Small-Time Asymptotics of Option Prices and First Absolute Moments
Small-Time Asymptotics of Option Prices and First Absolute Moments
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期权价格和第一绝对矩的小时渐近
DOI：
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发表时间：
2010
影响因子：
1
通讯作者：
Marcel Nutz
中科院分区：
文献类型：
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作者：
Johannes Muhle‐Karbe;Marcel Nutz
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We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process S follows a general martingale. This is equivalent to studying the first centered absolute moment of S. We show that if S has a continuous part, the leading term is of order √T in time T and depends only on the initial value of the volatility. Furthermore, the term is linear in T if and only if S 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 S so that calculations are necessary only for the class of Lévy processes.