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Unformatted text preview: Continuous Time Finance Final Exam Spring 2004 – Professor Kohn May 5, 2004 This was administered as a closed-book exam, however students were permitted to bring two sheets of notes (both sides, any font). Problems 1-10 require relatively short answers and are worth 10 points each. Problems 11 and 12 require longer answers and are worth 25 points each. Thus the total possible score is 150. PART I: SHORT ANSWER QUESTIONS (10 points each). (1) Is the following statement true or false? “If the interest rate r is constant then the market price of risk must also be constant.” (2) Suppose S is the price of a risky tradeable. Can S 2 also be the price of a tradeable? (3) In the Cox-Ingersoll-Ross short-rate model, the SDE for the short rate under the risk- neutral probability is dr = ( θ- ar ) dt + σ √ rdw , where σ and a are constant and θ ( t ) is a deterministic function of time. The prices of zero-coupon bonds under this model satisfy P ( t, T ) = V ( r ( t ) , t ) where V ( x, t ) solves the PDE V t + V x + V xx + V = 0 , with V ( x, t ) = at t = . Fill in the blanks. (4) Consider options on an underlying whose actual volatility is a function of time alone, i.e. whose subjective process is dS = μ ( S, t ) S dt + σ ( t ) S dw where σ ( t ) is a deterministic function of time. Assume the interest rate r is constant....
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This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.
- Fall '11