Question

There are following options available on the market a. CALL with a strike price of 100 PLN and premium of 5 PLN b. PUT with a strike price of 100 PLN and premium of 10 PLN Is an arbitrage possible- explain your strategy? Would it be possible if you could either buy or write above options with the same characteristic-explain your strategy. [1,5 pt.] Result: NO YES

Answer 1

CALL and PUT options are form of derivatives where call option gives the holder the right to buy the option but not obligation and vice versa. Call option is exercised if investor expects price of stock to increase in future and put option is exercised when investor expects price to fall in future

Buying a CALL and PUT means different it can also be said long on call and put when u buy call you have right but no obligation to buy and in put you have obligation to sell.

As a rational investor we can always make money by investing in CALL/PUT by taking benefits of stock price

In the above question we know the following

• STRIKE PRICE(K) = 100 (same price for both CALL and PUT)
• C(call price or premium ) = 5 which means premium paid to exercise call option
• P(put price or premium)= 10 which means premium paid to exercise put option
• S( stock price) = ? not given

As stock price is not given we assume it to be same as strike price that is 100

To know if there are any arbitrage opportunities existing we will use PUT- CALL PARITY THEORM

This theorm implies that when both call and put have same strike price so there can be arbitrage opportunity if stock price is different from strike price

$c+Ke^{-rt} = p+S$  

• t stands for time to expiry
• as the t is not given so we are ignoring it

so if we put the above value in this equation

$5&plus;100< 10&plus;100$

$5< 10$

so as price of put and call are not same there exists ARBITRAGE opportunity

clearly LHS is not same as RHS

so we sell the put option by paying premium of 10 and use the proceeds to buy the call option so we will benefit by this arbitrage and will make profit = 5 (put-call) (10-5)