lecture_slides-TermStructure_Binomial_#1

lecture_slides-TermStructure_Binomial_#1 - Financial...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Financial Engineering & Risk Management Introduction to Term Structure Lattice Models M. Haugh G. Iyengar Department of Industrial Engineering and Operations Research Columbia University
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Fixed Income Markets Fixed income markets are enormous and in fact bigger than equity markets. According to SIFMA , in Q3 2012 the total outstanding amount of US bonds was $35 . 3 trillion : Government $10.7 30.4% Municipal $3.7 10.5% Mortgage $8.2 23.3% Corporate $8.6 24.3% Agency $2.4 6.7% Asset-backed $1.7 4.8% Total $35.3 tr 100% – in comparison, size of US equity markets is approx $26 trillion. Fixed income derivatives markets are also enormous – includes interest-rate and bond derivatives, credit derivatives, MBS and ABS – will focus here on interest-rate and bond derivatives – using binomial lattice models. (The slides and Excel spreadsheet should be sufficient but Chapter 14 of Luenberger is an excellent reference for the material in this section.) 2
Background image of page 2
Binomial Models for the Short Rate Will use binomial lattice models as our vehicle for introducing: 1. the mechanics of the most important fixed income derivative securities - bond futures (and forwards) - caplets and caps, floorlets and floors - swaps and swaptions 2. the “philosophy” behind fixed income derivatives pricing – more on this soon. Fixed-income models are inherently more complex than security models - need to model evolution of entire term-structure of interest rates . The short-rate , r t , is the variable of interest in many fixed income models – including binomial lattice models r t is the risk-free rate that applies between periods t and t + 1 – it is a random process but r t is known by time t . 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The “Philosophy” of Fixed Income Derivatives Pricing We will simply specify risk-neutral probabilities for the short-rate, r t – without any reference to the true probabilities of the short-rate This is in contrast to the binomial model for stocks where we specified p and 1 - p – and then used replication arguments to obtain q and 1 - q . We will price securities in such a way that guarantees no-arbitrage Will match market prices of liquid securities via a calibration procedure – often the most challenging part. Will see that derivatives pricing in practice is really about extrapolating from liquid security prices to illiquid security prices. 4
Background image of page 4
Binomial Models for the Short-Rate ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± r 0 , 0 r 1 , 0 r 1 , 1 r 2 , 0 r 2 , 1 r 2 , 2 r 3 , 0 r 3 , 1 r 3 , 2 r 3 , 3 t = 0 t = 1 t = 2 t = 3 t = 4 We will take zero-coupon bond (zcb) prices to be our basic securities – will use Z k i , j for time i , state j price of a zcb that matures at time k Would like to specify binomial model by specifying all Z k i , j ’s at all nodes – possible but awkward if we want to ensure no-arbitrage .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 46

lecture_slides-TermStructure_Binomial_#1 - Financial...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online