Option Replicating portfolio

[Vibnad1991]

Hi, I am by no means an elite trader but i am trying to learn through my academic courses and indepedndent learning.

Question

current stock price 100
Every 3 month period it will increase by either 25% or fall by 20%
6 month call strike price of 90
Risk free 3 month IR 1%

If the stock price is 80 in month 3 , how could you replicate an investment in the stock by a combination of call options and risk free lending.


My response
To be honest, if the question had asked how to prodice a replicating portfolio with and investment in stock i could do this pretty easily from what i have learnt. First calculate the option delta, then buy the option delta value of shares. then borrow the present value of the difference between this number and the final payoff.

However, i am puzzled as to how to create a replicating porftolio of the investment in stock. I do fortunately have the answers, and they have begun by calculating the option delta, then taking the reciprocal of this value (1/option delta) to work out out how many call options are needed, then lended the present value of the difference between this value and the payoff.

i dont understand where this logic has come from. Any help from the vast amount of knowledgable traders here would be much appreciated.

Thankyou

 

[Traveler]

Aren't you just buying enough options to have the proper number of deltas as the long stock position, then investing the remainder of the cash you would have spent to buy the long stock at the risk-free rate?

I'm going to change the assumptions just to make the math easier.

You want 200 shares of AAPL and it's at 400. The 400 calls have a delta of .5, so you buy 4 of them. You then invest the difference of 200*400 - the call premium at the risk free rate, right?

 

[bc1]

Asking us to do your homework for you? You must be a Yale student or similar. Any answer I give you will sure to get you an F for your class unless your professor google searches his assignments and find you cheating. I can think of a couple more people who might chime in here and give you some flunking advice as well. Just reason through it and start your own trading account so you can do some live lessons even if it is a paper account. May as well start on a good platform like Thinkorswim with TDAmeritrade and it is free. Good Luck.