Pricing Calls with a Known Fixed Cash Dividend
Summary
The document discusses pricing a call option on a stock expected to pay a fixed cash dividend during the option’s life. It presents two approximations: convert dividends to a percentage yield when payments move with the share price, or subtract the present value of expected dividends from the stock price used in the option valuation. The latter approach is recommended for a single known cash dividend because its amount is fixed rather than tied to the future share price.
The explanation connects dividend treatment to the fact that option holders do not receive stock dividends. It gives a simple annualized-yield illustration for regular proportional dividends, but does not provide a full derivation or compare the approximation with a dividend-date binomial model. The suggested discounting convention is described as a risk-adjusted cost of equity, without further specification, so users need to check that the chosen valuation framework and discount rate are consistent with their assumptions.
Key ideas
- A fixed cash dividend can be represented by subtracting its present value from the stock price used in option valuation.
- A percentage dividend yield may suit dividends that vary with the share price.
- Option holders do not receive dividends paid to stockholders, which affects call valuation.
- The document recommends present-value adjustment for a known fixed dividend but does not compare it quantitatively with a tree model.
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# Pricing a vanilla call option with a fixed dividend # Pricing a vanilla call option with a fixed dividend I have started a finance course few months ago and am looking for a way to compute the price of a 1-year call option with a fixed dividend paid after 6 months. Using Black and Scholes I know how to compute the price of the option with a continuous dividend q but not for a fixed dividend D. My initial guess was to use a binomial tree, but I am not sure it is the optimal approach. If some of you are familiar with the topic, I would gladly read what they have to say. Thank you! :D Sophie ## Answer by RandyF (score 1) https://quant.stackexchange.com/a/22853 There are a couple of options that you can use to account for dollar amount dividends. Firstly, if dividends are expected to increase or decrease in proportion to the stock price, you can convert the dividends into a percentage by dividing the latest dividend by the last stock price on the day the dividend was declared and multiply by the number of dividends in a given year. For example, if the stock price is \$100 and the company issues a \$1 dividend quarterly, then the annualized yield is 4% (1/100*4). The continuously compounded yield for Black Scholes would be $ln(1+0.04)$. Alternatively, the reason that dividends are important in Black Scholes is because dividends would not be paid to the holders of the options. If you think about it, then, you could remove the present value of all dividends in the term of the option (discounted at a risk adjusted cost of equity) from the present value of the stock price. This would account for the future dividends paid and treat the company as a company that does not pay dividends. Because you are looking at one fixed dividend in 6 months, I would use the latter method because you do not know what the stock price will be at that time.
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