OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS

Erik Ekström and Johan Tysk
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Erik Ekström: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden
Johan Tysk: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 07, 901-907

Abstract: There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

Keywords: Dividend; price ordering; convexity; volatility; option (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0219024904002694

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