Quiz Three Solutions

Name: _______________________________________ ID NoQuestion

Answer 1

: _______________________________________ Answer 2

Answer 3

Answer 4

Ans

Sell 12000 shares

Buy 12000 Shares

3

+$15

-$3

2

-0.5

-0.6

3

Long 200 FCK Long 413 FMU Buy 2001 shares

Long 200 FCK Short 544 FMU Sell 27776 shares

4

5.3%

5.5%

th

1

2

3

4

5

Observe the option chain for Ford on Fri-13 October at the end of the question sheet. The data was taken from the CBOE.com website. The stock price at the time was $8.20. Sell 120 shares Buy 120 Shares If you sold 300 FOK options, how many shares should you buy/sell to create a delta neutral strategy? Using the information and correct answer in question 1, assume you have a delta neutral portfolio. If the share price moved from Zero, you are hedged against -$1,200+$1,500=$300 $8.20 to $8.30 and the FOK option moved from 0.67 to 0.62, what small share price movements is your P&L for your delta neutral strategy? Based on the stock and option movements in question 2, what is -0.3 -0.4 the implied delta of FOK? Observe the option chain for Ford on Fri-13th October at the end of Long 200 FCK Long 200 FCK the question sheet. The data was taken from the CBOE.com Short 413 FMU Long 544 FMU website. The stock price at the time was $8.20. Sell 3461 shares Buy 3572 shares Which of the following strategies is delta and gamma neutral? 4.9% 5.1% Annual Coupon Face Maturity (Semi-Annual Value (Years) 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 face value. Assuming continuous compounding and using the bootstrap method, the 18month zero-rate is calculated as (nearest decimal place)

2

NoQuestion

6

Maturity (Years) 1 2 3 4 5

Zero Rate (%) 4.25 4.75 5.5 6 6.75

Answer 1

Answer 2

Answer 3

Answer 4

7.5%

7.00%

6.5%

6.00%

Ans

1

The table above describes the zero rates for a number of maturities. Using this data, the forward interest rate for a 1-year loan commencing in three years time is; What is the value of the variable myVar after running the following four lines of MATLAB code? 7 myVar = 0 for i=11:-1:6 myVar=myVar+(10/i); end

Su =47.5 Cu= P

4.672

8.213

2.763

7.365

0.9555

1.045

1.250

1.514

4

S0 =45 C0= P

8 t0 =0

Sd =42.5 Cd P = T=0.25

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%

1

NoQuestion

Answer 1

Answer 2

Answer 3

Answer 4

1.104

1.762

1.815

1.096

Ans

u2S0 Cuu

uS0 Cu S0=45

udS0

C0

Cud dS0 Cd

d2S0

9

Cdd t0=0

t1=0.25

2

T=0.5

Given the 2-step binomial tree above and the following information:  u = 1.05  d = 0.95  Δt = 0.25; 

p=

e r∆t − d u −d

 r = 5% (risk free rate)  K = 45 (strike price) What is the value of the european call option C0? The secondary bond market is 10

A market place in a A market place of lesser regulatory region other than importance the region of the issuing entities domicile.

The market in which A market place with low securities are traded after liquidity having been initially offered in the primary market

3

•

• • •

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 FAU FAL FMU FML FCK FOK

Option Type

Strike

Option Price

Maturity

Option Delta

Option Gamma

Option Implied Vol.

CALL CALL PUT PUT CALL PUT

7.50 9.00 7.50 9.00 8.00 8.00

1.04 0.32 0.32 1.08 0.82 0.67

Jan10 Jan10 Jan10 Jan10 Mar10 Mar10

0.71 0.34 -0.29 -0.66 0.60 -0.40

0.086 0.083 0.079 0.083 0.215 0.195

45% 42% 49% 42% 37% 41%