midterm_1_-_questions_Winter_2008

Compute e x d 2pts if s t cov w t t w s you dont have

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Compute E [ X ]. d) [2pts] If s < t , Cov ( W t , t + W s ) = (You don’t have to justify to get full credit) 5. [3 points] An investor enters into a two-year swap agreement to purchase crude oil at $43.26 per barrel. A day after the swap is created, forward prices on oil rise and the new swap price on a similar swap is $44.12. If interest rates are 5.0% per year (annual effective interest rate), what is the market value of the swap on the day after it was created? ( a ) $1 . 60 ( b ) $1 . 58 ( c )$1 . 58 ( d )$1 . 60 Circle one of the four possible answers, and justify briefly your answer. Full credit cannot be obtained without a proper justification.
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8 of 10 6. [6 points] Today, the value S 0 of a stock is 20. The stock is modeled in a one period framework. After 1 year, the stock can be S T = 22 or S T = 18. Assume the interest rate is equal to 5% (continuously coumpounded). 24 ր 20 ց 18 One investor bets on the stock S with another investor: “I give you $ 2 if S T = 18 and you give me $ x if S T = 24 . What should be x to have a fair contract between the two investors (with no initial premium)? Hint: start by replicating the payoff of this derivative with Δ stocks and an investment in the bank account.
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10 of 10 Ito Formula: Let X t be a stochastic integral satisfying dX t = u ( t ) dt + v ( t ) dB t , with X 0 = x (0) .
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