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Unformatted text preview: dr t = a ( br t ) dt + dB t , where a and b are positive constants. (a) A stochastic process { U t , t } is dened by U t = e at r t . i. Derive an equation for the stochastic dierential dU t . ii. Solve the equation to nd U t . iii. Show that the spot rate satises r t = b + ( rb ) eat + Z t e a ( st ) dB s . 5. Dene ( n,t ) = E [ B n t ] for positive integer n and t 0. Use Itos formula to nd the recursive equation satised by ( n,t ). End1...
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 Three '11
 kim

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