Abstract
In this paper, we extend the Johnson, Pawlukiwicz, and Mehta [1] skewness-adjusted binomial model to the pricing of futures options and examine in some detail the asymptotic properties of the skewness model as it applies to futures and spot options. The resulting skewness-adjusted futures options model shows that for a large number of subperiods, the price of futures options depends not only on the volatility and mean but also on the risk-free rate, asset-yield, and other carrying-cost parameters when skewness exists.
Highlights
One of the interesting, as well as subtle, features of the Black-Scholes (B-S) [2] model and the binomial option pricing model (BOPM) with a large number of subperiods (n) is that the models depend only on the variance
We extend the Johnson, Pawlukiwicz, and Mehta [1] skewness-adjusted binomial model to the pricing of futures options and examine in some detail the asymptotic properties of the skewness model as it applies to futures and spot options
Given that one of the features of the JPM skewness model for spot options is that skewness changes the asymptotic properties of the u and d parameters, this paper examines in some detail the asymptotic properties of the skewness-adjusted binomial model as it applies to both futures and spot options
Summary
As well as subtle, features of the Black-Scholes (B-S) [2] model and the binomial option pricing model (BOPM) with a large number of subperiods (n) is that the models depend only on the variance In these models, the mean is not important in determining the value of spot options and the mean and net carry cost are not important for futures options. JPM show that skewness changes the asymptotic properties of the up (u) and down (d) parameters, elevating the relative importance of the mean in valuing options This property of their skewness model suggests that when distributions of logarithmic returns are characterized by skewness, the observed pricing biases associated with the B-S model may be due to the omission of skewness, and the mean. In the case of futures options, the presence of skewness elevates the importance of the mean, as well as the risk-free rate, the asset yield, and other parameters that are defined by the carrying-cost model
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