$4.32 Present value t0 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Ejercicio 2 Caso 1 t0 t1 t2 t3 t4 t5 t6
0.12 -1000 -900 -1000 -900 -1000 -900 -1000 -900 -1000 -900 -1000 -900 1000 900 ($3,604.78) ($3,604.78)
Ejercicio 3 s1 s2
6.3% anual 6.9% anual
¿tasa de descuento en d(0,2)?
0.1111111111
Ejercicio 4 Spot y forward rates Spot rates s1 s2
forward rate f(1,2)
6.3% anual 6.9% anual
1.142761 1.063 1.07503387
7.5%
1 Term structure of interest rates and swap valuation Suppose the current term structure of interest rates, assuming annual compounding, is as follows: s1 7.00%
s2 7.30%
s3 7.70%
s4 8.10%
What is the discount rate d(0,4)? (Recall that interest rates are always quoted on an annual basis u stated otherwise.)
Please submit your answer rounded to three decimal places. So for example, if your answer is 0.45 you should submit an answer of 0.457. d(0,4)
0.732
2 Swap Rates Suppose a 6-year swap with a notional principal of $10 million is being configured. What is the fixed rate of interest that will make the value of the swap equal to zero. (You should use the term structure of interest rates from Question 1.)
Please submit your answer as a percentage rounded to two decimal places. So for example, if your is 4.567% or equivalently 0.04567, then you should submit an answer of 4.57. 1 s1 7.00% d(0,i)
2 s2 7.30%
3 s3 7.70%
0.9345794393 0.868561462 0.800484432 d(0,M)
0.602874102
r
0.397125898 4.606931886
r=
4 s4 8.10% 0.73231381
8.62%
3 Hedging using futures Suppose a farmer is expecting that her crop of oranges will be ready for harvest and sale as 150,000 pounds of orange juice in 3 months time. Suppose each orange juice futures contract is for 15,000 pounds of orange juice, and the current futures price is F0=118.65 cents-per-pound.
Assuming that the farmer has enough cash liquidity to fund any margin calls, what is the risk-free price that she can guarantee herself.
F0 K T
centavos por 118.65 libra 17797500 0.25 AÑO
4 Minimum variance hedge Suppose a farmer is expecting that her crop of grapefruit will be ready for harvest and sale as 150,000 pounds of grapefruit juice in 3 months time. She would like to use futures to hedge her risk but unfortunately there are no futures contracts on grapefruit juice. Instead she will use orange juice futures. Suppose each orange juice futures contract is for 15,000 pounds of orange juice and the current futures price is F0=118.65 cents-per-pound. The volatility, i.e. the standard deviation, of the prices of orange juice and grape fruit juice is 20% and 25%, respectively, and the correlation coefficient is 0.7. What is the approximate number of contracts she should purchase to minimize the variance of her payoff?
Please submit your answer rounded to the nearest integer. So for example, if your calculations resu 10.78 contracts you should submit an answer of 11. S F P N=
0.25 0.2 0.7 9
point 5. Call Options Consider a 1-period binomial model with R=1.02, S0=100, u=1/d=1.05. Compute the value of a European call option on the stock with strike K=102. The stock does not pay dividends.
Please submit your answer rounded to two decimal places. So for example, if your answer is 3.4567 you should submit an answer of 3.46.
R S0 D U K
= 1.02; = 100.00; = 1.05; = 1.00; = 102.00;
uS0 = U * S0; dS0 = D * S0; Cu = uS0 - K; Cd = 0; H = ( ( Cu - Cd ) / ( uS0 dS0 ) ); HdS0 = H * dS0; PV = ( ( HdS0 / ( 1 + R ) ) ); HS0 = H * S0; C = HS0 - PV; return C; }
1.02 100 1.05 0.952380952 1 102 28.5 14.10891089 15.89108911
nual compounding, is as follows: s5 8.40%
s6 8.80%
ways quoted on an annual basis unless
or example, if your answer is 0.4567 then
being ue
nterest rates from Question 1.)
mal places. So for example, if your answer swer of 4.57. 5 s5 8.40%
6 s6 8.80%
0.668118641 0.602874102 4.606931886
ady for
5,000
5 cents-per-pound.
e herself.
eady for
nfortunately there
range juice futures.
cents-per-pound.
mber payoff? example, if your calculations result in
stock
example, if your answer is 3.4567 then
Quiz Instructions: Option Pricing in the Multi-Period Binomial
Questions 1-8 should be answered by building a 15-period binomial model whose parameters should be calibrated to a BlackScholes geometric Brownian motion model with: and a dividend yield of
T=.25 years, S0=100, r=2%, σ=30%
c=1%.
Hint Your binomial model should use a value of
u=1.0395.... (This has been rounded to four decimal places but you should not d
any rounding in your spreadsheet calculations.)
Submission Guidelines
Round all your answers to 2 decimal places. So if you compute a price of 12.9876 you should submit an answer of 12.99.
1. Quiz instructions Compute the price of an American call option with strike K=110 and maturity T=.25years.
point 2. Quiz instructions Compute the price of an American put option with strike K=110 and maturity T=.25years.
point 3. Quiz instructions Is it ever optimal to early exercise the put option of Question 2? Yes No
point 4. Quiz instructions If your answer to Question 3 is "Yes", when is the earliest period at which it might be optimal to early exercise? (If your answer to Question 3 is "No", then you should submit an answer of 15 since exercising after 15 periods is not an early exercise.)
point 5. Quiz instructions Do the call and put option prices of Questions 1 and 2 satisfy put-call parity? Yes No
point 6. Quiz instructions Compute the fair value of an American call option with strike K=110 and maturity n=10 periods where the option is written on a futures contract that expires after 15 periods. The futures contract is on the same underlying security of the previous questions.
point 7. Quiz instructions What is the earliest time period in which you might want to exercise the American futures option of Question 6?
point 8. Quiz instructions Compute the fair value of a chooser option which expires after n=10 periods. At expiration the owner of the chooser gets to choose (at no cost) a European call option or a European put option. The call and put each have strike K=100 and they mature 5 periods later, i.e. at n=15.
Answer 2.53
1.65
12.3
12.3
yes
5
No
2.5623 1. Price of the American call option is 2.53. 2. Price of the American put option is 12.30. 3. Yes, it is ever optimal.
12.3 2.6
1.65
7
6.67
11.88 106.6667
Risk neutral price
135.34
ption is 2.53. ption is 12.30.
http://www.chegg.com/homework-help/questions-and-answers/1-compute-price-america 5.5 2.56
13.68
12.33
wers/1-compute-price-american-call-option-strike-k-110-maturity-t-25-years-2-compute-price-amer-q10012905
ompute-price-amer-q10012905
Quiz Instructions: Term Structure Models I Questions 1-6 should be answered by building an
n=10-period binomial model for the short-rate, ri,j. The
lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2.
Questions Question: Quiz Instructions: Term Structure Models I Questio... Quiz Instructions: Term Structure Models I Questions 1-6 should be answered by building an n=10-period binomial model for the short-rate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2.
1 Quiz instructions Compute the price of a zero-coupon bond (ZCB) that matures at time t=10 and that has face value 100. Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you compute the answer to be 73.2367%, submit 73.24. 2 Quiz instructions Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t=4. Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you compute the answer to be 73.2367%, submit 73.24.
3 Quiz instructions Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration of t=4. Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you compute the answer to be 73.2367%, submit 73.24. 4 Quiz instructions Compute the price of an American call option on the same ZCB of the previous three questions. The option has expiration t=6 and strike =80. Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you compute the answer to be 73.2367%, submit 73.24. 5 Quiz instructions
Compute the initial value of a forward-starting swap that begins at t=1, with maturity t=10 and a fixed rate of 4.5%. (The first payment then takes place at t=2 and the final payment takes place at t=11 as we are assuming, as usual, that payments take place in arrears.) You should assume a swap notional of 1 million and assume that you receive floating and pay fixed.) Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer to be -220,432.23, submit -220432. 6 Quiz instructions Compute the initial price of a swaption that matures at time t=5 and has a strike of 0. The underlying swap is the same swap as described in the previous question with a notional of 1 million. To be clear, you should assume that if the swaption is exercised at t=5 then the owner of the swaption will receive all cash-flows from the underlying swap from times t=6 to t=11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)
Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer to be -220,432.23, submit -220432.
8/19/2016
Answer 1 2-Jun
61.62
129.38
129.28
2.21
33374
122270
