Risk Analysis in Finance and Insurance, 2nd Edition

Chapter 5

Fixed Income Securities: Modeling

and Pricing

5.1 Elements of deterministic theory of fixed income in-

struments

In this section, we study in continuous time bonds or fixed income instru-

ments of a financial market. In Chapter 2, we introduced bonds as basic se-

curities with an obligation to make certain payments at certain future times.

These payments are called coupons.Denote0<t

1

<t

2

< ... < t

N

= T

the times when coupon payments c

1

,...,c

N

are made. The last payment c

N

is usually denoted A and is referred to as the principal (nominal value, par

value) of the bond. The bond yields a profit that is fully characterized by these

two sequences (t

i

)

i=1