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The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, and (iii) for the restricted models option Δ is preferred over the more often used strike relative to spot price as measure for moneyness.

This chapter proposes a nonparametric estimator of the risk neutral density (RND) based on cross-sectional European option prices. The authors recast the arbitrage-free equation for option pricing as a functional linear regression model where the regressor is a curve and the independent variable is a scalar corresponding to the option price. Then, the authors show that the RND can be viewed as the solution of an ill-posed integral equation. To estimate the RND, the authors use an iterative method called Landweber-Fridman (LF). Then, the authors establish the consistency and asymptotic normality of the estimated RND. These results can be used to construct a confidence interval around the curve. Finally, some Monte Carlo simulations and application to the S&P 500 options show that this method performs well compared to alternative methods.

Starting from 2003, Microsoft and many other companies have either gradually reduced or completely replaced stock options with restricted stocks in their compensation plans. This raises an interesting question: which form of compensation is better, stock or options? This chapter makes an economic comparison between the two compensation vehicles and concludes that stock is preferred to options. The backdrop of the study is dynamic asset allocation within a utility maximization framework whereby the company may go bankrupt. The incorporation of bankruptcy risk into the analysis is motivated by the recent downfalls of companies such as Enron and WorldCom.

We demonstrate that vesting requirements and bankruptcy risk can lead to significant value discounts. When the restricted stock and options have a vesting period of 5 years, and account for 50% of the total wealth, the total discount is more than 60%, out of which 20% is due to bankruptcy risk. More importantly, we find that stock is a better compensation tool than options. For a given dollar amount of grant, the higher the stock proportion, the higher the expected utility. In fact, replacing options by stock can lead to a substantial amount of cost savings for the firm, while maintaining the same level of utility for the employee. For example, when options account for 50% of the total wealth and are subsequently replaced by stock, the granting cost is reduced by about 60%. Our findings therefore provide a theoretical support for the move to stock-only style of performance compensations.

Our chapter raises serious questions about the long-term efficiency of stock prices in relation to the realized returns of the underlying corporate real assets. In our large-scale calculations that cover horizons of 10, 20, 30, 40, and 50 years, returns on corporate real assets suffer a long-term decline, and have been below the yields of 10-year Treasury bonds since 1973. Real assets that received more external financing from capital markets and institutions actually report even lower realized long-term returns. The decline in realized returns cannot be attributed to declining risks as the volatilities of realized returns have been increasing over time. These surprising results may stimulate fresh debate on the roles and long-term performance of capital markets and institutions.

Purpose – The aim of this chapter is to examine the constant proportion portfolio insurance (CPPI) method when the multiple is allowed to vary over.

Methodology/approach – A quantile approach is introduced under the dependent return hypothesis. We use for example ARCH-type models.

Findings – In this framework, we provide explicit values of the multiple as function of the past asset returns and other state variables. We show how the multiple can be chosen to satisfy the guarantee condition, at a given level of probability and for particular market conditions.

Originality/value of paper – We show in this chapter that it is possible to choose variable multiples for the CPPI method if quantile hedging is used and in the case of dependent log returns. Upper bounds can be calculated for each level of probability and according to state variables. This new multiple can be determined according to the distributions of the risky asset log return and volatility.

The paper uses 101 years of Chilean and international financial assets returns to investigate mean-variance optimal portfolio allocations. The key conclusion is that the share of international unhedged investments is substantial even in minimum risk portfolios (20%), unless the period 1980–2002 is assumed to be drawn from a different distribution and previous history is disregarded. In addition to that, the paper finds that mean-variance optimal investors would have generated substantial demand for an asset replicating the return profile of an efficient pay-as-you-go pension scheme. Labour income and departures from log-normality of returns might, however, affect the latter conclusion.

We document three new facts about gender differences in executive compensation. First, female executives receive lower share of incentive pay in total compensation relative to males. This difference accounts for 93% of the gender gap in total pay. Second, the compensation of female executives displays lower pay-performance sensitivity. A $1 million dollar increase in firm value generates a $17,150 increase in firm-specific wealth for male executives and a $1,670 increase for females. Third, female executives are more exposed to bad firm performance and less exposed to good firm performance relative to male executives. We find no link between firm performance and the gender of top executives. We discuss evidence on differences in preferences and the cost of managerial effort by gender and examine the resulting predictions for the structure of compensation. We consider two paradigms for the pay-setting process, the efficient contracting model and the “managerial power” or skimming view. The efficient contracting model can explain the first two facts. Only the skimming view is consistent with the third fact. This suggests that the gender differentials in executive compensation may be inefficient.

In the strategic management literature, two mechanisms have been proposed to explain how managers generate economic rents: resource selection, and capability building. Resource selection is a Ricardian perspective where the productivity of resources are heterogeneously distributed among firms (Peteraf, 1993; Wernerfelt, 1984), and managers outsmart the factor markets by selecting resources based on their future values (Barney, 1986). The alternative Schumpeterian perspective is capability building, a mechanism that depends on deployment of resources to affect a desired end (Amit & Shoemaker, 1993; Mahoney, 1995). While capability building requires that managers develop a capacity to manage firm specific tangible and intangible processes, the resource selection mechanism demands managers to accurately assess expectations about the future value of resources.