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Term structure equation

Suppose that the short rate r(t) has the ℚ-dynamics
dr(t)=μ(t,r(t))dt+σ(t,r(t))dW(t)
then the price of the Zero coupon bond p(t,T)=F(t,r,T) should for all times of maturity T satisfy
∂F(t,r,T)/(∂t)=-μ(t,r)∂F(t,r,T)/(∂r)-1/2σ(t,r)2(∂2F(t,r,T)/(∂r2)+rF(t,r,T)
F(T,r,T)=1.

 

Questions: Magnus Wiktorsson
Last update: 2009 Nov 13 17:27:33. Validate: HTML CSS

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