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http://ssrn.com/abstract=1964634
 
 

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Arbitrage-free Asset Class Independent Volatility Surface Interpolation on Probability Space using Normed Call Prices


Pijush Gope


Independent; DZ Bank AG

Christian P. Fries


LMU Munich, Department of Mathematics; DZ Bank AG

November 27, 2011


Abstract:     
We consider arbitrage-free interpolation of arbitrage-free input data of European option prices. The method derived is independent of the underlying (equity, rates, FX, etc.). A particular contribution of the paper is that for the chosen coordinate system and a wide variety of interpolation methods, we prove that the method results in arbitrage-free interpolations. This result is achieved in two steps: first, we transform option prices to Normed Call Prices (NCP), which are independent of the application. Using NCPs as interpolants, the interpolation problem can be formulated independently of assumptions of deterministic rates. Besides, the constraints necessary for ensuring absence of arbitrage are much simpler in this interpolant system, as they do not involve any scaling at all. Having proposed our choice of the dependent variable, we turn to the independent variables, and transform the strike-maturity or moneyness-maturity coordinate system to a probability-maturity coordinate system, which results in an interpolation method called probability-space interpolation in maturity dimension on the proposed NCP system that we prove actually leads to arbitrage-free surfaces in both strike and maturity dimensions. The computational tractability is an added advantage of our interpolation scheme.

Number of Pages in PDF File: 27

Keywords: NCP, Volatility Surface, Volatility Smile, Probability Space, Arbitrage Free Interpolation

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Date posted: November 25, 2011 ; Last revised: October 18, 2013

Suggested Citation

Gope, Pijush and Fries, Christian P., Arbitrage-free Asset Class Independent Volatility Surface Interpolation on Probability Space using Normed Call Prices (November 27, 2011). Available at SSRN: http://ssrn.com/abstract=1964634 or http://dx.doi.org/10.2139/ssrn.1964634

Contact Information

Pijush Gope (Contact Author)
Independent ( email ) ( email )
Germany
DZ Bank AG ( email ) ( email )
Germany
Christian P. Fries
LMU Munich, Department of Mathematics ( email )
Theresienstrasse 39
Munich
Germany
DZ Bank AG ( email )
60265 Frankfurt am Main
Germany
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