Explanation Refer to the mutual fund quotation table: The PIMCO Fds Institutional, MortBckSec r is represented by the symbol PTRIX . The net asset value of the fund PIMCO Fds Institutional,

Contemporary Mathematics For Business & Consumers, Brief Edition, Loose-leaf Version

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ISBN: 9781305867192

Author: Robert Brechner, Geroge Bergeman

Publisher: South-Western College Pub

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Chapter 20.III, Problem 10RE

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To fill: The blanks for the statement, “Which PIMCO fund has the symbol PTRIX? What is the NAV? ____.”

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Chapter 20.III, Problem 9RE

Chapter 20.III, Problem 11RE

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Problem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…

Problem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…

Chapter 20 Solutions

Contemporary Mathematics For Business & Consumers, Brief Edition, Loose-leaf Version

Ch. 20.I - Techron Industries, Inc., has 1,400,000 shares of...Ch. 20.I - Prob. 2TIE Ch. 20.I - Prob. 3TIE Ch. 20.I - Prob. 4TIE Ch. 20.I - Bentley Systems. Inc., paid a dividend of $0.68...Ch. 20.I - Prob. 6TIE Ch. 20.I - You purchase 225 shares of Gulfstream Industries...Ch. 20.I - Prob. 1RE Ch. 20.I - Prob. 2RE Ch. 20.I - Prob. 3RE

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The blanks for the statement, “Which PIMCO fund has the symbol PTRIX? What is the NAV? ____ . ”

Solution Summary: The author explains that the PIMCO Fds Institutional, MortBckSec r is represented by the symbol

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To fill: The blanks for the statement, “Which PIMCO fund has the symbol PTRIX? What is the NAV? ____.”

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Chapter 20 Solutions