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Small-time asymptotics of option prices and first absolute moments (2011)
| Venue: | Journal of Applied Probability |
| Citations: | 14 - 2 self |
BibTeX
@ARTICLE{Muhle-karbe11small-timeasymptotics,
author = {Johannes Muhle-karbe and Marcel Nutz},
title = {Small-time asymptotics of option prices and first absolute moments},
journal = {Journal of Applied Probability},
year = {2011},
pages = {1003--1020}
}
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Abstract
We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process 푆 follows a general martingale. This is equivalent to studying the first centered absolute moment of 푆. We show that if 푆 has a continuous part, the leading term is of order 푇 in time 푇 and depends only on the initial value of the volatility. Furthermore, the term is linear in 푇 if and only if 푆 is of finite variation. The leading terms for pure-jump processes with infinite variation are between these two cases; we obtain their exact form for stable-like small jumps. To derive these results, we use a natural approximation of 푆 so that calculations are necessary only for the class of Lévy processes.
Keyphrases
small-time asymptotics first absolute moment option price absolute moment infinite variation leading term stock price process finite variation natural approximation pure-jump process vy process exact form at-the-money call option price stable-like small jump initial value general martingale continuous part
