“Skewness and Stock Option Prices”, Hans Gerber and Bruno Landry,July 1997

We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities.     

Preferential trade agreements and their role in world trade

This paper investigates the effects of preferential trade agreements (PTAs) on bilateral trade using a comprehensive data base of PTAs in force and a detailed matrix of world trade. Total trade between PTA partners is a poor proxy for preferential trade (trade in tariff lines where preferences are likely to matter): while the former was one-third of global trade in 2000–2002, the latter was between one-sixth and one-tenth. Gravity model estimates indicate that using total trade to assess the impacts of PTAs leads to a significant downward bias in the PTA coefficient: the semi-elasticity of trade with respect to PTA membership rises from 87% for total trade to 119% for preferential trade. Product exclusions and long phase-in periods significantly limit preferential trade; the marginal impact of South-South agreements on preferential trade is much higher than North-South PTAs, while the effect of North-North agreements is insignificantly different from zero.     

Pricing American options under stochastic volatility and stochastic interest rates

We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters, this method can accurately price options with time-to-maturity up to several years. The main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility, and correlations on the American put price.     

Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility

We derive an asymptotic expansion formula for option impliedvolatility under a two-factor jump-diffusion stochastic volatilitymodel when time-to-maturity is small. We further propose a simplecalibration procedure of an arbitrary parametric model to short-termnear-the-money implied volatilities. An important advantageof our approximation is that it is free of the unobserved spotvolatility. Therefore, the model can be calibrated on optiondata pooled across different calendar dates to extract informationfrom the dynamics of the implied volatility smile. An exampleof calibration to a sample of S&P 500 option prices is provided.(JEL G12)     

Poverty Effects of Higher Food Prices: A Global Perspective

The spike in international food prices between 2005 and the first half of 2008 drew much attention to the vulnerability of the poor to such shocks. This paper provides a formal assessment of the direct and indirect impacts of higher prices of agricultural goods on global poverty using a representative sample of 63–93% of the developing world's population. To assess the direct effects, the paper uses domestic food price data between January 2005 and December 2007—when the relative price of food staples rose by an average of 5.6%—to find that the number of individuals living under the extreme poverty line increased by 155 million, with almost three‐quarters of this increase taking place in East Asia. To take the second‐order effects into account, the paper links household survey data with a global general equilibrium model, finding that the same increase in consumer prices of agricultural goods (modeled by increasing demand for first‐generation biofuels) would raise the number of individuals living under extreme poverty by 32 million, with nearly the entire increase occurring in South Asia and Sub‐Saharan Africa.