PROBLEM SET 1 Solution

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Description

Problem 1 (10)

Let rt be a log return. Suppose that r1; r2; : : : are i.i.d. N( ; 2).

a) What is the distribution of rt(3) = rt + rt1 + rt2 .

b) What is the covariance between rt(k) and rt(k + l) for some integer t; k and l.

Problem 2 (20)

Suppose you bought an asset at initial price P0 = 20 and the asset price follows a lognormal geometric random walk where

Pt = P0 exp(rt + rt1 + + r1)

and ri are i.i.d. N(0:03; 0:0052).

  1. Simulate the annual price of the asset for the next 10 years i.e. (P1; P2; : : : ; P10) and plot it against time.

  1. Simulate P10 2000 times and estimated the expected value i.e E[P10].

  1. Compare your simulated result with the actual expected value of P10 .

Problem 3 (10)

Suppose in a normal plot that the sample quantiles are plotted on the vertical axis, rather than on the horizontal axis as in our lectures.

  1. What is the interpretation of a convex pattern?

  1. What is the interpretation of a concave pattern?

  1. What is the interpretation of a convex-concave pattern?

  1. What is the interpretation of a concave-convex pattern?

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Problem 4 (20)

Problem 5 (20)

Problem 6 (20)

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