Microsoft PowerPoint - PoF.ppt

Taylor series expansion 119

ƒ

Duration ... how sensitive the price is to changes in the yield; %-change in the price fo

r a given small change in the

YTM

Duration for a (straight) coupon / bullet bondk ... number of periods (CFs) per yearP ... PV of the bondif c=0

Ä

D=T

if T=1 and k=1

Ä

D=T=1

ƒ

Modified duration

P y P

y

D

D

P

y

P y

D

y

D

D

M

M

∂ ∂

− = + ≡ ⇒ +

∂ ∂

−

=

+

≡

1

1

;

1

(

)

∑=

=

T t

o

t

P

k

CF

PV

t

D

1

*

P *

y

P y

D

+

∂ ∂

−

=

1

Multi-period deterministic cash flows: FI securities - Market risk