Third-order short-time expansions for close-to-the-money option prices under the CGMY model
Third-order short-time expansions for close-to-the-money option prices under the CGMY model
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CGMY模型下接近价值期权价格的三阶短时展开
DOI：
10.1080/1350486x.2018.1429935
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发表时间：
2013
影响因子：
--
通讯作者：
C. Houdr'e
中科院分区：
文献类型：
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作者：
J. E. Figueroa;Ruoting Gong;C. Houdr'e
摘要在无限变量的CGMY L模型下，得到了接近现金的欧式期权价格的三阶近似，并将其推广到具有独立布朗分量的模型。所考虑的渐近机制，即随着到期日接近于零，执行价收敛于现货股价，这在应用中是相关的，因为流动性最强的期权具有接近现货价格的执行价。我们的结果揭示了连续成分的波动性和跳跃参数与期权价格在执行接近现货价格时到期时的行为之间的联系。特别是，发现了一种新的跃迁现象，其中三阶项表现出两种不同的渐近机制，取决于是否或。与二阶近似不同，这里的展开式被证明是非常准确的，因此它们实际上可以用于校准一些模型参数。作为说明，我们将CGMY模型的布朗分量的波动率和跳跃强度C校准为实际的期权价格。
ABSTRACT A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY Lévy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the maturity approaches zero, is relevant in applications since the most liquid options have strikes that are close to the spot price. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behaviour of option prices near expiration when the strike is close to the spot price. In particular, a new type of transition phenomenon is uncovered in which the third-order term exhibits two distinct asymptotic regimes depending on whether or . Unlike second-order approximations, the expansions herein are shown to be remarkably accurate so that they can actually be used for calibrating some model parameters. For illustration, we calibrate the volatility of the Brownian component and the jump intensity C of the CGMY model to actual option prices.