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-Hey all, recently I encountered the necessity to incorporate dividends into options pricing. Lets say I have the following american put option: Initial price - 100, T-0.25, Volatility is 30%, Number of periods is 3, Interest rate is 2%. Lets further say the u = 1.07 and d = 0.93458. Given the prior information I calculate that the risk neutral probabilities are q = 63.08% and q-1=36.92%

First I built the three period lattice given the parameters above: enter image description here The stock lattice was computed using the excel formula =B2*(B7 ^(0))*(B8^(0)), where B2 is the initial price of 100 and the B7 and B8 are u and d respectively that are exponentiated by the number of up or down movements at any time.

Now the option lattice was obtained from the stock lattice, first using the formula =MAX( H2 - E16, 0) at t=3, where the H2 is the strike price and E16 is the spot price, and then I calculated the t2, t1 and t0 using =MAX(MAX($H$2 - $D$16, 0), ($B$9 *$E$24 + $B$10 *$E$25)/$B$6), which should be read as =MAX(MAX(strike-spot,0), q *priceU + q-1*priceD)/(1+interest rate).

How would I modify these formulas in order to incorporate dividends, given that these are paid in each period and are proportional to the price of the stock. Given that the dividend is 1%.

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  • $\begingroup$ Hi Noir, I can't follow your formulas as they reference cells in your spreadsheet, you should replace the cell references with what the contain to make possible to follow. $\endgroup$
    – AfterWorkGuinness
    Oct 19, 2015 at 15:23
  • $\begingroup$ Yes, it is hard to understand, but googling a bit you can find this. finance.bi.no/~bernt/gcc_prog/recipes/recipes/node9.html $\endgroup$
    – arodrisa
    Oct 19, 2015 at 15:24

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You want to express your dividend as a continuous rate and subtract it from the risk free rate when calculating the probability of an up jump. See this Wikipedia article: https://en.wikipedia.org/wiki/Binomial_options_pricing_model#STEP_3:_Find_Option_value_at_earlier_nodes

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  • $\begingroup$ Thank you the explanation is very conclusive and clear, I don't know how I have missed it. $\endgroup$
    – Noir
    Oct 19, 2015 at 19:40
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    $\begingroup$ You're welcome. That's what the site's for. $\endgroup$
    – AfterWorkGuinness
    Oct 19, 2015 at 20:01

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