FUTURE & OPTIONS Assignment Solutions

1a. Answer

The current strike price of $80 will be split into two call options using 2-for-1 stock split rule. Hence, strike price for each call option will be $80/2 = $40.

1b. Answer

i.                    For a 20% stock Dividend

No of Shares		Strike Price		Maturity	Stock Dividend
200	80		6 Months		20%
Option Contact			Exercise Price
240			66.67

Hence, the option contract will become one to buy 200 x 1.2 = 240 shares with an exercise price 80/1.20 = 66.67.

ii.                  For a 20% cash dividend

There will be no effect for 20% cash dividend, because the terms of an options contract are not normally adjusted for cash dividends.

2a. Answer

i.                    If stock price volatility increases

This will result in an increase in value of a call option, based on rule of “The greater the expected volatility, the higher the option value”.

ii.                  If the time expiration increases

This will also result in an increase in value of call option, based on the rule of “The longer the time until expiration, the higher the option price”.

2b. Answer

i.                    For an European Call Option

European call option gives a right to the option holder to purchase one share stock for a certain price. The option itself cannot be worth more than the stock.

The upper bound for European Call Option is:  C ≤ S₀,   C ≤ S₀

In case this condition does not hold, we can make profit by selling an option and buying a stock.

ii.                  For an European Put Option

European put option gives the holder the right to sell one share of stock for the strike price. The put option cannot be worth more than the strike price.

The upper bound for European Put Option is:  P ≤ K,   P ≤ K

However, since European option can be exercised at maturity only, the European put option cannot be worth more than the present value of the strike price.

3a. Answer

Portfolio A: one European call option plus an amount of cash equal to.

Portfolio B: one share of underlying stock

After years portfolio A will yield an amount of cash equal to.

If, after  years, the stock price  is above, the call option in portfolio A will be exercised, the share sold and the portfolio will be worth. Otherwise, after  years,, the option is not exercised and the portfolio will be worth .

Hence after T years portfolio A is worth max(, and since portfolio B is always worth  after  years, the initial value of portfolio A must be no less that the initial value of portfolio B, which is just .

3b. Answer

Portfolio C: one European put option plus one share of underlying stock.

Portfolio D: an amount of cash equal to.

After  years portfolio D will be worth.

If, after years,, then the put option in portfolio C will be exercised; the share is sold for and the portfolio will be worth . Otherwise, if after years,, the option is not exercised and the portfolio will be worth .

So after  years portfolio C is worth  and the initial value of portfolio C must be no less that the initial value of portfolio D which is just.

3c. Answer

Portfolio A: one European call option plus an amount of cash equal to.

Portfolio C: one European put option plus one share.

After T years they are both worth () where ST is the stock price after T years.

These two portfolios must have identical initial values, hence the put-call parity equation is:

4a. Answer

A long straddle position is entered into simply by buying a call option and a put option with the same strike price and the same expiration month. The maximum profit potential on a long straddle is unlimited. The maximum risk for a long straddle will only be realized if the position is held until option expiration and the underlying security closes exactly at the strike price for the options.

4b. Answer

Breakeven price for call option will be = Strike Price + Cost of the call option = $20 + $5 = $25, and Breakeven price for put option will be = Strike Price - Cost of the put option = $20 - $3 = $22

4c. Answer

Profit and loss diagram for a long straddle looks like this:

5a. Answer

The delta of a European futures call option is usually defined as the rate of change of the option price with respect to the futures price (not the spot price).

In this case:

 - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Hence,

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - --0.8538

5b. Answer

The Value of risk-free portfolio at the end of six months is

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.3023

- - - - - - - - - - - - - - - - - - - - - - - - - - - -x

- - - - - - - - - - - - - - - - - - - - - - - - - - - - = 0.2875

5c. Answer

The Value of risk-free portfolio today is

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.3023

- - - - - - - - - - - - - - - - - - - - - - - - - - - -x

- - - - - - - - - - - - - - - - - - - - - - - - - - - - = 0.30199

5d. Answer

 The value of call option today is

- - - - - - - - - - - - - - - - - - - - - - - - - - - - $80 x

- - - - - - - - - - - - - - - - - - - - - - - - - - - - = $80 x 0.30199 = $24.16

6a. Answer

Stock Price = $80

Strike Price = $85

R_f = 0.1

Volatility ₌ 0.1

There are two six months period hence T= 0.5 for each period, The binomial tree will be as following:

                                                          $88.88

                             $88

$80                                                      $88.88

                                        $72

                                                      

                                                      $71.28

6b. Answer:

Yes, this could be exercised early at $88 in first period of 6 months, because the only difference between evaluating American and European option is that when pulling back for an American option, we need to always compare the pulled back value and the exercise value. If the pulled back value is greater than the exercise value, continue moving backwards along the tree using this value. And, if the pulled back value is less than the exercise value, then exercise is optimal and we need to use this value to move backwards along the tree.

7 Answer:

Information
Stock Price now (P)	80
Exercise Price of Option (EX)	75
Number of periods to Exercise in years (t)	0.25
Compounded Risk-Free Interest Rate (rf)	8.00%
Standard Deviation (annualized s)	20.00%
Equation Solution
Present Value of Exercise Price (PV(EX))	73.5149
s*t^.5	0.1000
d1	0.8954
d2	0.7954
Delta N(d1) Normal Cumulative Density Function	0.8147
Bank Loan  N(d2)*PV(EX)	57.8419
Value of Call	7.3348

8 Answer:

Information
Stock Price now (P)	80
Exercise Price of Option (EX)	75
Number of periods to Exercise in years (t)	0.25
Compounded Risk-Free Interest Rate (rf)	8.00%
Standard Deviation (annualized s)	20.00%
Equation Solution
Present Value of Exercise Price (PV(EX))	73.5149
s*t^.5	0.1000
d1	0.8954
d2	0.7954
Delta N(d1) Normal Cumulative Density Function	0.8147
Bank Loan  N(d2)*PV(EX)	57.8419
Value of Put	0.8497

--------------------------------------------------------------------------------------------------------------------------------------------------------------

Are you SEARCHING for SOLUTION(S) of this assignment or similar to this?

Our professional writers are available 24/7 we offer:

+ Lowest price then other online writing services.
+ Zero% plagiarism at all.
+ Free Harvard Style Referencing.
+ Free amendments in your work for unlimited number of times.
+ Pay only after your order is accepted.
+ Secured payment methods (Skrill, Bank Transfer, Western Union).

--------------------------------------------------------------------------------------------------------------------------------------------------------------

Like Us on Facebook!