Smooth and Bid-Offer Compliant Volatility Surfaces Under General Dividend Streams

Quantitative Finance, Vol. 13, No. 11, 1801–1812, (2013)

Swiss Finance Institute Research Paper No. 13-68

26 Pages Posted: 8 Nov 2012 Last revised: 23 Dec 2013

Olivier Bachem

ETH Zürich - Department of Mathematics

Gabriel G. Drimus

Institute of Banking and Finance, University of Zürich

Walter Farkas

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance; ETH Zürich - Department of Mathematics

Date Written: July 6, 2013

Abstract

Given bid-offer quotes for a set of listed vanilla options, a fundamental need of option market makers is to interpolate and extrapolate the available quotes to a full arbitrage-free surface. We propose a methodology which directly controls the trade-off between smoothness and bid-offer compliance of the resulting volatility surface. Unlike previous literature, the method applies simultaneously to all listed maturities and aims to smooth the implied risk neutral densities. Additionally, we consider asset dynamics which allow for general dividend streams - continuous, discrete yield and discrete cash - a modeling aspect of key importance in option markets.

Keywords: implied volatility surface, risk neutral density, discrete dividends

JEL Classification: C63, G13

Suggested Citation

Bachem, Olivier and Drimus, Gabriel G. and Farkas, Walter, Smooth and Bid-Offer Compliant Volatility Surfaces Under General Dividend Streams (July 6, 2013). Quantitative Finance, Vol. 13, No. 11, 1801–1812, (2013); Swiss Finance Institute Research Paper No. 13-68. Available at SSRN: https://ssrn.com/abstract=2172256 or http://dx.doi.org/10.2139/ssrn.2172256

Olivier Bachem

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

Gabriel G. Drimus (Contact Author)

Institute of Banking and Finance, University of Zürich ( email )

Plattenstrasse 14
Zürich, CH-8032
Switzerland

Walter Farkas

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance ( email )

Plattenstrasse 14
CH-8032 Zurich, Zurich 8032
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

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