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A stock price is currently $36. During each three-month period for the next six months it is expected to increase by 9% or decrease by 8%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off(max[(40-ST),0])2where is the stock price in six months.
What are the payoffs at the final nodes of the tree? [1 mark]
Use no-arbitrage arguments (you need to show how to set up the riskless portfolios at the different nodes of the binomial tree). [2 mark]
Use risk-neutral valuation. [1 mark]
Verify whether both approaches lead to the same result. [1 mark]
If the derivative is of American style (ST in the payoff function refers to the stock price when the option is exercised), should it be exercised early?
It has been established that smoking is associated with lung cancer. But you are interested to determine in your sample if the proportion of men who did not have lung cancer is different from women who also did not have lung cancer in their smoking history. Refer to the Data Set. Does your data provide sufficient evidence that the proportion of men without lung cancer who smoke and not smoke different from women without lung cancer? Test your hypothesis at the 5% significance level.
5. One mole of a certain polar substance is dissolved into 1000 cm3 of a non-polar liquid having dielectric constant 3.0 at 27° C. the dielectric constant of the solution is 3.2 at the same temperature. Determine the dipole moments of polar molecules. 6. The relative permittivity of argon at 0 C and at 1 atmospheric pressure is 1.000435. Calculate the polarizability of the atom if the gas contains 2.7 X 1025 atoms/m3. Given Eo = 8.85 X 10-12 F/m
Consider the region enclosed by the curves g(2)=e" and f(t) = 0 for re [0,1]. Sketch a picture of this region, and then find the volume of the solid obtained by rotating this region about the I-axis using the slicing method. Also, describe in a short paragraph the shape of this solid.
At 20 years old, Josh is an avid saver. He wants to put an equal amount each year from age 21 to 50 (30 years) such that starting at age 65 he can make a guaranteed annual withdrawal of $25,000 forever without touching the corpus, which will be the inheritance money for his family. He will make no deposits during the years of age 51 through 65. At a conservative return of 4% per year for all the years, what amount must he invest each year from age 21 through 50? The amount that must be invested each year is $
For least squares fit for the regression ŷ = ßo + ßix, argue that in the case of simple linear regression Y = Bo + B1X +€, the least squares line always passes through the point (ō, ū).
Question 1 (d) (d) h = 2,6 kn n = 180 = 40.10-6S = 0 he +15V 3k3 n 47 kn C -01 10 kn I kn ፥ EC 3k3 () small signal ac model dynamic equivalent circuit (ii) Complete h-parameter small signal model of the transistor amplifier stage (ii) Derive and calculate formulas for Zi, Z., Av, Ai, and Ap also express all the gains in dB's.
Exercise 2. Find the volume of the solid obtained by rotating the region bounded by the curves f(x)=1+3/, g(x) = 0 and x = 1 and x = 2 about the z-axis. Sketch this solid.
