Semester One Examinations, 2022

FINM7405 Finance

Question 1

The price of a European put that expires in 6 months and has a strike price of $10 is $2. The underlying stock price is currently valued at $9, and risk-free rate is 2% p.a.

a) To price a European call, we can use the put-call parity:

��� = ��� + ���0 − ������^{−������}

= 1.0995

b) The call price of $1.20 is clearly overvalued (fair price is $1.0995). Thus:

Note: X=$10, r = 2%, T = 6 months, p = $2, S0 = $9. Further notice that you cannot write the call at the fair price of $1.0995 because the price traded in the market is NOT $1.0995. Notice also that we borrow Xe-rT=$9.9005 at t=0. Also, in the table above, we make the net payoff at t=T equals to zero.

To explain, consider the scenario when ST > X at the maturity of the options. The holder of the option will exercise her right to buy the share at X=$10 i.e. we (as the writer of the call) must sell the share (which we had already bought at t=0) at X=$10. Using this fund, we return a sum of X=$10 to the lender (whom we borrowed from at $9.9005 at t=0). At the same time, we won’t exercise the put because ST > X. In summary, the net payoff at t=T is zero.

Consider now the scenario when ST < X at the maturity of the options. The call holder will not exercise her right to buy the share. We, however, as the holder of the put, will exercise our right to sell the share (which we had already bought at t=0) for X=$10. Using this fund, we return a sum of X=$10 to the lender (whom we borrowed from at $9.9005 at t=0). In summary, the net payoff at t=T is zero.

Notice that we are completely hedged because the net payoff in the above two scenarios is zero. That is, the profit of $0.1005 obtained at t=0 is completely riskfree i.e. it is an arbitrage profit.

Alternative solution (in the table below, we make the net payoff at t=0 equals to zero):

This value ($0.1015) is simply the future value of $0.1005 from the top table i.e., 0.1005e0.02*0.5 = 0.1015

c) The call price of $1.00 is clearly undervalued (fair price is $1.0995). Thus:

Notice that you cannot hold the call at the fair price of $1.0995 because the price traded in the market is NOT $1.0995. Also, in the table above, we make the net payoff at t=T equals to zero.

To explain, consider the scenario when ST > X at the maturity of the options. First, notice that we receive X=$10 from the borrower whom we lent to at t=0. Then, as the holder of the call, we’ll exercise our right to buy the share at X=$10. Using this share, we return it back to the party who short-sell to us i.e. we settle the short-sale debt. In summary, the net payoff at t=T is zero.

Consider now the scenario when ST < X at the maturity of the options. First, notice that we receive X=$10 from the borrower whom we lent to at t=0. Then, as the holder of the call, we won’t exercise our right to buy the share (since ST < X). But as the writer of the put, we must buy the share at X=$10 from the holder of the put (she will exercise her right to sell to us at X=$10) Using this share, we return it back to the party who short-sell to us i.e. we settle the short-sale debt. In summary, the net payoff at t=T is zero.

Notice that we are completely hedged because the net payoff in the above two scenarios is zero. That is, the profit of $0.0995 obtained at t=0 is completely riskfree i.e. it is an arbitrage profit.

Alternative solution (in the table below, we make the net payoff at t=0 equals to zero):

This value ($0.1005) is simply the future value of $0.0995 from the top table i.e., 0.0995e0.02*0.5 = 0.1005

Question 2        

Consider the following information on the options available on stock Netflix. You intend to buy one March maturity call option on company Netflix’s stock with exercise price $280 and buy one March maturity put option on the same underlying asset with strike price $300. The information of the options on the stock of the company is as follows (use last price as the price of the options):

a. Graph the payoff and profit/loss of this portfolio at option expiration.

b. What will be the profit/loss on this portfolio if company Netflix trades at $290 on the option maturity date?

Profit from long call = max(290-280,0)-47.8 = -37.8

Profit from long put = max(300-290,0)-37.5 = -27.5

Total profit/loss = -37.5+(-27.5) = -65

c. Given the portfolio that you have constructed, what is most likely your view of the future for the price of Netflix’s stock?

You are unsure of the stock price change direction in the future and believe that the price is volatile and is going to have a large move.