Suppose that the price S(t) of a share follows the GBM with parametersS, μ, o, r.Consider an option with the expiration time T and a payoff functionR(S(T))=Aif S(T) < B,if S(T) > B.(Here A and B are positive constants.)(a) Compute the no-arbitrage price of this option.(b) Suppose now that the above share provides a dividend yield of rate qwhich is paid continuously and is reinvested in the share. What is theprice C of the derivative with the same payoff function? (c) Suppose that a discrete proportionate dividend of rate d is paid at timeT/2 and is immediately reinvested in the share. The expiration time ofthe option is t, 0 < t ≤ T. Write down the formulae for the price of thisoption in the following 2 cases: t ≤T/2 and T/2 < t ≤ T.(d) Consider again the case when no dividend is paid and the expirationtime is T.If you are the seller of this option, what should be your hedging strategy?Namely, how many shares must be in your portfolio and how muchmoney should be deposited in the bank at time t, 0 ≤ t ≤ T, in orderfor you to be able to meet your obligation at time T?

Introduction: In probability theory, a probability distribution is a mathematical function that…

Answered: Suppose that the price S(t) of a share…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 7% per year for each of the next four years and 6% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1(t-1) %, where t is the security's maturity. The liquidity premium (LP) on all Rinsemator Group's bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Rating U.S. Treasury AAA AA A BBB O 10.77% 11.82% Rinsemator Group issues 7-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. O 5.25% Default Risk Premium O 11.22% 0.60% 0.80% 1.05% 1.45% Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond. O The yield on an AAA-rated…
2. Show that the present value at time 0 of 1 payable at times 11, 15, 19, 23, 27, and 31, where the effective rate per annum is i, is given by a32-98 +
Assume that after one time period, the value of a stock (whose present value is R80) would be either R120 or R60. Suppose that, for any y, at a cost of Cy, one can purchase at a time-0 the option to buy y shares of the stock at time-1 at a price of R90 per share. For what values of C, no-arbitrage will be possible? (Provide necessary details).
Suppose that the real money demand function is L(Yr+ ? ?=0.3Yr+c) Where Y is real output, r is the real interest rate, and πe is the expected rate of inflation. Real output is constant over time at Y = 1500. The real interest rate is fixed in the goods market at r = 0.5 per year. (a) Suppose that the nominal money supply is growing at the rate of 10% per year and that this growth rate is expected to persist for ever. Currently, the nominal money supply is M = 400. What are the values of the real money supply and the current price level? (Hint: What is the value of the expected inflation rate that enters the money demand function?)
Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R? → R+ defined by f(1, k) = 21 + 5k,
Prove that the accumulation function associated with the force of interest satisfies the principle of consistency.
Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 Step 2 With PV = 100,000, i = If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 nearest cent. PMT = PV PMT = = 1 − (1 + i)¯″¸ 100000 0.043 and n = "I 12 544.54…
A7. (a) Which of the following statements is true? Select one of the options i. – iv. (dy of the function Y = 4x6 - 3x³ +7x - 5 is equal to The derivative %3D i. 24x6 - 9x3 + 7 ii. 24x5-9x2 +7 ii. 24x5 9x3 + 7 iv. None of the above Given that the demand function is p = 42 -3q , where q represents the output level and p is the price, write down an expression for the total revenue (R) function in terms of q. (b) i. %3D Find the output level which maximises the total revenue function. Note that you need to clearly show that this output level leads to a maximum. ii.

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