The Instantaneous Volatility and the Implied Volatility Surface for a Generalized Black-Scholes Model

被引：1

作者：

Takaoka, Koichiro ^{[1
]}

Futami, Hidenori ^{[2
]}

机构：

[1] Hitotsubashi Univ, Grad Sch Commerce & Management, Kunitachi, Tokyo 1868601, Japan

[2] Tokio Marine & Nichido Fire Insurance Co Ltd, Chiyoda Ku, Tokyo 1020075, Japan

来源：

ASIA-PACIFIC FINANCIAL MARKETS | 2010年 / 17卷 / 04期

关键词：

Black-Scholes model; Option pricing; Local volatility model; Implied volatility;

D O I：

10.1007/s10690-009-9112-6

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

Takaoka (Asia-Pacific Financial Markets 11:431-444, 2004) proposed a generalization of the Black-Scholes stock price model by taking a weighted average of geometric Brownian motions of different variance parameters. The model can be classified as a local volatility model, though its local volatility function is not explicitly given. In the present paper, we prove some properties concerning the instantaneous volatility process, the implied volatility curve, and the local volatility function of the generalized model. Some numerical computations are also carried out to confirm our results.

引用

页码：391 / 436

页数：46

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