Pricing Perpetual Options for Jump Processes

Abstract

We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition. In the second model in which the jumps are downwards, we show that the value of the strategy corresponding to a constant option-exercise boundary satisfies a certain renewal equation. Then the optimal exercise strategy is obtained from the continuous junction condition. Furthermore, the same model can be used to price certain reset options. Finally, we show how the classical model of geometric Brownian motion can be obtained as a limit and also how it can be integrated in the two models.     

Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility

Abstract

The author applies the principle of equivalent utility to price and reserve equity-indexed life insurance. Young and Zariphopoulou (2002a, b) extended this principle to price insurance products in a dynamic framework. However, in those papers, the insurance risks were independent of the risky asset in the financial market. By contrast, the death benefit for equity-indexed life insurance is a function of a risky asset; therefore, this paper further extends the principle of equivalent utility. In a second extension, the author applies the principle of equivalent utility to calculate reserves, as introduced by Gerber (1976). In a related paper, Moore and Young (2002) price equity-indexed pure endowments, the building blocks of equity-indexed life annuities.     

Pecking order as a dynamic leverage theory

Static tradeoff theories, which do not explicitly treat the impact of transaction costs, do not explain the policy of asymmetry between frequent small debt transactions and infrequent large equity transactions. Nor do these theories explain why the debt ratio is allowed to wander a considerable distance from its alleged static optimum, or how much of a distance should be tolerated. We offer a class of diffusion models that mimic this behaviour in a stochastic-dynamic framework and are designed to optimize a financing strategy using any static tradeoff theory as input. The models developed reveal the determinants of the size and frequency of equity transactions and the range of values over which leverage variations are tolerated in four generic scenarios. They also yield a new formulation of the cost of capital that recognizes stochastic transaction costs and a penalty for deviation from any static-optimal leverage. Our class of models augments the pecking order theory, provides a flexible quantitative framework for its implementation as a decision tool, and facilitates the formulation of additional hypotheses for its empirical validation. Symmetrically, our results show the importance of dynamic factors in designing and interpreting empirical tests of static tradeoff theories. The results presented have important implications for the role played by static tradeoff theories in a stochastic-dynamic framework. One such implication is that the static-optimal leverage has no direct effect on the firm's leverage policy in this setting. The target leverage for refinancing transactions is different from the static-optimal leverage, and the mean leverage is generally different from both. As a consequence, the latter cannot be used to estimate the former. Another implication is that even when the mean leverage equals the static optimum, mean reversion is not an optimal behaviour and therefore not a legitimate test for the existence of a static tradeoff in a dynamic context. Still another implication is that wide variations in leverage ratios cannot be interpreted as evidence of leverage indifference. It follows that the pecking order theory is consistent with static tradeoff theories and does not require the assumption of leverage indifference.     

Just looking for a good game: competitive balance in the Korean Professional Baseball League

Rottenberg’s uncertainty of outcome hypothesis is about preferences that can vary across fans and sports. We provide the first evidence of the empirical power of the hypothesis in the Korean Professional Baseball League (KPBL). In a panel data set, team-level aggregation over years shows that fans of this league attend in ways consistent with the hypothesis at the level of game uncertainty and consecutive season uncertainty, but only the first is statistically significant. KPBL fans appear to just be looking for a good game. This is consistent with the nearly complete concentration of post-season participation among a very few teams outside of the major population centre in Seoul and a lack of local team identification among KPBL fans. Our work adds to the diversity of league structures in the competitive balance literature since talent levels in KPBL are the result of parent company advertising choices rather than geographic identification. There are research questions and a policy implication.     

CONVERTIBLE BOND PRICING MODELS

Convertible bonds are an important segment of the corporate bond market, with worldwide outstandings approaching US$235 billion. Simple pricing models value a convertible bond as being equivalent to a straight bond with an embedded option that enables the bond holder to convert to a specific amount of common stock. The straight bond is subject to both interest rate and credit risk, whereas the option to convert is dependent on the underlying stock price, which exposes the convertible bond holder to equity risk. The complexity of these features means that convertible bonds tend to be treated casually in major derivatives and corporate finance textbooks. This paper presents a survey of the theoretical and empirical aspects of convertible bond pricing. The limitations of these studies are highlighted to identify those areas of research that may improve the valuation process and facilitate the application of these securities for corporate financing.     

An optimization approach to strategic sourcing: A case study of the United States Air Force

The DoD annually procures billions of dollars worth of systems, supplies, and services in support of the national military strategy. Faced with budget cuts and other resource constraints, the DoD must transform its procurement process to ensure cost-effective sourcing of critical supplies and services. One aspect of current transformation in the DoD is the use of a strategic sourcing approach for the procurement of services at military installations. Using the Air Force's strategic sourcing process as our context, we developed an optimization model for selecting a set of proposals from among multiple offerors for services to be performed at multiple installations. The selection achieves the most favorable objective by balancing the confidence level in an offeror's past performance with the cost of services to the Air Force. The research findings, which are based on a realistic scenario, demonstrate improvements over the current sourcing process in both overall performance and cost.     

Bias Reduction in Dynamic Panel Data Models by Common Recursive Mean Adjustment*

The within‐group estimator (same as the least squares dummy variable estimator) of the dominant root in dynamic panel regression is known to be biased downwards. This article studies recursive mean adjustment (RMA) as a strategy to reduce this bias for AR(p) processes that may exhibit cross‐sectional dependence. Asymptotic properties for N,T→∞ jointly are developed. When ( log ²T)(N/T)→ζ, where ζ is a non‐zero constant, the estimator exhibits nearly negligible inconsistency. Simulation experiments demonstrate that the RMA estimator performs well in terms of reducing bias, variance and mean square error both when error terms are cross‐sectionally independent and when they are not. RMA dominates comparable estimators when T is small and/or when the underlying process is persistent.