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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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).
Mr. Tan call his resident wife and deposited P100,000 to their joint account and the P100,000 is to be invested in the cooperative. The time deposit on bank is a 5 year term with interest rate at 7% while the other deposit to the cooperative is 1 year time deposit at 5% interest rate. (1) Compute for the interest earned after maturity date on the deposits (2) Compute for the final tax rate for the deposits. (3) Suppose that the time deposit in the bank was pre-terminated at year (4) what is the final tax rate?
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In the world of mathematical finance, an important skill for any quantitative analyst is to price derivatives. These usually come in the form of options as well as other more exotic financial instruments. For this project we will focus on something called European Call options. We will see how you can estimate the price of an underlying asset (usually a stock) at some time in future T and use this to find how much an option should cost today. First, lets take a look at what a European call option actually is. The idea behind the European call option is that you will enter into a contract with someone that grants you the right, but not the obligation, to purchase some number of shares of a stock at a pre-determined price, called the strike price. In this paper we will say that the payoff for a European call option can be given by: max {S(t) – K, 0}. The reason we do this is because, it would not make sense to exercise the option if the price of the underlying asset is below the strike…
5. (2xy-3) dx+ (2ry+ 4) dy =0 6. 2y + cos 3x 4r + 3y sin 3x 7. - y) dx + (- 2ry) dy = 0 8. 1 + In x + In x) dy 9. (x – y + y² sin x) dx = (3ry + 2y cos x) dy 10. (x + y*) dx + 3ry² dy = 0 11. (y In y *) dx + x In y dy = 0 In Problems 21-26 solve the given initial-value nrmblem
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

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