Hi,I have a bond in a test portfolio - in which I want the outstanding notional to be dependent on the rate path. I looked at amortising swaps to get some idea, in the case of bonds, I know the the amortising rate can be defined to be date dependent i.e on given days the outstanding notional is clearly defined at time of issuance. How can I build this - i.e make the outstanding notional rate dependent.any pointers welcome.regards

Hi,I am not sure about what you want to do.Do you want to price this bond?Like you said, the notionnal can be date dependent. If you know initially which notionnal will be used at which date (not rate dependent but just date dependent), you can price your bond as usual with the sum of discounted cash flows.If the notionnal is a function of your rate, I think the pricing depends on the function, but you can always price it with Monte Carlo simulation.

I have a similar question where my notional does change. Annually, the notional will be mutlipied by the greater of the 30 year treasury bond yield and a floor, say 3%. To value such a contract, I was running running monte carlo simulations (running 10,000 currently). Here I project out 30 year yields and determine where the floor would be exercised on an annual basis and determine the payoff. I discount any payoff at the current zero coupon treasury yield rates for when the payoff happens. I'm not sure if discounting in such a manner the right way to do it. thoughts?When I do the above (assuming that is a reasonable approach) I struggle with how to model the 30 year interest yield process. Most of the model's I read about are for the short rate and not sure I can use them for the long rate. Even if I can use them for the long rate, I struggle with how to ensure they are risk-neutral. For example, if I extend the geometric brownian motion process model for stocks to the 30 year yield process (Ho-Lee's Oxford guide to financial modeling discusses this approach as do other texts) how do I ensure the process will produce a fair value? What do I use for the drift rate? It makes sense to me how to risk adjust the stock modeling process (basically set the drift rate to the risk free rate), but it's not clear how this works for the interest rate modeling process. thx.

Hi,-Either you assume deterministic rates and then you can initially know when your floor will apply.Then you discount your payoffs with exp (-\int_0^t r(s) ds) which is the same as ZC(0,t) in this case.But I don't think it is very appropriate in your case because you may need the zero coupon for very long maturities.-Or you assume stochastic rates and then I think you will have to model the entire yield curve (Hull White for example?) in the same time as your underlying. Then you discount again your payoffs with exp (-\int_0^t r(s) ds) which is not the same as ZC(0,t) in this case.