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### Current Value of Forward Price of Bond with Credit Spread

Posted: **November 19th, 2004, 3:12 pm**

by **RealIllusion**

Can anyone answer the following question: Suppose we have a bond with a "credit spread" over LIBOR, so that its spot price is calculated by discounting all future payments using a yield curve which is shifted above the ("risk-free") LIBOR curve, with the amount of the shift being equal to the credit spread. Now suppose we want the current value (at time t) of the forward price (at time T) of this bond, and that one coupon payment is due in between t and T. What is the current value of this forward price? Is it equal to the spot price of the bond, minus the current value of the aforementioned coupon payment as discounted by the shifted yield curve? Or is it equal to the spot price of the bond, minus the current value of the aforementioned coupon payment as discounted by the unshifted LIBOR curve?

### Current Value of Forward Price of Bond with Credit Spread

Posted: **November 22nd, 2004, 9:29 pm**

by **Aaron**

Neither one. Both of these are methods for computing the present value of the bond minus the first coupon payment, but the forward price must be compounded forward to the delivery date.It is not correct to discount at unshifted LIBOR, because the coupon payment is not risk-free. However, discounting at shifted LIBOR assumes the credit spread is constant at all tenors. This is unlikely to be true, but it might not make a significant difference in your case.You compound forward at unshifted LIBOR, assuming there is no credit risk to the forward transaction.

### Current Value of Forward Price of Bond with Credit Spread

Posted: **November 23rd, 2004, 10:34 am**

by **RealIllusion**

Aaron, many thanks for your reponse. I'm aware that, in order to obtain the forward price, we have to compound forward the spot price minus income, with compounding done at LIBOR. However, what I'm looking for is the current value of this forward price. To obtain this we discount the forward price back to the calculation date. I think that the end result of this calculation will give us the spot price of the bond, minus the coupon payment discounted at the appropriately shifted rate.I agree that the credit spread will in general be tenor-dependent, and that this should be taken into account when discounting the coupon. I was just seeking confirmation that the current value of the forward price comes out as the spot price minus the discounted coupon payment, with this discounting being done at the shifted rate rather than the LIBOR rate. (This is my view, but my colleague believes that the coupon should be discounted at LIBOR.)

### Current Value of Forward Price of Bond with Credit Spread

Posted: **November 23rd, 2004, 8:41 pm**

by **Aaron**

It would only make sense to discount the coupon payment at LIBOR if it were riskless. Someone might assume this if the credit spread were very steep. With a AA issuer, for example, there is almost no chance of a default within six months, the credit spread is almost entirely due to the risk of rating migration over several years.Another reason to assume this is if the forward contract were cancelled if the coupon payment were missed. A standard forward contract would not be, but some arrangements modeled as a forward contract have this feature. However, in this case you should really do a different calculation altogether since the payment of the coupon is obviously highly correlated with the value of the bond at delivery.