Interest Rate Risk
Dr HK Pradhan XLRI Jamshedpur

Hull Ch 7 Fabozzi chapters on duration & Convexity, Ch-7, Convexity Stochastic Process notes

Session Objectives j
 Valuation of fixed income securities  Risks in fixed income securities
 Traditional measures of risk
– (we know PVBP, duration and convexity, M-Square) M Square)

 VaR based risk measures  Interest rate volatility calculations  Portfolio risk & Cash flows mapping issues  Var for Interest Rate Derivatives  Interest rate risk and Bond portfolio management

Profile of Interest Rate Markets, Instruments & Institutions

Bond Price
P

1  y 

C1

1



1  y 

C2

2



1  y 
Ct

C3

3



1  y n

Cn

price

Sum of the present values of each cashflows p

P



n

t 1

1  y 

t



M

1  y n

yield
 price < par (discount bond)  price = par (par bond)  price > par (premium bond)

Concept of Accrued Interest p
 When you buy a bond between coupon dates, you pay the seller: Clean Price plus the Accrued Interest
– pro-rated share of the fi coupon: i d h f h first interest d does not compound b d between coupon payment dates.

LD
Days Accrued Interest  Total

T from last Coupon between Coupon Date Dates Days

ND
(Coupon)

Dirty

Price  Clean price  Accrued

Interest

Accrued Interest  Face *

C T  LD * 2 ND  LD

Bond Valuation
Value of a bond is the present value of future cashflows, so the pricing equation of the bond is:

tP 

1  y  n C1

v



1  y 
Ct

C2

1 v



1  y 


C3

2v

 M

1  y n1v

Cn

tP  t 1

1  y  1  y  v t 1

1  y v 1  y n1

When v= 1, what happens?

This gives the dirty price (also known as the full price) The dirty price is the fair value or market value of the bond You