ASYMPTOTIC EQUIVALENCE IN LEE'S MOMENT FORMULAS FOR THE IMPLIED VOLATILITY, ASSET PRICE MODELS WITHOUT MOMENT EXPLOSIONS, AND PITERBARG'S CONJECTURE
ASYMPTOTIC EQUIVALENCE IN LEE'S MOMENT FORMULAS FOR THE IMPLIED VOLATILITY, ASSET PRICE MODELS WITHOUT MOMENT EXPLOSIONS, AND PITERBARG'S CONJECTURE
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隐含波动率的Lee矩公式、无矩爆炸的资产价格模型以及PITERBARG猜想的渐近等价
DOI：
10.1142/s0219024912500203
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发表时间：
2012
影响因子：
0.5
通讯作者：
Archil Gulisashvili
中科院分区：
文献类型：
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作者：
Archil Gulisashvili
在本文中，我们研究了随机资产价格模型中隐含波动率的渐近行为。我们为Lee矩公式中渐近等价的有效性提供了充要条件，并得到了无矩爆炸的资产价格模型隐含波动率的新渐近公式。作为一个应用，我们证明了 Piterbarg 猜想的修改版本。 Piterbarg 提出的渐近公式可以被认为是在模型没有矩爆炸的情况下大罢工隐含波动率的 Lee 矩公式的替代品。我们还描述了几种特殊资产价格模型中隐含波动率的渐近行为，例如 CEV 模型、Carr 和 Wu 的有限矩对数稳定模型、受跳跃大小双指数定律的复合泊松过程扰动的 Heston 模型，以及 Rogers 和 Veraart 的 SV1 和 SV2 模型。
In this paper, we study the asymptotic behavior of the implied volatility in stochastic asset price models. We provide necessary and sufficient conditions for the validity of asymptotic equivalence in Lee's moment formulas, and obtain new asymptotic formulas for the implied volatility in asset price models without moment explosions. As an application, we prove a modified version of Piterbarg's conjecture. The asymptotic formula suggested by Piterbarg may be considered as a substitute for Lee's moment formula for the implied volatility at large strikes in the case of models without moment explosions. We also characterize the asymptotic behavior of the implied volatility in several special asset price models, e.g., the CEV model, the finite moment log-stable model of Carr and Wu, the Heston model perturbed by a compound Poisson process with double exponential law for jump sizes, and SV1 and SV2 models of Rogers and Veraart.