Monte Carlo Simulation of Interest Rates and Prepayments

[Mesut]

What are your thoughts on how one would go about modelling these two practically? What steps would you follow?

 

[Colin McKee]

I my not be the best to answer this as I havent worked in ALM or financial stochastic modelling in the past. My only thought would be that its not going to be easy. Might be that someone else would know how its done.

 

[Mesut]

I suspect this is the province of risk modellers or quants. Would any of your colleagues in risk metrics (st9) or investments help lay down the steps? This being an applications paper, I thought it would be good (for work purpose... and pay rise) to actually have the steps for doing this rather than just passing the exam?

 

[David Wilmot]

It is tricky to convey something this complex in a short posting, however I hope that the attached provides you with the necessary information to pursue this avenue of research, if you wish to do so.

Interestingly, using PCA analysis of changes in the yield curve, the first three principal components typically 'explain' around 95% of the movement in spot rates at all maturities. They can be interpreted as changes to: level, slope and curvature. Each component can then be used to (stochastically) model possible future changes in the yield curve.

 

[Mesut]

Thanks so much. Planning to study this in detail now that the exam is over!

 

[Oxymoron]

Interest rates tend to have an inverse relationship of prepayments, since for mortgage type loans, as interest rates fall, it's easier to refinance it from an other borrowing.

Prepayment hazards are primarily classified by two parameters :- maturation (age of the contract) and calendar (event that affects all contracts owing to an economic event, such as changes in interest rates).

A dual time breslow/parametric markov chain method can be used to segregate the maturation effect from the calendar effect from the pre-payment hazard rate.

The calendar effect is then regressed with the economic variables (interest rates included). The economic variables can be orthogonalized with the PCA or modeled as a joint VaR - depending upon how you want it to be.

The economic variables are then simulated forward using a reasonable model of your choice - the expectation of calendar effect is then determined using the regression equation - and the regression idiosyncratic error is simulated and added to it.

 

[Mesut]

Now that is clear and concise...any chance you are a CERA?

 

[Oxymoron]

Now that is clear and concise...any chance you are a CERA?

nah - just done with 11 papers. I'm building this grand reserving model for my company which is involved in automotive financing. The model incorporates these components.

 

[Edwin]

Interest rates tend to have an inverse relationship of prepayments, since for mortgage type loans, as interest rates fall, it's easier to refinance it from an other borrowing.

Prepayment hazards are primarily classified by two parameters :- maturation (age of the contract) and calendar (event that affects all contracts owing to an economic event, such as changes in interest rates).

A dual time breslow/parametric markov chain method can be used to segregate the maturation effect from the calendar effect from the pre-payment hazard rate.

The calendar effect is then regressed with the economic variables (interest rates included). The economic variables can be orthogonalized with the PCA or modeled as a joint VaR - depending upon how you want it to be.

The economic variables are then simulated forward using a reasonable model of your choice - the expectation of calendar effect is then determined using the regression equation - and the regression idiosyncratic error is simulated and added to it.

you f****ng have an interesting job Ox!

 

[Oxymoron]

you f****ng have an interesting job Ox!

A small payoff for sacrificing study leaves, paper passing incentives and the security of being in insurance!