market power is present in the oil market, the directions of change in consumption and price might contrast with those in a competitive market. As a result, the market structure affects not only the effectiveness of the policy instruments used to reduce oil consumption, but also the terms of trade and carbon leakage. In particular, reduced oil consumption, as a result of increased fuel‐efficiency standards, will unambiguously increase the price of oil under a monopoly.     

Optimal Timing of Climate Change Policy: Interaction Between Carbon Taxes and Innovation Externalities

This paper addresses the impact of endogenous technology through research and development (R&D) on the timing of climate change policy. We develop a model with a stock pollutant (carbon dioxide) and abatement technological change through R&D, and we use the model to study the interaction between carbon taxes and innovation externalities. Our analysis shows that the timing of optimal emission reduction policy strongly depends on the set of policy instruments available. When climate-specific R&D targeting instruments are available, policy has to use these to step up early innovation. When these instruments are not available, policy has to steer innovation through creating demand for emission saving technologies. That is, carbon taxes should be high compared to the Pigouvian levels when the abatement industry is developing. Finally, we calibrate the model in order to explore the magnitude of the theoretical findings within the context of climate change policy.      

Relative Guarantees

Many real-world financial contracts have some sort of minimum rate of return guarantee included. One class of these guarantees is so-called relative guarantees, i.e., guarantees where the minimum guaranteed rate of return is given as a function of the stochastic return on a reference portfolio. These guarantees are the topic of this paper. We analyse a wide range of different functional specifications for the minimum guaranteed rate of return, hereunder both so-called maturity and multi-period guarantees. Several closed form solutions are presented.     

A Generalization of the Formulas for Options on the Maximum or the Minimum of Several Assets

Abstract

This paper generalizes the option on the maximum or the minimum of two assets (several assets) within a stochastic interest rate framework. A Gaussian model is used to describe the interest rates. Closed-form solutions for the market values are presented. The use of the options is illustrated with numerical examples.     

A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates

Abstract

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.     

Human capital investment and optimal portfolio choice

We analyze how an individual should optimally invest in human capital when he also has financial wealth. We treat the individual's possibilities to take more education as expansion options and apply real option analysis. In addition, we characterize the individual's optimal consumption strategy and portfolio weights. The individual has a demand for hedging financial risk, labor income risk, and also wage level risk.     

On adaptation and the demand for health

The purpose of this paper is to analyse the impacts of adaptation to failing health. This is done by integrating adaptation processes in a Grossman type of pure consumption model. Model simulations show that adaptation affects the health variables by lowering the incentives to invest in health, as well as smoothing the optimal health stock path over the life cycle. Whether or not the risk of mortality is an object of choice has important effects when studying adaptation, as well as for the joint development of the health variables.