Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility
Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility
复制标题
具有随机波动性的 Lévy 跳跃模型下接近价值期权的短时扩张
DOI：
10.1007/s00780-015-0281-z
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发表时间：
2014
影响因子：
1.7
通讯作者：
Sveinn Ólafsson
中科院分区：
文献类型：
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作者：
José E. Figueroa;Sveinn Ólafsson
在Figueroa-López et al.（Math. Finance，2013）中，针对一大类指数Lévy模型，推导出了实值期权价格的二阶近似，无论是否有布朗分量。本条有两个目的。首先，我们放松了对Lévy密度施加的正则性条件，使这种扩展能够很好地定义。其次，我们证明了公式扩展到“接近金钱”罢工的情况下，连续布朗分量被替换为一个独立的随机波动率过程的杠杆作用的情况下。
In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.