ACCOUNTING FOR RISK AVERSION, VESTING, JOB TERMINATION RISK AND MULTIPLE EXERCISES IN VALUATION OF EMPLOYEE STOCK OPTIONS

We present a valuation framework that captures the main characteristics of employee stock options (ESOs), which financial regulations now require to be expensed in firms' accounting statements. The value of these options is much less than Black–Scholes prices for corresponding market-traded options due to the suboptimal exercising strategies of the holders, which arise from risk aversion, trading and hedging constraints, and job termination risk. We analyze the combined effect of all of these factors along with the standard ESO features of multiple exercising rights, and vesting periods. This leads to the study of a chain of nonlinear free-boundary problems of reaction-diffusion type. We find that job termination risk, vesting, finite maturity and non-zero interest rates are significant contributors to the ESO cost. However, we find that in the presence of vesting, the impact of allowing multiple exercise rights on ESO cost is negligible.     

The Effect of Regional Growth Characteristics on Regional Housing Prices

As contrasted with strictly national housing reports, this article highlights the regional variations in population growth patterns and recently built owner-occupied housing as a means of determining single-family housing price components (i.e., developed lot values, homebuilding costs, and builder's profit and overhead) by region. The assertion that escalating lot costs and increases in new housing costs will limit the demand for single-family housing is challenged on a national basis and treated individually for the West, Northeast, South, and North Central Regions of the country.     

HEDGING WITH INTERNATIONAL STOCK INDEX FUTURES: AN INTERTEMPORAL ERROR CORRECTION MODEL

In this paper we extend the traditional price change hedge ratio estimation method by applying the theory of cointegration to hedging with stock index futures contracts for France (CAC 40), the United Kingdom (FTSE 100), Germany (DAX), and Japan (NIKKEI). Previous studies ignore the last period's equilibrium error and short-run deviations. The findings of this study indicate that the hedge ratios obtained from the error correction method are superior to those obtained from the traditional method as evidenced by the likelihood ratio test and out-of-sample forecasts. Using the procedures developed in this paper, hedgers can control the risk of their portfolios more effectively at a lower cost.     

Are Momentum Profits Robust to Trading Costs?

We test whether momentum strategies remain profitable after considering market frictions induced by trading. Intraday data are used to estimate alternative measures of proportional and non-proportional (price impact) trading costs. The price impact models imply that abnormal returns to portfolio strategies decline with portfolio size. We calculate break-even fund sizes that lead to zero abnormal returns. In addition to equal- and value-weighted momentum strategies, we derive a liquidity-weighted strategy designed to reduce the cost of trades. Equal-weighted strategies perform the best before trading costs and the worst after trading costs. Liquidity-weighted and hybrid liquidity/value-weighted strategies have the largest break-even fund sizes: $5 billion or more (relative to December 1999 market capitalization) may be invested in these momentum strategies before the apparent profit opportunities vanish.     

The lottery as an alternative source of state revenue

Conclusion In this paper the authors have developed an economic model of state lotteries that determines the probability of whether a given state will adopt a lottery or not, determines the probability of whether a given state is likely to adopt a lottery sooner rather than later, and determines the state's expected net spendable revenues generated by adopting and operating a lottery. The authors found that a given state will tend to adopt a lottery and will tend to adopt the lottery sooner, the higher the relative tax effort of the state, the higher the mean personal income of the state's residents (or the lower the fraction of the state's residents that are in poverty), the greater the restrictions on raising other taxes in the state, the greater the state's spendable revenue generated from parimutuel betting in the state, the larger the fraction of the state's border that is contiguous with other states with lotteries, and since 1980, the greater the annual number of tourists or visitors in the state.A state's expected net spendable revenue from adopting and operating a lottery is greater the higher the mean personal income of residents in the state, the greater the annual number of tourists or visitors in the state, the smaller the fraction of the state's border that is contiguous with other states with lotteries, and the smaller the parimutuel industry in the state. The ability of a given state's residents to cross the border to purchase lottery tickets in contiguous states, and the ability to engage in parimutuel betting in a state are substitutes for the purchase of lottery tickets in the given state and significantly reduce the expected net spendable revenue from adopting and operating a lottery in that state.From a policy making standpoint, legislators often appear to support the adoption of a lottery for their state without fully considering a realistic expected level of net spendable revenue that the proposed lottery is likely to generate for that particular state.⁸ Often these legislators apparently do not consider important determinants of expected lottery profits such as the level of personal income of state residents, the annual number of tourists in the state, and the presence or absence of adjacent states with lotteries. Also, legislators do not consider fully the impact that adopting a lottery will have on existing parimutuel betting industries in the state. Likewise, legislators apparently do not consider the negative impact of parimutuel betting on the expected net spendable revenue generated by the proposed lottery. Legislative decisions made in the absence of full information often tend to be inefficient decisions. The present study may encourage policy makers to become better informed on the issue of lottery adoption for their state.     

Rational Expectations, Market Fundamentals and Housing Price Volatility

This paper derives a forward-looking rational expectations house price model and empirically tests its ability to explain short-run fluctuations in real house prices. A novel approach to proxying the imputed rents of owner-occupied housing, as a function of observable housing market fundamentals, is combined with a housing market arbitrage relation to derive a present value model for real house prices. Tests of the rational expectations, nonlinear cross-equation restrictions reject the joint null hypothesis of rational expectations and the asset-based housing price model for quarterly, single-detached house prices in the city of Vancouver, British Columbia from 1979–1991. The model fails to fully capture observed house price dynamics in two real estate booms but tracks real house prices well in less volatile times, suggesting that prices may temporarily deviate from fundamental values in real estate price cycles.     

Maturity cycles in implied volatility

The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [8]. The time-variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. By extending the mathematical analysis to incorporate model parameters which are time-varying, we show this behaviour can be explained in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients.Received: December 2003, Mathematics Subject Classification (2000): 91B70, 60F05, 60H30JEL Classification: C13, G13Jean-Pierre Fouque: Work partially supported by NSF grant DMS-0071744.Ronnie Sircar: Work supported by NSF grant DMS-0090067. We are grateful to Peter Thurston for research assistance.We thank a referee for his/her comments which improved the paper.     

Labour–Intensive Industrialization in Hong Kong, 1950–70: A Note on Sources and Methods

This research note critiques published quantitative sources on employment in manufacturing enterprises during a crucial epoch of rapid industrialization, and uses newly discovered archival sources to investigate organizational dualism, the co-existence of labour and capital-intensive modes of production. New quantitative data demonstrates that a high proportion of the industrial workforce was employed in small enterprises, notably workshops using labour-intensive techniques. New surveys of two ‘traditional’ Hong Kong industries (rattan ware furniture and basket ware; and umbrella making) show that factory, workshop, and home-based production co-existed within the same sector across the whole period, 1950–70.