Question

Suppose stock ABC is worth 100 at t=0 and there are two scenarios for the stock price at t=1

• The stock price can go up to 110
• The stock price can go down to 90

Now consider a PUT option on ABC with exercise price 100.

In the portfolio of stock and zero coupon bond that replicates the payoff of the put option (the replicating portfolio), what is your position in ABC stock

Select one:

a. You are long 1/2 share of ABC stock

b. You are short 1/4 share of ABC stock

c. You are short 1/2 share of ABC stock

d. You are long 1/4 share of ABC stock

Answer 1

Replicating portfolio of a put option is long position in bond and short position in stock

Delta=(Range of put values)/(Range of stock values)
=(MAX(100-110,0)-MAX(100-90,0))/(110-90)
=-0.5

c. You are short 1/2 share of ABC stock