Testing whether arbitrage opportunities exist in term structure

[wadswort]

Hi guys,

I'm simulating a term structure via the Vasicek model and then adding some spread to that curve. My final product is the curve with which I will discount my cash flows with. I am wondering how I can check to see whether any arbitrage opportunities exist on my simulated curve. Can you guys explain to me how to do this and whether you have any algorithmic/code suggestions I should keep in mind when I implement this.

Thanks

 

[aaronhotchner]

Arbitrage cannot exist with only one quoted rate. You have to arbitrage your rates against something else. So the short answer is that there are no arbitrage opportunities in your curve because that would be impossible.

 

[John]

If you do not calibrate your models to the market instrument being traded (the observables), any interest rate-based instrument (let's say zero coupon bond) that is being priced by your models , would introduce arbitrage opportunities for others, since almost surely, it (again using as example a zero coupon bond) would be mispriced (either too high or too low).

I suggest you calibrate your models (i.e. tweak the model parameters) so that at least you can approximate the value of zero-coupon bonds (or anything equivalent) being traded on the market.