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Options Written On Stocks With Known Dividends

Author

Listed:
  • 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)

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.

Suggested Citation

  • Erik Ekström & Johan Tysk, 2004. "Options Written On Stocks With Known Dividends," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(07), pages 901-907.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:07:n:s0219024904002694
    DOI: 10.1142/S0219024904002694
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