Estimating discrete dividends by no-arbitrage

Abstract

We develop and showcase a simple no-arbitrage methodology for the valuation of discrete dividend payments, based exclusively on market prices of options via the put-call parity. Our approach integrates all available option market data and simultaneously calibrates the market-implied discount curve, thus ensuring consistency across spot and derivative markets. We illustrate our method using stocks of European blue-chip companies.

Keywords:

• Dividends
• Arbitrage
• Put-call parity
• Market-implied discount curve

JEL Classification:

• G17
• G13
• G14

Acknowledgements

All authors wish to thank two anonymous referees for helpful comments and suggestions. We also thank Peter Ruckdeschel and Ralf Korn for discussions and comments on earlier versions of this paper. Sarah Grün gratefully acknowledges financial support from the Fraunhofer Society for the Advancement of Applied Research. Sascha Desmettre wishes to thank Deutsche Forschungsgemeinschaft for funding within the Research Training Group 1932 ‘Stochastic Models for Innovations in the Engineering Sciences’.

Notes

No potential conflict of interest was reported by the authors.

1 By contrast, note that assumption 2.1 necessarily holds whenever individual dividend payments are replicable by market instruments (and tax effects are neglected). This is the case, in particular, if the financial market model is complete or dividends are assumed to be deterministic.

2 Eurex introduced derivatives on dividends of individual stocks, including futures, in 2010.

3 Note that there was a 2-for-1 stock split for Merck on 30 June 2014.

4 In addition, for shorter time horizons more derivatives are available for our estimation methodology.