Hull-White relation

eljefe · January 8th, 2010, 10:48 pm

HiTrying to figure out if the relation r(t) = x(t)+alpha(t) from page 74 in Brigo & Mercurio still holds under the forward measure ?

manolom · January 9th, 2010, 8:27 pm

both sides of the equation are random vars. => taking expectation under any measure would lead to both expectations being equal. Remember also that expectation is linear.

eljefe · January 9th, 2010, 8:54 pm

QuoteOriginally posted by: manolomboth sides of the equation are random vars. => taking expectation under any measure would lead to both expectations being equal. Remember also that expectation is linear.Hi.. Thank you for replying :-)Not quite sure if I understand the answer however. Are you saying that x(t) under the forward measure can be found by x(t)=r(t)-alpha(t) ??Again thank you for your help

ikeuchi · January 11th, 2010, 11:09 am

x(t) changes and the relation holds. but it is short rate under fwd meas. see B&M 3.2.1 and 3.8.