A stock price is currently trading at $50. Assume that the stock follows a one-step binomial model in which a time step is equal to half a year. The stock will either increase in value by 10% or fall in value by 5% in the binomial tree with actual probabilities of 60% and 40%, respectively. The annual effective risk-free interest rate is 4%. The stock pays no dividends.

Find a fair (no-arbitrage) price of a European call option written on the stock with expiration in a half year and strike price of $50.

a.

1.92$

b.

2.88$

c.

5.00$

d.

2.28$

e.

None of the above

Assume that the stock indeed follows the one step binomial tree described above but the actual price of the call from the previous question seen in the market is $2.02. Does the market allow arbitrage opportunities? What will be an arbitrage strategy if your answer to the previous question is Yes?

a.

The market does not allow arbitrage opportunities

b.

Yes, the market allows arbitrage opportunities. Borrow $31.07 by using T-bills, short 0.667 stock shares and short the option

c.

Yes, the market allows arbitrage opportunities. Lend $31.33 by using T-bills, short 0.667 stock shares and buy the option

d.

Yes, the market allows arbitrage opportunities. Borrow $29.81 by using T-bills, buy 0.667 stock share and buy the option

e.

None of the above

What are the semiannual expected rates of returns on the stock and the call option given that the option is fairly priced?

a.

E(r_S)=4%, E(r_P)=31.58%

b.

E(r_S)=4%, E(r_P)=17.32%

c.

E(r_S)=5%, E(r_P)=10.71%

d.

E(r_S)=4%, E(r_P)=21.98%

e.

None of the above

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