This problem is based on the fundamental option pricing formula for the continuous-timemodel developed in class, namely the value at time 0 of an option with maturity T andpayoff F is given by:We consider the two options below:Fo=-rT= eEq[F].1A. An option with which you must buy a share of stock at expiration T = 1 for strikeprice K = So.B. An option with which you must buy a share of stock at expiration T = 1 for strikeprice K given byTK =TSt dt.(Note that both options can have negative payoffs.) We use the continuous-time Black-Scholes model to price these options. Assume that the interest rate on the money marketis r.(a) Using the fundamental option pricing formula, find the price of option A. (Hint:use the martingale properties developed in the lectures for the stock price processin order to calculate the expectations.)(b) Using the fundamental option pricing formula, find the price of option B.(c) Assuming the interest rate is very small (r ~0), use Taylor expansions to find thefirst order approximation in r of the two results in (a) and (b).(d) Can we intuitively explain the relationship between the two formulas obtained inpart (c) ?

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Answered: This problem is based on the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the three stocks in the following table. P+ represents price at time t, and 0 represents shares outstanding at time t. Stock C splits two-for-one in the last period. B C Pe 98 58 116 Divisor %0 100 200 200 126 P1 103 53 Rate of return Required: a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t=0 to t= 1). (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % 01 100 200 200 P₂ 103. 53 63 b. What will be the divisor for the price-weighted index in year 2? (Do not round intermediate calculations. Round your answer to 2 decimal places.) 92 100 200 400 % c. Calculate the rate of return of the price-weighted index for the second period (t-1 to t=2).
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Sketch 4. To reduce the paperwork and administrative cost, a company wants to know whether employees are satisfied with the new reimbursement policy for meals during business travel. In an annual survey last year, 65% of all employees reported that they were satisfied with the old policy. To evaluate the new policy, the company conducts a new survey of 254 employees, and finds that 160 of them support it. Is the new policy even less popular than the old one? Use a = 0.01. 635 PM P Type here to search 2/20/2022
At the beginning of year 1, a new machine must be purchased at the cost of 130K TL. The cost of maintaining a machine i years old is given in the table below. Due to the inflation, the purchase cost of a new machine at the beginning of Year 2, Year 3, and Year 4 would be 140K, 150K, and 165K respectively. The trade-in value is fixed at 50K for a replaced machine regardless of the age. Your goal is to minimize the total cost (purchasing plus maintenance) of having the machine for four years. Determine the year(s) in which a new machine should be purchased and calculate the total cost. Age at the beginning of the year Maintenance cost for the next year(K TL) 20 1 35 2 65 120
Suppose Becky gets a sales bonus at her place of work that gives her an extra $400 of disposable income. She chooses to spend $300 and save the remaining $100. From this, you can tell that Becky's marginal propensity to consume (MPC) is0.75 , and her marginal propensity to save (MPS) is0.25 . Mathematically, it must always be true that: Saving = a. Disposable income+Comsumption b. Comsumption-Disposable income c. Disposable income-Consumption Therefore, it must also be true that: MPS = a. 1-MPC b. 1+MPC c. MPC
4. A particular automobile is worth $15,200 today and will be worth $9,800 in three years. a) At what rate is the car depreciating per year? b) Find a linear depreciation function, ft), for this car, with t= the number of years from today. c) Use your function from part b) to determine the value of this car 5 years from now,
Assume (FT2 = FT1 (1 + TIT2) + T1CT2 is the equilibrium situation. Also assume that T2- T1 is one year, that T1CT2 = $1 and that TirT2 = 10%. %3D Assume the initial prices are FOT1 = 100 & FOT2 = 133. A trader goes long the FT1 contract and short the FT2 contract believing these are not equilibrium prices and that he will profit when they adjust to equilibrium. Say the next day, t+ 1, the t+1FT1 price moves to 115 and t+1FT2 adjusts to an equilibrium price. If the trader round trips his positions on day t+1, what is his profit or loss on the FT2 position? profit of 11 loss of 11 cannot be determined from the information given profit of 5.5
A manufacturer estimates that when q units of a certain commodity are produced, the profit obtained is P(q) thousand dollar share. Can please solve this ASAP. Please show me the steps I have no idea how. I am doing a practice problem.
Consider the following model of a market for a good, in which Qs is quantity produced, Qd is quantity purchased and P is the price of the good. Qs=j+kP Qd=l-mP When Qs=Qd, what will the price be? a. (k+m)/(l-j) b. (l-j)/(k+m) c. (k-m)/(l+j) d. (l+j)/(k-m)
A university spent $1.8 million to install solar panels atop a parking garage. These panels will have a capacity of 800 kilowatts (kW) and have a life expectancy of 20 years. Suppose that the discount rate is 10%, that electricity can be purchased at $0.10 per kilowatt-hour (kWh), and that the marginal cost of electricity production using the solar panels is zero. Hint: It may be easier to think of the present value of operating the solar panels for 1 hour per year first. Approximately how many hours per year will the solar panels need to operate to enable this project to break even? 2,642.82 O 1,321.41 3,435.67 3,171.38 $89,843.45 $251,561.65 If the solar panels can operate only for 2,379 hours a year at maximum, the project would not ▼ break even. $215,624.27 Continue to assume that the solar panels can operate only for 2,379 hours a year at maximum. $179,686.89 In order for the project to be worthwhile (i.e., at least break even), the university would need a grant of at least
. If the supply and demand functions for a commodity are given by 8 p − q = 290 and (p+2)q =5720, respectively, find the price that will result in market equilibrium.
If S begins by asking an initial price x and B cannot afford to pay more than P, what is the highest offer which B should make in reply to the price x asked by S?

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