CH29HullOFOD6thEd - Interest Rate Derivatives: HJM and LMM...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Options, Futures, and Other Derivatives , 6 th Edition, Copyright © John C. Hull 2005 29.1 Interest Rate Derivatives: HJM and LMM Chapter 29
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Options, Futures, and Other Derivatives, 6 th Edition, Copyright © John C. Hull 2005 29.2 HJM Model: Notation P ( t,T ) : price at time t of a discount bond with principal of $1 maturing at T t : vector of past and present values of interest rates and bond prices at time t that are relevant for determining bond price volatilities at that time v ( t,T , t ): volatility of P ( t,T )
Background image of page 2
Options, Futures, and Other Derivatives, 6 th Edition, Copyright © John C. Hull 2005 29.3 Notation continued ƒ( t , T 1 , T 2 ) : forward rate as seen at t for the period between T 1 and T 2 F ( t , T ) : instantaneous forward rate as seen at t for a contract maturing at T r ( t ) : short-term risk-free interest rate at t dz ( t ) : Wiener process driving term structure movements
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Options, Futures, and Other Derivatives, 6 th Edition, Copyright © John C. Hull 2005 29.4 Modeling Bond Prices (Equation 29.1, page 680) ) for process a get we approach Letting for process the determine to lemma s Ito' use can we Because all for providing function any choose can We t,T F T T ) ,T f(t,T T T T t P T t P ) ,T f(t,T t t t v v t dz T t P T t v dt T t P t r T t dP t t ( . )] , ( ln[ )] , ( ln[ 0 ) , , ( ) ( ) , ( ) , , ( ) , ( ) ( ) , ( 1 2 2 1 1 2 2 1 2 1 - - = = + =
Background image of page 4
Options, Futures, and Other Derivatives, 6 th Edition, Copyright © John C. Hull 2005 29.5 The process for F ( t , T ) Equation 29.4 and 29.5, page 681) factor one than more is there when hold results Similar have must we ( ) , ( write we if that means result This s(t, ) Ω T, s(t, ) Ω T, m(t, )dz Ω T, s(t, dt Ω T, t, m T t dF t dz T t v dt T t v T t v T t dF T t t t t t t t T t T t τ = + = - = ) , ) ) ( ) , , ( ) , , ( ) , , ( ) , (
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/19/2010 for the course BUSINESS A 2600 taught by Professor Alexandrowhich during the Spring '08 term at University of Toronto- Toronto.

Page1 / 22

CH29HullOFOD6thEd - Interest Rate Derivatives: HJM and LMM...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online