Assume a stock has a value of $100. Using at the money call and put options on the stock with 0.5 years to expiration and a constant interest rate of 6%, what is the necessary amount that needs to be invested in a zero coupon bond in order to synthetically replicate the underlying stock ? Anyone can give me the answer and explanation ?

Put call parity

Call + Rf/(1+r)^t = Put + Stock. Just plug and chug

Are there differences in using “in-the-money” or “out-of-the-money” call and put options ?

yes, the cost of the opition

In case that “in-the-money” or “out-of-the-money” call and put options are used, the calculations are completely same as that of “at the money” ?

AMC Wrote: ------------------------------------------------------- > In case that “in-the-money” or “out-of-the-money” > call and put options are used, the calculations > are completely same as that of “at the money” ? call-put parity stands for any strike price (you can verify that by analyzing cash flows at expiration). If the strike price happens to be equal to the underlying price, both options would be at the money. Most often though, one of the options is going to be in-the-money and the other out-of-the money because the strike is the same. You can’t have a situation when both options are in-the-money or both options are out-of-the money because the have the same strike.

Yes AMC it would be the same formula but the X which is the strike price of the call and put would be different which would also change c and p, the prices of the call and the put. If the call is in the money, it would be more expensive that when it was at the money, but the put would then be out of the money instead of at the money and thus less expensive. The formula holds but the inputs would simply change to reflect the moneyness of the options. Also remember that the face value of the zero bond would change (it is also equal to the strikes) and thus the amount you need to invest today would be the present value of that bond. so X/(1+r)^t= S + p - c with changed values of p, c and X

maratikus & CFALEB, TKVM !