A European-style derivative security on the S&P 500 has the following payoff

structure at the maturity date in 3 years:

where ST is the index level at the maturity date. The index spot level is 2,078 and its volatility is 20%. The risk-free interest rate is 4% and the index dividend yield is 2%. We consider a 6-step binomial tree.

(a) Use Excel to draw this payoff pattern for the following range [1000 , 3000] with a step of 50.

(b) Price this security using a 6-step binomial tree. Show all details.

(c) Compute the delta of this derivative at each node of the tree. What do you notice for the nodes at time 2.5 years?

S. 1500 1500 + 2x (ST-1750) 2500 f S, s1500 f 1500 ST S1750 1750 if 2250 s S STS2250