Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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Modeling Implied Volatility Surfaces Using Two-dimensional Cubic Spline with Estimated Grid Points

  • Yang, Seung-Ho (Department of Industrial and Management Engineering Pohang University of Science and Technology) ;
  • Lee, Jae-wook (Department of Industrial and Management Engineering Pohang University of Science and Technology) ;
  • Han, Gyu-Sik (Division of Business Administration Chonbuk National University)
  • Received : 2010.02.27
  • Accepted : 2010.05.20
  • Published : 2010.12.01
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Abstract

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

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References

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