The spot price of the TECHWIG index at the Warsaw Stock Exchange in Poland is 10

Question

The spot price of the TECHWIG index at the Warsaw Stock Exchange in Poland is 1020 Polish Zoty (PLN). The risk-free interest rate for the next six month period is 1.98% (this is a six month rate, not annualized). A certain famous Polish actor, whose first name is Cezary, writes a 1025 six month European call option on TECHWIG and receives a premium of PLN 2. In order to write the option, Cezary must post a margin equal to 20% of the value of the TECHWIG index at the time of option writing. He will earn interest on the margin and on the premium paid to him for the option, at the risk-free rate. In six months, TECHWIG closes at 1030. Cezary does not pay commissions or taxes, because he is a celebrity. Calculate his rate of return on this transaction, expressed as the annual effective rate of return. Cezary does not currently have any long position in TECHWIG, and will not have any through the option expiration.

A. –2.45% B. –0.06% C. 0.98% D. 1.06% E. 1.98%

Explanation / Answer

Premium received for writing a call option = $2

Now the loss made since the call option price rises = 1030-1025 = -5 (Loss)

Now the margin to be kept = 20% of 1020 = $204

Now he earns interest of 1.98% on 204 and the premium of $2 = 0.0198*206 = 4.0788

So total profit = 2-5+4.0788 = 1.0788

Six month profit = 1.0788/204 = 0.52882%

So annual profit = (1+0.0052882)^2 -1 = 1.06% per annum

Answer is Option D: 1.06%

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