Unformatted text preview: dr t = a ( br t ) dt + σdB t , where a and b are positive constants. (a) A stochastic process { U t , t ≥ } is deﬁned by U t = e at r t . i. Derive an equation for the stochastic diﬀerential dU t . ii. Solve the equation to ﬁnd U t . iii. Show that the spot rate satisﬁes r t = b + ( rb ) eat + σ Z t e a ( st ) dB s . 5. Deﬁne μ ( n,t ) = E [ B n t ] for positive integer n and t ≥ 0. Use Itˆo’s formula to ﬁnd the recursive equation satisﬁed by μ ( n,t ). End1...
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This note was uploaded on 06/12/2011 for the course ASB 2003 taught by Professor Kim during the Three '11 term at University of New South Wales.
 Three '11
 kim

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