Forums  > Pricing & Modelling  > Pricing of irregular floating coupons  
     
Page 1 of 1
Display using:  

sol2


Total Posts: 3
Joined: Nov 2018
 
Posted: 2018-11-07 09:06
I don’t know theoretically accurate solution to the following problem that I frequently face valuing irregular floating rate notes. Can somebody help me out?

Problem
Let’s assume that there is a market of zero-coupon risk-free bonds.
Price of a bond at time t with maturity at T and face=1 is P(t,T).
Bond’s interest rate is R(t,T) = (1/P(t,T)-1)/(T-t).
Forward interest rate from T_1 to T_2 at t is F(t,T_1,T_2) = (P(t,T_1)/P(t,T_2) – 1)/(T_2 – T_1).
There is a tradable derivative “f” that pays R(T_1, T_2) (interest rate R fixed at T_1) at T_3>T_2.

Question
What is value of “f” at t=0?

The question is trivial for the case T_3=T_2: f(0) = P(0,T_2)*F(0,T_1,T_2) – “discounted forward rate”. Is it possible to find f(0) for T_3>T_2?

sol2


Total Posts: 3
Joined: Nov 2018
 
Posted: 2018-11-09 08:16
Come on! It should be a simple question for those who know theory... :-( Anyone?

pj


Total Posts: 3604
Joined: Jun 2004
 
Posted: 2018-11-09 09:16
If your product at time T_3 is worth X.
How much will it be worth at T_2?
Hint: Discounting.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

sol2


Total Posts: 3
Joined: Nov 2018
 
Posted: 2018-11-09 13:35
pj, THANK YOU for the answer!!!

So your solution is f(0) = P(0,T_3)*F(0,T_1,T_2). I am not sure that it is right (but some people usually do what you suggest). Can you prove it strictly?

Solution to the “T_3=T_2” case is based on changing probability measure to a measure where numeraire is P(t,T_2), i.e. g(t)/P(t,T_2) is a martingale for any traded instrument g(t). Or you can simply hedge f(t) with bonds P(t,T_1) and P(t,T_2).

But it doesn’t work for the “T_3>T_2” case. It is not that simple, I think.

I hope that people here understand that you can’t just discount however you want and whatever you want…

nikol


Total Posts: 1360
Joined: Jun 2005
 
Posted: 2018-11-09 17:32
@pj

you are heart-kinded.
and you will suffer
Evil Grin

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

jiuer7845
Banned

Total Posts: 8
Joined: May 2021
 
Posted: 2021-05-30 11:27
Pandora Charms

Jordan 1

YEEZY SUPPLY

Adidas UK

Pandora Charms

Pandora Jewelry

Nike Outlet

Adidas Shoes

Nike Shoes

Nike Outlet

Pandora Jewelry

Pandora Outlet

Jordan Shoes

Air Jordan 4

Pandora Charms

Pandora Jewelry

Pandora Rings

Pandora Bracelets

Adidas Yeezy

Yeezy

Pandora Charms

Nike Outlet

Adidas Yeezy

Air Max 720

Nike Air Max 270

Air Jordan 11

Air Force 1

Air Jordan 1

Nike Jordans

Jordan 1s

Pandora Charms

Pandora UK

Nike Jordan 1

Nike Air VaporMax Flyknit 3

Jordan 1

Pandora Sale

Jordan 11

Nike Air VaporMax

Pandora Jewelry Official Site

Nike Vapormax Flyknit

Air Jordan 1 Mid

Yeezy 350

Adidas yeezy

Yeezy Shoes

Yeezy 350

Adidas Yeezy

Yeezy 350

Nike Shoes

Yeezy

Nike Outlet

Yeezy

NFL Shop Official Online Store

Nike UK

Yeezy Shoes

Yeezy

Yeezy 350

https://www.pandoracharms.uk.com/ Pandora Charms https://www.adidasuk.uk.com/ Adidas UK https://www.jordan1.uk.com/ Jordan 1 https://www.supplyyeezys.us/ YEEZY SUPPLY https://www.pandoracharms.cc/ Pandora Charms
Previous Thread :: Next Thread 
Page 1 of 1