Consider two probabilities P and Q defined on the sample space 05 (w1, w2, w3) in...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider two probabilities P and Q defined on the sample space 05 (w1, w2, w3) in the following way: p(w1) = 0, p(w2)=0.4, p(w3) -0.6, and a(w1)=0.4, q(w2) -0, q(w3) = 0.6. Are P and Q equivalent probability measures? b. Now, we change our exercise values. Suppose that, instead, p(w1) = 0, p(w2) = 0.4, p(w3) -0.6, and q(w1) 5-0, q(w2)=0.3, q(w3) -0.7. Are P and Q equivalent probability measures now? 2. An investor has taken a long position in a futures contract in oil. The spot price of oil is expected to follow a Brownian motion process, with 50-90 and a monthly variance equal to 25, and time is measured in months. a. What is the probability that the price of oil will exceed $100 in 25 months? b. What is the probability that the oil price will reach 100 in less than 25 months? c. What is the median hitting time for 5* - 100? That is, what hitting time t corresponds to the probability P100 #t] -0.5? d. What is the probability that the oil price hits 50 before it hits 100? e. What is the expected hitting time for either of the two barriers? 3. Consider a one-time period, two-potential outcome framework where there exists Company Q stock currently selling for $50 per share and a riskless $100 face value T-bill currently selling for $80. Suppose Company Q faces uncertainty, in that it will pay its owner either $30 or $70 in 1 year. Further assume that the physical probability that the stock price will drop is 0.2. a. List the risk-neutral probabilities for this payoff space. b. Compute values for the Radon Nikodym derivative for this change of measure. c. Value call and put options on this stock, with exercise prices equal to X = $60. d. Does putticall parity hold for this example? 4. Suppose that we pay S0-0.7 to purchase a security, with potential payoffs given as follows: S1 = 2, 52 = 1, and 53-0 such that under physical probabilities, EPS-0:8 and a variance equals EP{S-EP(S)^2)= 0.76. a. Find the risk-neutral probabilities in measure based on the market price of the stock. b. Calculate Radon Nikodym derivatives for this change of measure. Consider two probabilities P and Q defined on the sample space 05 (w1, w2, w3) in the following way: p(w1) = 0, p(w2)=0.4, p(w3) -0.6, and a(w1)=0.4, q(w2) -0, q(w3) = 0.6. Are P and Q equivalent probability measures? b. Now, we change our exercise values. Suppose that, instead, p(w1) = 0, p(w2) = 0.4, p(w3) -0.6, and q(w1) 5-0, q(w2)=0.3, q(w3) -0.7. Are P and Q equivalent probability measures now? 2. An investor has taken a long position in a futures contract in oil. The spot price of oil is expected to follow a Brownian motion process, with 50-90 and a monthly variance equal to 25, and time is measured in months. a. What is the probability that the price of oil will exceed $100 in 25 months? b. What is the probability that the oil price will reach 100 in less than 25 months? c. What is the median hitting time for 5* - 100? That is, what hitting time t corresponds to the probability P100 #t] -0.5? d. What is the probability that the oil price hits 50 before it hits 100? e. What is the expected hitting time for either of the two barriers? 3. Consider a one-time period, two-potential outcome framework where there exists Company Q stock currently selling for $50 per share and a riskless $100 face value T-bill currently selling for $80. Suppose Company Q faces uncertainty, in that it will pay its owner either $30 or $70 in 1 year. Further assume that the physical probability that the stock price will drop is 0.2. a. List the risk-neutral probabilities for this payoff space. b. Compute values for the Radon Nikodym derivative for this change of measure. c. Value call and put options on this stock, with exercise prices equal to X = $60. d. Does putticall parity hold for this example? 4. Suppose that we pay S0-0.7 to purchase a security, with potential payoffs given as follows: S1 = 2, 52 = 1, and 53-0 such that under physical probabilities, EPS-0:8 and a variance equals EP{S-EP(S)^2)= 0.76. a. Find the risk-neutral probabilities in measure based on the market price of the stock. b. Calculate Radon Nikodym derivatives for this change of measure.
Expert Answer:
Answer rating: 100% (QA)
Here are the solutions to the probability problems 1a Are P and Q equivalent probability measures No ... View the full answer
Related Book For
Understanding Basic Statistics
ISBN: 9781111827021
6th Edition
Authors: Charles Henry Brase, Corrinne Pellillo Brase
Posted Date:
Students also viewed these accounting questions
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
Read the case study "Southwest Airlines," found in Part 2 of your textbook. Review the "Guide to Case Analysis" found on pp. CA1 - CA11 of your textbook. (This guide follows the last case in the...
-
An investment bank has the following customers. Investor A Long forward contract to buy 1000 ounces of gold at HK$10000 per ounce in 3 months Investor B Short European put options to sell 500 ounces...
-
2 3 -4 6,-12,-18 If A = (a) 0 3a 2b 24 (b) -6,4,9 and KA= then the value of k, a,b are respectively (c) -6,-4,-9. (d) -6,12,18
-
Douglas Davis, controller for Marston, Inc., prepared the following budget for manufacturing costs at two different levels of activity for 2010: During 2010, Marston worked a total of 80,000 direct...
-
At what points are w = z 5 - z and w = cos (z 2 ) not conformal?
-
Helium at \(68{ }^{\circ} \mathrm{F}\) and 14.7 psia in a large tank flows steadily and isentropically through a converging nozzle to a receiver pipe. The cross-sectional area of the throat of the...
-
Gepetto Shoe Store uses the retail inventory method for its two departments, Womens Shoes and Mens Shoes. The following information for each department is obtained. Instructions Compute the estimated...
-
A fund manager wants to hedge the exposure of her US equity portfolio using futures contracts on the S&P 500. Her portfolio has a value of 10 million USD and a beta of 1.4. The S&P 500 futures is...
-
Ellery Products manufactures various components for the fashion industry. Ellery buys fabric from two vendors: Ewers Textiles and Bramford Materials. Ellery chooses the vendor based on price. Once...
-
discuss an Industry and technologies used in the lean production process?
-
Chen Company has been operating for several years, and on December 31, 2015, presented the following statement of financial position (amounts in thousands). The net income for 2015 was 25,000. Assume...
-
Komissarov Company has a debt investment in the bonds issued by Keune Inc. The bonds were purchased at par for 400,000 and, at the end of 2015, have a remaining life of 3 years with annual interest...
-
Hislop (2008) reconceptualized Frenkel et al.s knowledge work framework to make it compatible with the all work is knowledge work perspective. The utility of the revised framework was illustrated by...
-
Develop sketches of your social components. What interface elements will you utilize to increase self-expression, sharing, collaboration and ambient intimacy?
-
A researcher wants to see if U.S. News & World Report rankings influence the number of applications received by colleges and universities. He obtains the unadjusted data shown in Table 1.17 on...
-
Jefferson Company reported $4,000,000 of sales during the month and incurred variable expenses totaling $2,800,000 and fixed expenses totaling $720,000. A total of 80,000 units were produced and sold...
-
A red card is illuminated by red light. What color will the card appear? What if its illuminated by blue light?
-
In a marketing survey, a random sample of 730 women shoppers revealed that 628 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores). (a) Let p represent the...
-
Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial...
-
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = 2.42 and z = 1.77
-
Consider the ammonia process in which \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) (with impurities \(\mathrm{Ar}\) and \(\mathrm{CH}_{4}\) ) are converted to \(\mathrm{NH}_{3}\) at high pressure...
-
Consider the simulation flowsheets in Figure 7.36, which were prepared for ASPEN PLUS. The feed stream, S1, is specified, as are the parameters for each process unit. Complete the simulation...
-
Use a process simulator to determine the flow rate of saturated vapor benzene at \(176.2^{\circ} \mathrm{F}\) and \(1 \mathrm{~atm}\) to be mixed with \(100 \mathrm{lbmol} / \mathrm{hr}\) of liquid...
Study smarter with the SolutionInn App