# â€‹Replicating Call Option

Question â€“

Determine the value of the call option in previous question by replicating the call option

Solution: Letâ€™s look at the pay-offs from a package consisting of 0.5714 stocks and borrowing a principal of Rs. 35.71 from the bank. The total amount to be repaid is Rs. 36.42 (including interest)

 Stock Price = Rs. 63.75 Stock Price = Rs.113.33 0.5714 Shares Rs. 36.42 Rs. 64.75 Repayment of loan + interest -36.42 -36.42 Total Payoff 0 Rs. 28.33

• The pay-offs are exactly the same as in the previous example for the call option. It follows that
• the value of the call today should be equal to the value of 0.5714 shares less Present Value of
• Rs. 36.43
• Thus, value of Call = Rs. 12.86

Replicating Call Option:

 Stock Price Scenario 1 63.75 Scenario 2 113.33 Option Value Value of âˆ†Stock 0 36.43 28.33 64.76 Payoff from Option 0 -28.33 Portfolio Value 36.43 36.43
• Two questions remain, how did we determine the number of stocks i.e. 0.5714 and how did we determine the amount to be borrowed?
• The number of shares to be held is give by the option delta, given by:

• The amount to be borrowed is equal to the present value of the difference between the pay-offs from the option and pay offs from the delta shares, i.e. 0.5714 share. In our example:
• The amount to be borrowed equals Present Value or PV of 36.43