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Volatility and Dividends - Volatility Modelling with Cash Dividends and Simple Credit Risk

37 Pages Posted: 7 Jun 2008 Last revised: 16 Nov 2010

Hans Buehler

JP Morgan Chase, London; Technical University of Berlin - Institut fur Mathematik

Date Written: February 2, 2010

Abstract

This article shows how to incorporate cash dividends and credit risk into equity derivatives pricing and risk management.

In essence, we show that in an arbitrage-free model the stock price process upon default must have the form S(t) = { F(t) - D(t) } X(t) D(t) ] where X is a local martingale with X(0)=1, the curve F represents the "risky" forward and D is the floor imposed on the stock price process in the form of appropriately discounted future dividends.

We show that the method presented is the only such method which is consistent with the assumption of cash dividends and simple credit risk. We discuss the implications for implied volatility, no-arbitrage conditions and we derive a version of Dupire's formula which handles cash dividend and credit risk properly.

We discuss pricing and risk management of European options, PDE methods and in quite some detail variance swaps and related derivatives such as gamma swaps, conditional variance swaps and corridor variance swaps. Indeed, to the our best if our knowledge, this is the first article which shows the correct handling of cash dividends when pricing variance swaps.

The present version 1.31 has been updated after several comments from readers.

Keywords: Cash Dividends, Dividends, Volatility, Implied Volatility, Variance Swaps, PDE, Credit Risk, Hazard Rate, Black Scholes, Affine Dividends

JEL Classification: D89

Suggested Citation

Buehler, Hans, Volatility and Dividends - Volatility Modelling with Cash Dividends and Simple Credit Risk (February 2, 2010). Available at SSRN: https://ssrn.com/abstract=1141877 or http://dx.doi.org/10.2139/ssrn.1141877

Hans Buehler (Contact Author)

Technical University of Berlin - Institut fur Mathematik ( email )

Institut fur Mathematik, Sekr. MA 6-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

HOME PAGE: http://gammalong.com

JP Morgan Chase, London ( email )

Equities and Investor Services QR
4/F 25 Bank Street
London, E14 5JP
United Kingdom

HOME PAGE: http://www.jpmorgan.com

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