In this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below.Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. Thismodel is a CRR model.251591064timeFigure 1: Stock evolution for Problem 1.(a) Find the values of up and down factors u and d, and the risk-neutral probability q.(b) We consider a European put with strike price Kthe price of this option at time 0.==16 and expiration T = 2 years. Find(c) Provide the number of shares of stock that the replicating portfolio contains at each pos-sible position.(d) You find this option available on the market for $2. What do you do? (Short answer.)(e) We consider an American put with strike price K= 16 and expiration T=2 years. Findthe price of this option at time 0 and describe the optimal exercising strategy.(f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Findthe price of this option at time 0 and describe the optimal exercising strategy.

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Answered: In this problem, we consider a 2-period…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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A stock has monthly returns of 4%, 5%, 2%, and -3%. Its geometric average return is closest to: O 195 O 2.43 O 3.36 O 4.17
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The demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation: trt = 12 + 2t. What are the forecast errors for the 5th and 6th years?
Consider the following data: Stock M N Average return 26% 16% Risk (Std. Dev.) 20% 10% If the return on stocks M and N are perfectly negatively correlated, what is the range of risk (std dev) associated with all possible portfolio combinations? A. Range of the risk: between 0= risk s10 % OB. Range of the risk: between 0 < risk 10% OC. Range of the risk: between 5% and 10%. OD. Range of the risk (std. dev): between 15% to 20% OE. None of the above
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Question 6 Having studied Fixed Income Securities, you are now working as an analyst for a well known bond fund. Your manager asks you to replicate the JP Morgan T-Bond Index using a tracking error minimization approach. You are to replicate this index as closely as possible using a medium duration Treasury bond (M-BOND) and a long duration Treasury bond (L-BOND). These expire in approximately 7.15 years’ and 29.25 years’ time respectively. The following variance-covariance matrix, based on daily returns over the preceding six months, is given to you to use in your replication: Note: As usual, variances are given on the diagonal, e.g. the variance of M-BOND is 0.0042%. As usual, covariances appear in the non-diagonal elements, e.g. the covariance of M-BOND and L-BOND is 0.0057%. (a) Suppose the optimal weights for M-BOND and L-BOND are 0.7 and 0.3. Calculate the expected tracking error of the portfolio and explain how you interpret this number. (b) Calculate the correlation matrix…
The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. a) Construct a time series plot. What type of pattern exists in the data? b) Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1=1 if Quarter 1, 0 otherwise; Qtr2=1 if Quarter 2, 0 otherwise; Qtr3=1 if Quarter 3, 0 otherwise. c) Compute the quarterly forecasts for next year. d) Let t=1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1; ...; and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.
Question 3 (Minimum-variance Hedging) A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient…
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Four hundred driver's license applicants were randomly selected and asked whether they passed their driving test (Pass; = 1) or failed their test (Pass; = 0); data were also located on their gender (Male; = 1 if male and = 0 if female) and their years of driving experience (Experience,, in years). The following table summarizes the results from several probit, logit and linear probability models. Dependent variable: Pass. Regression Model Probit Logit LPM Logit LPM Probit (4) Probit (7) Regressor (1) (2) (5) (6) (3) 0.008 0.034 0.049 Experience 0.047 (0.158) (0.009) (0.019) (0.003) - 0.337 -0.624 -0.073 - 0.178 Male (0.163) (0.306) (0.037) (0.261) -0.012 Malex Experience (0.021) 0.714 1.052 2.194 0.903 0.808 Constant 0.772 1.284 (0.035) (0.124) (0.243) (0.024) (0.128) (0.223) (0.203) Use the results in column (7) to answer the following questions. Akira is a man with 12 years of driving experience. What is the predicted probability that he will pass the test? The predicted probability…

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