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Description
Problem 1 (10)
Let r_{t} be a log return. Suppose that r_{1}; r_{2}; : : : are i.i.d. N( ; ^{2}).
a) What is the distribution of r_{t}(3) = r_{t} + r_{t1} + r_{t2} .
b) What is the covariance between r_{t}(k) and r_{t}(k + l) for some integer t; k and l.
Problem 2 (20)
Suppose you bought an asset at initial price P_{0} = 20 and the asset price follows a lognormal geometric random walk where
P_{t} = P_{0} exp(r_{t} + r_{t1} + + r_{1})
and r_{i} are i.i.d. N(0:03; 0:005^{2}).

Simulate the annual price of the asset for the next 10 years i.e. (P_{1}; P_{2}; : : : ; P_{10}) and plot it against time.

Simulate P_{10} 2000 times and estimated the expected value i.e E[P_{10}].

Compare your simulated result with the actual expected value of P_{10} .
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.

What is the interpretation of a convex pattern?

What is the interpretation of a concave pattern?

What is the interpretation of a convexconcave pattern?

What is the interpretation of a concaveconvex pattern?
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Problem 5 (20)
Problem 6 (20)
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