24.1 Interest rate derivatives More advanced models Chapter 24 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 24.1 Interest Rate Derivatives: More Advanced Models Chapter 24
24.2 The two-Factor hul white Model (equation 24.1, page 571) e()+-ax」+o;dz du=-budt + dz where x=f(r)and the correlation between dz, and dz2 is p The short rate reverts to a level dependent on u, and u Itself Is mean reverting Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 24.2 The Two-Factor Hull-White Model (Equation 24.1, page 571) dx t u axdt dz du budt dz x f r dz dz u u = + − + = − + = ( ) ( ) 1 1 2 2 1 2 where and the correlation between and is The short rate reverts to a level dependent on , and itself is mean reverting
24.3 Analytic Results Bond prices and European options on zero-coupon bonds can be calculated analytically when fr)=r Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 24.3 Analytic Results • Bond prices and European options on zero-coupon bonds can be calculated analytically when f(r) = r
Options on Coupon-Bearing Bonds We cannot use the same procedure for options on coupon-bearing bonds as we do in the case of one -factor models If we make the approximate assumption that the coupon-bearing bond price is lognormal we can use blacks model The appropriate volatility is calculated from the volatilities of and correlations between the underlying zero-coupon bond prices Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 24.4 Options on Coupon-Bearing Bonds • We cannot use the same procedure for options on coupon-bearing bonds as we do in the case of one-factor models • If we make the approximate assumption that the coupon-bearing bond price is lognormal, we can use Black’s model • The appropriate volatility is calculated from the volatilities of and correlations between the underlying zero-coupon bond prices
24.5 Volatility structures In the one-factor ho-lee or hull-White model the forward rate s ds are either constant or decline exponentially. Al forward rates are instantaneously perfectly correlated In the two-factor model many different forward rate S.D. patterns and correlation structures can be obtained Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 24.5 Volatility Structures • In the one-factor Ho-Lee or Hull-White model the forward rate S.D.s are either constant or decline exponentially. All forward rates are instantaneously perfectly correlated • In the two-factor model many different forward rate S.D. patterns and correlation structures can be obtained