Postby edupristine » Thu Nov 05, 2015 10:03 am
Solution 3: Develop a two-step tree for the expected price.
USD 50 – a) 40% (+5)= $55 - 2nd step – a) 40%(+5)= $60 b) 60%(-5)= $50
b) 60% (-5)= $45- 2nd step- a)40%(+5)= $45 b) 60%(-5)= $45
40%*40% = 0.16, 40%*60%= 0.24, 60%*60%= 0.36
Mean = 0.16x60 + 0.24x50 + 0.24x50 + 0.36x40 = 48
Variance = 0.16x(60-48)2 + 0.24x(50-48)2 + 0.24x(50-48)2 + 0.36(40-48)2 = 48
SD = sqrt(Variance) = 6.93
Question: Matt is asked to check for arbitrage opportunity in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1 year zero coupon bond is priced at USD 97.42 and a 1 year 12% bond paying coupons semi-annually is priced at 104.18. What should be the price of 1 year Treasury bond which pays 8% semi-annually?
Choose one answer.
a. 102.40 incorrect
b. 101.93 correct
c. 99.58 incorrect
d. 101.42 Incorrect
The correct answer is B
The solution is to replicate the 1 year 8% bond using the other two treasury bonds. The cash flow from the portfolio of two Treasury bond should be equal to cash flow of 8% bond. Weight of each bond needs to be determined in the portfolio.
Replicating the cash flow at the end of 1 year 1st equation
(100 x B1) + (106 x B2) =104
Replicating the cash flow at the end of 6 months 2nd equation
6 x B2 = 4
After solving both the equations, B1 = 33.33% & B2 = 66.67%
Therefore the price of the 8% bond = 0.3333 x 97.42 + 0.6667 x 104.18 = 101.93
Doubt Solution:
[(100+0%*100)*B1] + [(100+12%/2*100)*B2] = 104
(100+0) B1+ (100+6) B2 = 104
100 B1 +106 B2= 104….Eq 1
6 B2= 4…….Eq 2
B2= 4/6 = 0.666
100 B1 + 106 (0.667) = 104
100 B1 + 70.702= 104
100 B1= 104-69.96
100 B1= 34
B1 = 0.34
Question:
Thomson is a risk manager for investment bank XYZ. He is considering buying a 6-month American Call option on a non dividend paying stock OPQ. The current stock price of OPQ is USD 100 and the strike price of the option is USD 95. The stock price can move up or down by 25% each period. Thomson’s view is that the stock price has a 75% probability of going up each period and a 25% probability of going down. In order to find the no-arbitrage price of the option, Thomson uses two-step binomial tree model using annual risk-free rate of 12% with continuous compounding.
Question: What is the risk neutral probability of the stock price going down?
Choose one answer.
a. 56% Incorrect
b. 54.5% Incorrect
c. 43.9% Correct
d. 45.6% Incorrect
The correct answer is C
U = 1.25, D = .75
Probability of up move = (e(r)t – D)/(U-D) = (e0.12x(3/12) – 0.75)/(1.25-0.75) = .5609
Probability of down move = 1-Pu = .4391
Incorrect
Marks for this submission: 0/1.
Question 8
Marks: 1
What is no arbitrage price of the Call option closest to:
Choose one answer.
a. 21.18 Correct
b. 37.66 Incorrect
c. 21.82 Incorrect
d. 39.26 Incorrect
The correct answer is A
No arbitrage Value :
Use Binomial Two step model. Using its values calculate
Expected call value of 6 months= {(risk neutral prob of up)^(2)*SUU-original value}+ (risk neutral prob. of up * risk neutral prob. of down*SUD) + (risk neutral prob. of down * risk neutral prob. of up *SDU) + {(risk neutral prob. of down ^2)*SDD}
Call Price= Expected call value of 6 months / e(risk free rate)(t)