2013/8/13 Hull-White

Hull-White Model dr = [(t ) ar ]dt + sdztR t dR(t)= [(t ) aR(t) ]dt + s dW(t): dR*(t)= aR*(t)dt + s dW(t) ((t ) = 0 and r (0) = 0) (t)=R(t)-R*(t) fitExample Zero rate s = 0.01 a = 0.1Dt = 1 year

jmax = ceil [0.184/(aDt)] = 2 mean reversion Branch :

Define node (i,j) -> t=i*Dt R*=j*D R

: Type A nodedR*(t)= aR*(t)dt + s dW(t)

: Type B nodedR*(t)= aR*(t)dt + s dW(t)

: Type C nodedR*(t)= aR*(t)dt + s dW(t)

QijaiQij Node(i,j)$1 Q00 =1a0 =3.824%

Qijai

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