
Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2.14, Problem 12P
To determine
To find:The complex form of
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For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram?
A
55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92
B
55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91
C
55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93
D
55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 2 Solutions
Mathematical Methods in the Physical Sciences
Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...
Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.4 - For each of the following numbers, first visualize...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - First simplify each of the following numbers to...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Find each of the following in rectangular (a+bi)...Ch. 2.5 - Prove that the conjugate of the quotient of two...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Find the absolute value of each of the following...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Solve for all possible values of the real numbers...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Describe geometrically the set of points in the...Ch. 2.5 - Show that z1z2 is the distance between the points...Ch. 2.5 - Find x and y as functions of t for the example...Ch. 2.5 - Find and a if z=(1it)/(2t+i).Ch. 2.5 - Find and a if z=cos2t+isin2t. Can you describe...Ch. 2.6 - Prove that an absolutely convergent series of...Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Test each of the following series for convergence....Ch. 2.6 - Prove that a series of complex terms diverges if...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Find the disk on convergence for each of the...Ch. 2.7 - Verify the series in (7.3) by computer. Also show...Ch. 2.8 - Show from the power series (8.1) that...Ch. 2.8 - Show from the power series (8.1) that ddzez=ezCh. 2.8 - Find the power series for excosx and for exsinx...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Express the following complex numbers in the x+iy...Ch. 2.9 - Show that for any real y,eiy=1. Hence show that...Ch. 2.9 - Show that the absolute value of a product of two...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Use Problems 27 and 28 to find the following...Ch. 2.9 - Prob. 38PCh. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Follow steps (a), (b), (c) above to find all the...Ch. 2.10 - Using the fact that a complex equation is really...Ch. 2.10 - As in Problem 27, find the formulas for sin3 and...Ch. 2.10 - Show that the center of mass of three identical...Ch. 2.10 - Show that the sum of the three cube roots of 8 is...Ch. 2.10 - Show that the sum of the n nth roots of any...Ch. 2.10 - The three cube roots of +1 are often called...Ch. 2.10 - Verify the results given for the roots in Example...Ch. 2.11 - Define sin z and Cos z by their power series....Ch. 2.11 - Solve the equations ei=cosisin,forcosandsin and so...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - Find each of the following in rectangular form...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - In the following integrals express the sines and...Ch. 2.11 - Evaluate eax(acosbx+bsinbx)a2+b2 and take real...Ch. 2.11 - Evaluate e(a+ib)xdx and take real and imaginary...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Verify each of the following by using equations...Ch. 2.12 - Show that enz=(coshz+sinhz)n=coshnz+sinhnz. Use...Ch. 2.12 - Use a computer to plot graphs of sinh x, cosh x,...Ch. 2.12 - Using (12.2) and (8. l), find, in summation form,...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find the real part, the imaginary part and the...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - Find each of the following in the x+iy form and...Ch. 2.12 - The functions sin t, cos t, …, are called...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Prob. 12PCh. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Evaluate each if the following in x+iy, and...Ch. 2.14 - Show that (ab)c can have more values than abc. As...Ch. 2.14 - Use a computer to find the three solutions of the...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Prob. 7PCh. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Find each of the following in the x+iy form and...Ch. 2.15 - Show that tan z never takes the values +1. Hint:...Ch. 2.15 - Show that tanh z never takes the values +1.Ch. 2.16 - Show that if the line through the origin and the...Ch. 2.16 - In each of the following problems, z represents...Ch. 2.16 - In each of the following problems, z represents...Ch. 2.16 - Z=(1+i)t-(2+i)(1-t). Hint: Show that the particle...Ch. 2.16 - z=z1t+z2(1t). Hint: See Problem 4; the straight...Ch. 2.16 - In electricity we learn that the resistance of two...Ch. 2.16 - In electricity we learn that the resistance of two...Ch. 2.16 - Find the impedance of the circuit in Figure 16.2...Ch. 2.16 - For the circuit in Figure 16.1: (a) Find in terms...Ch. 2.16 - Repeat Problem 9 for a circuit consisting of R, L,...Ch. 2.16 - Prove that...Ch. 2.16 - In optics, the following expression needs to be...Ch. 2.16 - Verify that eit, eit, cost, and sint satisfy...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Find one or more values of each of the following...Ch. 2.17 - Prob. 13MPCh. 2.17 - Find the disk of convergence of the series ...Ch. 2.17 - For what z is the series z1nn absolutely...Ch. 2.17 - Describe the set of points z for which Re(ei/2z)2.Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - Verify the formulas in Problems 17 to 24....Ch. 2.17 - (a) Show that cosz=cosz. (b) Is sinz=sinz? (c) If...Ch. 2.17 - Find 2eiiiei+2. Hint: See equation (5.1).Ch. 2.17 - Show that Rez=12(z+z) and that Imz=(1/2i)(zz)....Ch. 2.17 - Evaluate the following absolute square of a...Ch. 2.17 - If z=ab and 1a+b=1a+1b, find z.Ch. 2.17 - Write the series for ex(1+i). Write 1+i in the rei...Ch. 2.17 - Show that if a sequence of complex numbers tends...Ch. 2.17 - Use a series you know to show that n=0(1+i)nn!=e.
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- Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forward
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- c) Using only Laplace transforms solve the following Samuelson model given below i.e., the second order difference equation (where yt is national income): - Yt+2 6yt+1+5y₁ = 0, if y₁ = 0 for t < 0, and y₁ = 0, y₁ = 1 1-e-s You may use without proof that L-1[s(1-re-s)] = f(t) = r² for n ≤tarrow_forward5. 156 m/WXY = 59° 63 E 7. B E 101 C mFE = 6. 68° 8. C 17arrow_forwardScoring: MATH 15 FILING /10 COMPARISON /10 RULER I 13 Express EMPLOYMENT PROFESSIONALS NAME: SKILLS EVALUATION TEST- Light Industrial MATH-Solve the following problems. (Feel free to use a calculator.) DATE: 1. If you were asked to load 225 boxes onto a truck, and the boxes are crated, with each crate containing nine boxes, how many crates would you need to load? 2. Imagine you live only one mile from work and you decide to walk. If you walk four miles per hour, how long will it take you to walk one mile? 3. Add 3 feet 6 inches + 8 feet 2 inches + 4 inches + 2 feet 5 inches. 4. In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get? 5. Add 8 minutes 32 seconds + 37 minutes 18 seconds + 15 seconds. FILING - In the space provided, write the number of the file cabinet where the company should be filed. Example: File Cabinet #4 Elson Co. File Cabinets: 1. Aa-Bb 3. Cg-Dz 5. Ga-Hz 7. La-Md 9. Na-Oz 2. Bc-Cf…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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