Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.     

A theoretical framework to evaluate different margin‐setting methodologies

The margin system is the first line of defense against the default risk of a clearinghouse. From the perspectives of a clearinghouse, the utmost concern is to have a prudential system to control the default exposure. Once the level of prudentiality is set, the next concern will be the opportunity cost of the investors, because high opportunity cost discourages people from hedging futures, and thus defeats the function of a futures market. In this article, we first develop different measures of prudentiality and opportunity cost. We then formulate a statistical framework to evaluate different margin‐setting methodologies, all of which strike a balance between prudentiality and opportunity cost. Three margin‐setting methodologies, namely, (1) using simple moving averages; (2) using exponentially weighted moving averages; (3) using a GARCH approach, are applied to the Hang Seng Index futures. Keeping the same prudentiality level, it is shown that the one using a GARCH approach by and large gives the lowest average overcharge. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:117–145, 2004     

The index futures markets: Is screen trading more efficient?

This article uses a nonparametric test based on the arc‐sine law (see, e.g., Feller, 1965 ), which involves comparing the theoretical distribution implied by an intraday random walk with the empirical frequency distribution of the daily high/low times, in order to address the question of whether the abandonment of pit trading has been associated with greater market efficiency. If market inefficiencies result from flaws in the market microstructure of pit trading, they ought to have been eliminated by the introduction of screen trading. If, on the other hand, the inefficiencies are a reflection of investor psychology, they are likely to have survived, unaffected by the changeover. We focus here on four cases. Both the FTSE‐100 and CAC‐40 index futures contracts were originally traded by open outcry and have moved over to electronic trading in recent years, so that we are able to compare pricing behavior before and after the changeover. The equivalent contracts in Germany and Korea, on the other hand, have been traded electronically ever since their inception. Our results overwhelmingly reject the random‐walk hypothesis both for open‐outcry and electronic‐trading data sets, suggesting there has been no increase in efficiency as a result of the introduction of screen trading. One possible explanation consistent with our results would be that the index futures market is characterized by intraday overreaction. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:337–357, 2004     

An empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short‐ and long‐run hedge ratios

This article analyzes the effects of the length of hedging horizon on the optimal hedge ratio and hedging effectiveness using 9 different hedging horizons and 25 different commodities. We discuss the concept of short‐ and long‐run hedge ratios and propose a technique to simultaneously estimate them. The empirical results indicate that the short‐run hedge ratios are significantly less than 1 and increase with the length of hedging horizon. We also find that hedging effectiveness increases with the length of hedging horizon. However, the long‐run hedge ratio is found to be close to the naïve hedge ratio of unity. This implies that, if the hedging horizon is long, then the naïve hedge ratio is close to the optimum hedge ratio. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:359–386, 2004     

Dynamics of the federal funds target rate: a nonstationary discrete choice approach

We apply a discrete choice approach to model the empirical behaviour of the Federal Reserve in changing the federal funds target rate, the benchmark of short‐term market interest rates in the US. Our methods allow the explanatory variables to be nonstationary as well as stationary. This feature is particularly useful in the present application as many economic fundamentals that are monitored by the Fed and are believed to affect decisions to adjust interest rate targets display some nonstationarity over time. The chosen model successfully predicts the majority of the target rate changes during the time period considered (1994–2001) and helps to explain strings of similar intervention decisions by the Fed. Based on the model‐implied optimal interest rate, our findings suggest that there is a lag in the Fed's reaction to economic shocks during this period. Copyright © 2004 John Wiley & Sons, Ltd.