Suppose that the price S(t) in year t of stocks of Bancroft & Sons is modelled by a stochastic process which has a risk-neutral distribution at time t =3 givenby£120with probability 0.3,S(3):=£140with probability 0.5,£160with probability 0.2.Assume that interest is compounded continuously at nominal rate 2%.(a) Assuming no-arbitrage, determine the current price S(0) of Bancroft & Sons stock. Enter your answer correct to the nearest pound.Answer:(b)Determine the no-arbitrage price of a European put option on Bancroft & Sons stock with strike 150 and expiry 3 years. Enter your answercorrect to the nearest pound.Answer:

Part (a): Current Price S(0) of Bancroft & Sons StockTo find the current price S(0), we…

Answered: Suppose that the price S(t) in year t…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 8RE: Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25...

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Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?
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1. Bank A offers an interest rate of ra = 5% per annum with continuous compounding. Bank B offers simple annual compounding but the interest rate is ra = 1% with prob- ability p and rB = 8% otherwise. You wish to invest Bo %3D = £1000 for a duration of 1 year. (a) Find the value of p (say p") so that the the return from Bank A is equal to the expected return of Bank B. (Hint: The return of Bank B is a discrete random variable.) (b) Suppose that p = p". Which bank do you prefer? Briefly justify your answer.
Let Y denote the present value of a ten-year deferred 30-year temporary life annuity- immediate on (30). If i = 0 and mortality is uniformly distributed with w = = 100, calculate the probability that the sum of the payments will exceed E(Y).
1) An insurance company sells a one-year automobile policy with a deductible of 2. The probability that the insured will incur a loss is 0.05. If there is a loss, the probability of a loss of amount N is K 'N for N = 1, .., 8 and K a constant. These are the only possible loss amounts and no more than one loss can occur. Determine the net premium for this policy.
The team meeting will be held in 3 days from the date of the assignment and because of the limitation of time the Chief economist has given you the following guidelines: (a) Is there a trend in total accidents? (b) Is there seasonality in total accidents? (c) Consider the following change in the time series model: y; = P1yt-1 + ut where ut follows a white noise process. What is the condition we need to impose on p1 in order for the series yt to be weakly stationary? Why? (d) Consider the following change in the time series model: y; = Bo + B1x1-1+ B2xt-2 + u where y, is some outcome variable of interest, and x-1 and x-2 are strictly exogenous explanatory variables. How would you test for the presence of serial correlation in the residual uz? (e) Briefly explain how you would carry out econometric analysis of the model in (d) if u, is found to be stationary, but positively serially correlated.
58 (b) A survey conducted over last 25 years indicated that in 10 years the winter was mild, in a years it was cold and in the remaining 7 it was very cold. A company sells 1,000 woolen coats in a mild year, 1,300 in a cold year and 2,000 in a very cold year. You are required to find the yearly expected profit of the company if a woolen coat costs Rs. 1730 and it is sold to stores for Rs. 2480. soneH
Suppose you have inherited K100,000 from your father-in-law that can be invested in a combination of only two stock portfolios, with the maximum investment allowed in either portfolio set at K75,000 . The first portfolio has an average rate of return of 10%, whereas the second has 20%. In terms of risk factors associated with these portfolios, the first has a risk rating of 4 (on a scale 0 to 10), and the second has 9. Since you wish to maximize your return, you will not accept an average rate of return below 12% or risk factor above 6. Formulate the linear programming model for the problem. How much should you invest in each portfolio? Solve the problem by simplex method.
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10. Stock J has a beta of 1, an expected return of 15%. The equity risk premium is 10%, and the risk-free rate is 2.5%. Calculate Jensen's alpha measure for Stock J. (a) 2.5% (b) -2.5% (c) 0% (d) -7.5%
Q2 Suppose X and Y are the net profits of two different investments. It is known that they have the same expected return, i.e., E(X) = E(Y), furthermore, it is known that Sd(X) = 30, Sd(Y) = 20 and Corr(X,Y) = p. %3D 1. Suppose p = 0.2, find w for the best portfolio wX + (1 – w)Y. |
The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-

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