Option hedging


I need some help in understanding the CFAI mock exam question below thank you.

Delport sells to another client 3,000 three-month equity call options with an exercise price of EUR 825. The underlying equity is priced at EUR 800 per share. Each call option has a premium of EUR 29.42 Delport hedges this position by buying 1,322 shares of the underlying equity. He calculates his net cash outlay to be EUR 969,340. Delport sets his performance benchmark as the net cash outlay continuously compounding at the risk-free rate of 2.25% (using days in period/365). Five days later, the price of the equity is EUR 815, and Delport calculates the new fair value of the call options to be EUR 35.30.

C. Determine the percentage difference between the hedged position’s value and Delport’s benchmark. Show your calculations.


Delport’s current hedged position consists of a long position in equities and a short position in call options. His net cash outlay equals: = (# of shares bought × price per share) – (# of call options sold × option premium) = 1,322 × 800 – (3,000 × 29.42) = $969,340 The value of Delport’s performance benchmark continuously compounded at 2.25%, for five days equals: = 969,340 × e(0.0225 × 5 / 365) = $969,638.82 The value of Delport’s long equity position in five days equals: = 1,322 × 815 = $1,077,430 _ The value of Delport’s short call option position in five days equals: = –3,000 × 35.30 = –$105,900 _ The value of Delport’s hedged position equals: = 1,077,430 – 105,900 = $971,530. Therefore, the percentage difference between the hedged position’s value and Delport’s performance benchmark equals: (971,530 – 969,638.82) / 969,638.82 = 0.195%

Regarding the underlined part, why is the call option premium subjected to revaluation when option premium value increased? Doesn’t the seller receive the call premium at the start? To me its realised gain. So why does the short call position revalue?

thank you.

Trading Options mean you are trading on premiums. If you are on the short position and not closing out the position before the settlement date, you receive the premium at the expiration date plus the loss if exercised. But if you are closing out your position before the settlement date, you will realize gain/loss depending on the current premium when you offset your position.