Abstract
In recent years, small-time asymptotics of option prices have received much attention. In this paper, we derive short-time first-order expansions for price and implied volatility of at-the-money call options under the exponential Normal Tempered Stable model in two methods. The first method is similar to the approach used by Figueroa-López and Forde for the CGMY model. The other is based on the explicit form of characteristic functions of the Normal Tempered Stable processes. Our numerical results show that the expansions herein remarkably approximate the prices obtained by Fourier transform, even for options with maturities as long as a few years. For this reason, our expansions can be used for parameter calibration and model testing in a simple and efficient way.
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