Financial Modelling in Python

P1: JYS

c10 JWBK378-Fletcher May 12, 2009 19:2 Printer: Yet to come

152 Financial Modelling in Python

, shift method = shift convention.modified following

, fee

currency = "USD")

return sched

10.2 PRICING A TARN

In this section we illustrate how we can use the components to price a Target Redemption

Note, commonly referred to as a TARN. We will use the code developed in section 9.2 to do

the actual pricing. So what is a TARN? A TARN is a swap consisting of a funding leg paying

LIBOR plus a spread in exchange for an exotic coupon leg receiving a coupon of the form

c

t

= max



f, c + g × L

tT

s

T

e



(10.6)

with f the floor, c a fixed coupon amount, g the leverage and L

tT

s

T

e

the LIBOR rate for the

period (T

s

, T

e

) observed at t ∈

{

T

1

, T

2

,...,T

n

}

, a discrete set of times. The whole contract

knocks out if the total accrued coupon reaches a predefined target. Typically if the swap hasn’t

triggered before it ends, then the holder of the TARN receives a guaranteed accrued amount

called the redemption floor. In addition, if the swap triggers, then the holder receives an accrued

amount no greater than the redemption cap. In most TARN structures both the redemption

floor and redemption cap are equal to the target.

Before moving on to discuss the payoff classes for the TARN, it is helpful to first look at

the mathematical form of the exotic coupon in more detail. The exotic coupon, denoted by C

t

in the formulae below, can be split ...