Question

Assume a one-period (annual) binomial model with the following characteristics: current stock price is $25, the up factor for each period is 1.05, the down factor for each period is 0.95, and the risk-free rate is 3 percent.

(a) (4 pts) Draw the binomial tree for the stock with the appropriate pricing.

(b) (2 pts) What is the current hedge ratio for a European call for that stock if it has a strike price of $22 and will expire in one year?

(c) (2 pts) What is the current value of that same call?

Answer 1

a)

B)

Payoff difference between up move and down move will be max (26.25-22,0)- max(23.75-22,0)= 4.25-1.75= 2.5

Range of values across 2 possible outcome = 26.25-23.75= 2.5

So hedge ratio or Delta = Payoff difference/Range of values across 2 outcomes = 2.5/2.5= 1

C: Call Price = Payoffs / risk free rate

Total Payoff = 0.5* Payoff in upmove + 0.5* Payoff during down move

= 0.5* max(26.25-22,0) + 0.5* max(23.75-22,0)= 0.5*4.25+0.5*1.75= 3

Call option price = 3/1.03 = 2.912