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​Replicating Call Option

 

Question –

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


Solution: Let’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 ∆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   





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