Hi. Can somebody please provide some commentary to my method for the below question?

I need to calculate the delta of the put and call option with a strike price of 100 with the following information i was given and calculated.

Stock Price (Sn)=100, Strike Price (K)=100, u=1.2, d=0.9, probability of u=0.684, probabilty of d = 0.316

Option Price of Call: MAX[Sn-K,0]=\$20

Option Price of Put: MAX[K-Sn,0]=\$10

Therefore, the delta call is (20-10)/(120-90) = 1/3

and the delta of a put is 1/3-1= -2/3

So that the summation of the delta put and call = 1

I think I have this correct just making sure my method is correct, I know you can use the Black-Scholes method for N(d1) however I am not given any volatility figures only the probabilites and steps for up and down movements. (unless you can calculate volatility from the up and down step). Feedback welcome I believe that you’re mistaken.

The delta for a call is the change in the call price divided by the change in the underlying price.

Therefore, you need to determine the price of the call at the up node and the price of a call at the down node; the price of a put doesn’t enter into the calculation.

Furthermore, you’re looking only at the intrinsic value of the call (and the put); you also need the time value to get the price.

Thanks,

With the time value I only have examples with solutions that show workings for just the intrinsic values (pearson, fundamentals of futures and options markets) they work out the up node option value as the difference between stock price and strike price. Value of the Call at the lower node will be 0, the value at the upper node will be 20.

So when I calculate the lower numbers in the binomial tree they always represent the call value of the option?