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     

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.     

Collateral affects return risk: evidence from the euro bond market

Covered bonds and senior bonds are prominent securities in the euro bond market. Senior bonds are unsecured, while covered bonds are secured—backed by collateral. Our results show that the presence of collateral reduces the total risk in individual bonds by more than 70%. Compared to diversified portfolios of senior bonds, diversified portfolios of covered bonds have a significantly lower level of systematic risk. However, the fraction of systematic risk to total risk is higher for covered bonds. By decomposing the variance of bond returns, we find that around 33% of the risk in senior bonds is systematic, versus 53% in covered bonds. Both types of bonds contain instrument-specific risk.

     

Backdating executive stock options—An ex ante valuation

When backdating executive stock options (ESOs), the exercise price is set in favor of the recipient executive. Relative to a non-backdated benchmark, we find an (ex ante) upper bound for the cost of backdating to shrink from 10% to about 3.7%, as a consequence of the regime change represented by the Sarbanes-Oxley act (SOX).We frame the backdating behavior as a (compound) exotic option, considering both simple and extended models of the underlying ESO—in the latter case we draw on the analytical ESO models of Sircar and Xiong (2007). Post-SOX, we use a Longstaff-Schwartz inspired least squares Monte Carlo approach.     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.     

Institutional spending policies: implications for future asset values and spending

University endowments, sovereign wealth funds, and foundations support spending. In this paper, we analyze how different spending policies affect future asset values and spending opportunities. We show that the covariance between the asset returns and the spending rate implied by the spending policy is important in this regard. Many of the spending policies used in practice aim at smoothing the spending level by letting current spending be a function of both current asset values and earlier spending levels. One feature of these types of spending policies is that the funds can be depleted. Depleted funds cannot support spending.