Option and Dividend Yield Chapter 15

Quiz

15. 1) A portfolio is currently worth \$10 million and has a beta of 1. 0. An index is currently standing for 800. Explain how a set option which has a strike cost of 700 can be used to offer portfolio insurance. Index decreases to 700

10*(800/700)= almost 8. 75 million

Buying put options= 10, 000, 000/800= 12, 500

If you opt for the options at 800, the significance will be doze, 500 instances the index with a hit price of 700 as a result providing prevention of a drop in the value of the portfolio below \$8. 75 million. Each contract is about 100 instances the index, a total of 125 contracts would be needed. 15. 2) " Once we know how to value options on the stock having to pay a dividend yield, we realize how to worth options in stock indices and values. " Explain this affirmation. A stock index is similar to a stock paying a dividend produce, only if the dividend yield is the gross yield with the index. Foreign currencies are similar to a stock paying a dividend deliver, the gross yield getting the foreign free of risk interest rate. 12-15. 3) An investment index happens to be 300, the dividend deliver on the index is 3% per annum, as well as the risk-free interest rate is 8% per annum. What exactly is lower certain for the price of a couple of months European phone option within the index when the strike price is 290? (300e^-0. 03*. 5)- 290e^-. 08*. 5 sama dengan \$16. 90

15. 4) A foreign currency is currently well worth \$. eighty. Over each of the next two months it is expected to increase or perhaps decrease in worth by 2%. The home and foreign risk-free interest rates are 6% and 8%, respectively. Precisely what is the value of a two-month Euro call option with a affect price of \$. eighty?. 8160

. 0147

. 8323

. 0323

p= (e^. 06-. 08)*. 08333 -. 98 as well as 1 . 02-. 98 = 0. 4584

. 7997

. 0000

.. 8000

. 0067

. 7840

. 0000

. 7683

. 0000

The purchase price of just one unit of currency is \$. 0067

15. 5) Explain how corporations can use range-forward contracts to hedge their forex risk when due to acquire certain amount of the foreign currency in the future. Corporations are able to use range frontward contracts to hedge their very own foreign exchange risk when they are as a result of receive a specific amount of money in the future by buying a put option which has a strike selling price below the current exchange level. Also they will sell a call alternative with a strike price over a current exchange rate. This ensures that the exchange level obtained intended for the foreign money is between your two affect prices minimizing the risk. 12-15. 6) Determine the value of a three-month at-the-money European call option on the stock index when the index is at two hundred fifty, the risk totally free interest rate is 10% each year, the movements of the index is 18% per annum, plus the dividend yield on the index is 3% per annum. S_0 = 250

K= two hundred fifity

r=. twelve

Пѓ=. 18

T=. 25

q=. goal

d_1= ln(250/250)+(. 10-. 03+. 18^2/2). 25 as well as. 18в€љ. twenty-five = zero. 2394

d_2 = d_1-. 18в€љ. 25 =. 1494

Call value

250N(0. 2394)e^-. 03*. 25 -- 250N(. 1494)e^-. 10*. 25

=250 *. 5946e^-. 03*. 25 -- 250 *. 5594e^-. 10*. 25

=\$11. 15

The phone call price is \$11. 15.

12-15. 7) Estimate the value of an eight month European set option on a currency having a strike cost of 0. 50. The present exchange charge is. 52, the movements of the exchange rate can be 12%, the domestic risk-free interest rate is definitely 4% per year, and the international risk free interest is 8% per annum. S_0 =. 52

K=. 40

r=. '04

r_f=. 08

Пѓ=. doze

T=. 6667

d_1= ln(. 52/. 50)+(. 04-. 08+. 12^2 / 2)*. 6667 /. 12в€љ. 6667 sama dengan. 1771

d_2 = d_1 -. 12в€љ. 6667 =. 0791

put price

. 50N(-. 0791)e^-. 04*. 6667 -. 52N(-. 1771)e^-. 08*. 6667

. 50*. 4685e^-. 04*. 6667 --. 52*. 4297e^-. 08*. 6667

=. 0162

The put option cost is \$. 0162.

15. 23)

Time to maturity = 47/252 = 0. 1865

Derivagem result sama dengan 10. 23% of intended volatility

The buying price of the set = 2 . 25 & 126e^-. 53*. 1865= p+125. 56e^-. 03*. 1865 p=2. 1512

A European phone has the same volatility being a European put when have the same hit price. 12-15. 24)

The value Euro Put choice is 18. 39.

American put choice:

The value of a north american put alternative is 16. 97.

15. 25) Imagine...

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