A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS
A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS
复制标题
资产价格模型中短期隐含波动率跳跃的新视角
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
P. Tankov
中科院分区：
文献类型：
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作者：
A. Mijatović;P. Tankov
本文研究了指数Lévy类跳跃资产价格模型中临近到期的期权隐含波动率微笑的行为。我们引入了一个新的重整罢工变量的属性，隐含波动率收敛到一个非常有限的形状，这是一个函数的扩散组件的过程和跳跃活动（Blumenthal-Getoor）指数的跳跃组件。我们的极限隐含波动率公式将标的资产价格过程的跳跃活动与隐含波动率曲面的短端联系起来，并从期权价格的角度揭示了有限变差跳跃和无限变差跳跃之间的差异：在后者中，极限微笑的翅膀由正跳跃和负跳跃的跳跃活动指数决定，而在前者中，机翼具有恒定的模型独立斜率。这一结果从理论上证明了在基于短期期权价格的校准中，无限变差Lévy模型优于有限变差模型.
We analyze the behavior of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalization of the strike variable with the property that the implied volatility converges to a nonconstant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal–Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short‐end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model‐independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on short‐maturity option prices.