8/14/2019 Quiz Three Solutions

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Name: _______________________________________ ID : _______________________________________

NoQuestion Answer 1 Answer 2 Answer 3 Answer 4 Ans

1

Observe the option chain for Ford on Fri-13 th October at the end ofthe question sheet. The data was taken from the CBOE.comwebsite. The stock price at the time was $8.20.If you sold 300 FOK options, how many shares should you

buy/sell to create a delta neutral strategy?

Sell 120 shares Buy 120 Shares Sell 12000 shares Buy 12000 Shares 3

2

Using the information and correct answer in question 1, assumeyou have a delta neutral portfolio. If the share price moved from$8.20 to $8.30 and the FOK option moved from 0.67 to 0.62, whatis your P&L for your delta neutral strategy?

Zero, you are hedged againstsmall share price movements

-$1,200+$1,500=$300 +$15 -$3 2

3Based on the stock and option movements in question 2, what isthe implieddelta of FOK?

-0.3 -0.4 -0.5 -0.6 3

4

Observe the option chain for Ford on Fri-13 th October at the end ofthe question sheet. The data was taken from the CBOE.comwebsite. The stock price at the time was $8.20.Which of the following strategies is delta andgamma neutral?

Long 200 FCK

Short 413 FMUSell 3461 shares

Long 200 FCK

Long 544 FMUBuy 3572 shares

Long 200 FCK

Long 413 FMUBuy 2001 shares

Long 200 FCK

Short 544 FMUSell 27776 shares

4

5

Face

Value

Maturity

(Years)

Annual Coupon

(Semi-Annual

Payment) Bond Price

100 0.25 0 98.9

100 0.5 0 97.7

100 1 0 95.25

100 1.5 8 104.00

The table above describes four treasury bonds. All mature at facevalue. Assuming continuous compounding and using the bootstrapmethod, the 18month zero-rate is calculated as (nearest decimal

place)

4.9% 5.1% 5.3% 5.5%

2

8/14/2019 Quiz Three Solutions

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NoQuestion Answer 1 Answer 2 Answer 3 Answer 4 Ans

6

Maturity

(Years)

Zero Rate

(%)

1 4.25

2 4.75

3 5.5

4 6

5 6.75

The table above describes the zero rates for a number ofmaturities. Using this data, the forward interest rate for a 1-yearloan commencing in three years time is;

7.5% 7.00% 6.5% 6.00%

1

7

What is the value of the variable myVar after running thefollowing four lines of MATLAB code?myVar = 0for i=11:-1:6

myVar=myVar+(10/i);end

4.672 8.213 2.763 7.365 4

8

Note the 1-step binomial model above. What is the value of the

put option P0?The strike price, K = 45 and the risk free rate is 5%

0.9555 1.045 1.250 1.514

1

t0=0 T=0.25

S0=45

C0=

Sd=42.5

Cd=

Su=47.5

Cu=

t0=0 T=0.25

S0=45

P0=

Sd=42.5

Pd=

Su=47.5

Pu=

8/14/2019 Quiz Three Solutions

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NoQuestion Answer 1 Answer 2 Answer 3 Answer 4 Ans

9

S0

=45

C0

dS0

Cd

uS0

Cu

u2S0

Cuu

udS0

Cud

d2S0

Cdd

t0=0 t1=0.25 T=0.5

S0

=45

C0

dS0

Cd

uS0

C

u

u2S0

Cuu

udS0

Cud

d2S0

Cdd

t0=0 t1=0.25 T=0.5

Given the 2-step binomial tree above and the followinginformation:

u = 1.05

d = 0.95

t = 0.25;

du

dep

tr

=

r = 5% (risk free rate)

K = 45 (strike price)What is the value of the european call option C0?

1.104 1.762 1.815 1.096 2

10The secondary bond market is A market place in aregulatory region other than

the region of the issuingentities domicile.

A market place of lesserimportance The market in whichsecurities are traded afterhaving been initially offeredin the primary market

A market place with lowliquidity3

8/14/2019 Quiz Three Solutions

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Answer all questions

All questions carry equal marks.

Answer 1, 2, 3 or 4 on the right-hand side Ensure you have entered your name and Student ID on the first page

Option Chains for Ford Stock Price = $8.20

Option

ID

Option

Typ

e

Strike Option

Price

Maturity Option

Delta

Option

Gamma

Option

Implied Vol.FAU CALL 7.50 1.04 Jan10 0.71 0.086 45%

FAL CALL 9.00 0.32 Jan10 0.34 0.083 42%

FMU PUT 7.50 0.32 Jan10 -0.29 0.079 49%

FML PUT 9.00 1.08 Jan10 -0.66 0.083 42%

FCK CALL 8.00 0.82 Mar10 0.60 0.215 37%FOK PUT 8.00 0.67 Mar10 -0.40 0.195 41%