-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: 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%.