FRE6083_HW4

FRE6083_HW4 - FRE 6083 Homework 4 Question 1 Scaling Normal...

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Unformatted text preview: FRE 6083 Homework 4 Question 1 Scaling Normal VaR with independent and with autocorrelated returns. A portfolio has daily returns, discounted to today, that are normally with zero expectation and standard deviation 1 . 5%. (a) Calculate the 1% 1-day VaR. (b) Calculate the 1% 10-day VaR assuming that daily returns are independent. (c) Calculate the 1% 10-day VaR assuming that daily returns follow a first order autoregressive process with autocorrelation 0 . 25, u1D45F u1D461 − u1D707 = 0 . 25( u1D45F u1D461 − 1 − u1D707 ) + u1D716 u1D461 , u1D716 u1D461 ∼ u1D456u1D456u1D451 u1D441 (0 , u1D70E 2 ) and u1D70E = 1 . 5%. Hint Let u1D44B u1D458 = u1D45F u1D458 + ... + u1D45F u1D458 +9 . Question 2 Relationship between exponential and Gamma random variables. Let u1D44B be a random variable with a Gamma distribution, u1D453 ( u1D465 ∣ u1D6FC, u1D6FD ) = uni007B.alt03 u1D6FD u1D6FC Γ( u1D6FC ) u1D465 u1D6FC − 1 u1D452 − u1D6FDu1D465 for u1D465 > 0; u1D6FC, u1D6FD > otherwise (a) Show that the moment generating function (MGF) of...
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This note was uploaded on 02/16/2011 for the course FE 6083 taught by Professor Neveskyi during the Spring '11 term at NYU Poly.

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