Option price is a sum of intrinsic & extrinsic values. Intrinsic simply means the in the money value. So there not much math behind it. Extrinsic is the TIME Value and a lot of factors impact this - like time, volitility, rate of interest… etc… how ever when the contract expires - times expires too which mean there is no TIME VALUE left. So the option price has only intrinsic value left. So since you option is out of the money - it is worthless as there is no intrinsic value as well.
Intrinsic value: It is the difference between Strike and Spot. In case of Call option (Spot - Strike) and Put option (Strike – Spot). If intrinsic value is positive then it is call In the money option, if negative then value is taken as zero and the option is called out of the money option.
Time Value: As we know every asset has time value. Today Rs.100 won’t be the same after 1 year. The inflation rate determines its value. Similarly option is also asset and it has value on time basis.
Since out of the money is having intrinsic value Zero and the time value is also Zero (on the day of expiry). Out of the money options expires with no value.
An option contract is an agreement between the option buyer and writer to supply the underlying at the strike price on expiry day.
When you buy Nifty call option strike at 6800, the option seller (writer) agrees that he will give you Nifty at the rate of 6800 on expiry day. On expiry day if Nifty is at 6700, as per the agreement you can get NIFTY at the rate 6800, but you can buy it from market 100 point less. So this contract is worthless and the option expires worthless.
Simple answer is, the person who has sold the Out of Money Option will not come under any the obligation to pay back, as the underlying price has closed below the strike price at which he/she has sold on expiry date.
Lets take an example to explain this. Assuming that by end of April, Nifty is expected to reach 6900 & bought 2 lots (50 scrips/lot) of Nifty 6800 Call at Rs.40 (2 x 50 x 40 = 4000). Rs2000 per lot is at risk to gain a gross profit of Rs.5000. Considering the spot price on April 11th, Nifty was at 6776, which means the call is still out of the money. If this investment has to turn profitable, then the nifty spot should  go beyond 6800 by April 23rd (contract expiry date). The profit on this investment will be calculated as
6776 - 6800 - 40 = -64 / scrip. Hence this indicates that the 6800CE is out of money option with respect to the Nifty Spot Price
Ex 2:
If Nifty Spot Price has to reach 6900 by contract end date as assumed then
Nifty Spot Price = 6900
Call Strike Price = 6800
6800CEÂ premium paid = Rs.40/scrip
6900 - 6800 - 40 = +60 / scrip. This indicates a profit after investment per scrip.
Further, the exchange charges will be applicable as required.
The above two examples indicate that based on spot price, the value of P/L is calculated. However, the retail trader will incur loss up to the premium paid by him per scrip only. This is the concept of limited loss but with unlimited potential to make profit if the trade to turn in your favor.
