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I have implemented a Trinomial tree method that takes into account of discrete dividends and been getting good results on Tvs and other greeks generally. However, at the exdividend date, my theta is getting some weird result. My theta is calculated as follows:Theta = (V_{1,1} - V_{0,0})/dt where V_{t,i} represents the option value at node i at time t, dt is the tree step size.I have also another version of Theta calculation as follows:Theta = (V_{1,1} - V_{0,0} - Delta*(S_{1,1} - S{0,0})) / dt.I am expecting to have a +ve theta for my deep ITM Put, and a very -ve theta for my deep ITM Call, where the dividend payout is about 5% of the spot. The time to maturity is 0.25, rate is 5%, vol is 20%. Somehow I don't get the expected result from either formula. Anyone would like to throw a comment?

some more detail as to how you have implemented dividends would be helpful. have you done this using a dividend yield or discrete dividends ? I fhte latter how have you tken them into account ?

QuoteOriginally posted by: daveangelsome more detail as to how you have implemented dividends would be helpful. have you done this using a dividend yield or discrete dividends ? I fhte latter how have you tken them into account ?The dividends are implemented as arrays of times/amounts. the standard recombining tree is generated by first subtract the PV of the divs and later add them back to each indivudial nodes. American exercise is assumed by checking the max of intrinsic value at each node and the "expected" option value from the tree parameters.The Tv is to be calculated as V_{0,0}, as described earlier. The values of TV, Delta and gamma seems to be ok. But the theta is significantly off. For example,spot=1248, strike=1500,time=0.21,vol=0.2, rate=0.05,American Put option, with dividend { 0.00097032 years, $10 } gives theta as -$8.8/day. From a qualitative point of view, such a deep ITM Put just prior ex-dividend date, I assume I will get a much higher value (like 0 or even +ve theta) for theta. The rational is because the spot is going to drop as much as 10 the day after, and hence the put option would worth more.

but wouldnt this american put be worth parity i.e 252 (1500-1248) ?

It would of course. But how about the Theta? Or do you mean the Theta should be zero?

QuoteOriginally posted by: calvinkitIt would of course. But how about the Theta? Or do you mean the Theta should be zero?I dont think Dave knows the answer....

QuoteOriginally posted by: MabodQuoteOriginally posted by: calvinkitIt would of course. But how about the Theta? Or do you mean the Theta should be zero?I dont think Dave knows the answer....I think Mabod is dying to tell you

Using your tree, plot the price of an American call with discrete dividends as a function of the maturity date. What happens to the call price as its maturity passes over a dividend date?