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논문검색

Volatility smiles and skews under a static no arbitrage extension of the Carr-Geman-Madan valuation of options in incomplete markets

초록

영어

It is well known that the pattern of implied volatilities in foreign currency options forms a smile shape which is referred to as a volatility smile. On the other hand, the volatility skew is a general pattern of implied volatilities in equity options. In this paper, we consider the Carr-Geman-Madan valuation of options in incomplete markets on which the preference structure of the market participants are reflected. Through a simple continuous static no arbitrage extension, we examine how the smiles and skews are related.

목차

Abstract
 1 Introduction
 2 CGM valuation
  2.1 CGM model
  2.2 Continuous extension
 3 Static no arbitrage
  3.1 Static no arbitrage condition
  3.2 The validity of condition (iii)
 4 Smile and Skew
  4.1 Analytic result for smile and skew
  4.2 Numerical illustration
 References

저자정보

  • Intae Jeon Department of Mathematics, The Catholic University of Korea.
  • Cheol-Ung Park Department of Mathematics, The Catholic University of Korea.
  • Sang-Il Han Department of Mathematics, The Catholic University of Korea.

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