Hi I am really a begginer and have been given a project to do. This is what I believe I need to do in order to get started. Please help me out if you are more experienced and please tell me if I am on the right track.Now suppose that I the issuer of a convertble bond (that is callable after say two years with a callable value of X say) wishes to change my exposure from that of paying a fixed coupon to a floating one. I thus enter into a short position in an interest rate swap when the convertible bond is issued. Now when the stock price reaches this callble value the convertible bond is called implying in a sense that the holder of the bond is forced to convert the convertible bond into equity, at some time t<maturity. But now I am left with an interest rate swap right so I basically need to have an interest rate swap that knocks-out or ceases to exist when the converible bond is exercised. So that is my project in a nut shell. I need to be able to price such an interest rate swap.So I believe I have a payoff of:Principal*(fixed rate in swap - floating rate)*(Discount factor) , if the stock price < X=the callable value 0 , if the stock price >=XSo the way I thought of going about pricing this is to simulate a sock price path using monte carlo methods as well as an interest rate path for the floating rate path and as soon as the stock price hits X stop, look at the interest rate path up to that point calculate the payoff at each point and discount all the payoffs along the path.If you do believe I am on the right track, what I will need to know is what interest rate model do you think is more efficient? What is generally used in practice? Are there any journals that will be useful to me?Thank you so much, I will definitely appreciate any help I can get!

Hi Nachos.Its a interesting project to say the least . You are looking at a practical way of managing the exposure from the point of view of the issuer. since u are receiving fixed and paying floating on the interest rate swap. The easiest thing to do would be to buy a RECEIVER SWAPTION . with the maturity of the option equal to the call date from now. So once you callback your bond, u also exercise your option .Lets take a practical example . Lets assume you have a convertible bond with 5 years to maturity . which is callable after 1 year . At the same time you want to enter a Interest Rate Swap to receive fixed and pay floating . You can instead do this by buying receiver swaptions .It will basically be a 1*5 Receiver swaption. If the interest rates fall ur receiver swaption will be in the money , compensating you , for the bond portion of the convertible , Since u want to call it back, you also exercise your option, . In the event if the interest rates move up , u would be u could still call ur bonds and let your option expire OTM.hope this helps Amitabh

Amitabh's solution would do it, but it doesn't take into account the share price and whether you would need to exercise the swaption. Your ideal product is a swaption exercisable subject to a share price barrier being knocked in. This means that you need to take a model which:1. Is consistent with yield curve2. Is consistent with interest rate market vols (caplets etc)3. Is consistent with equity derivative market vols.So this is a really nasty 3-factor problem where the 3 factors are 2 interest rate factors and 1 equity factor. Typically you are better off using montecarlo than trying to build a finite difference scheme for 3 factors. Fortunately you don't need to consider credit risk as from the issuer's perspective this deal is risk free. So at least it's not a 4 factor problem.In general you are going to have a big problem estimating long dated interest rate and equity volatilities. But worse is the problem of trying to say something useful about the correlations between these things. This means that any value you get will be very suspect.To this end you need to find products which already exist (or which you can reliably price) such that these products super-replicate your payoff. i.e. that in any state of the world the value of the product is greater than or equal to the value of the nasty product you are trying to price. The price of this product will then form an upper bound for the price of the product you are trying to price. etc.A second solution is to try to find your natural counterparty and negotiate. In this case, it's the CB asset swapper, who has exactly the same problem, but the other way around. However ... CB asset swapping involves splitting the CB into credit, interest rate and equity components for a riskless profit. If an asset swapper can do this, why should you (as an issuer) sell a CB? Why don't you directly sell the separate pieces to the asset swapper's counterparties? i.e. just issue a straight bond plus equity warrants and swap the fixed to floating? Or just issue a floating rate CB? Or issue an FRN plus equity warrants? etc.This is a huge subject requiring a certain amount of thought. Lots to discuss.

In addition to Johnny's excellent reply, you have a difficult agency problem. Let's say interest rates go up a lot so the bond issuer would like to get out of the swap. It might call the bond to do that, even if calling the bond was not optimal without the swap. Therefore, I think the swap counterparty would prefer to cancel the swap if the bond issuer's equity reaches some pre-determined value (say the conversion price of the bond) rather than upon conversion.Another point is that the bond issuer might not want to get out of the swap when the bond is converted. Presumably, it wants floating rate exposure because that matches its cash flows. Even if it calls this particular bond, it may want to issue another bond. After all, there's no particular reason to pay down debt just because the stock price went up and you issued a lot of new equity. Even if it doesn't issue more debt, it may find that the swap cash flows fit its revenue, if that was true with the bond outstanding, it should be true afterwards.

I would like to thank you for your ideas, I think that I will definitely have to discuss the issues that have been brought up with my supervisors and see what happens. I will keep you informed on the progress.Thanks again!