The interest rate risk of a bond may be measured by how much its price changes as interest rates change. The change in the price of a fixed-rate coupon bond when market interest rates change is due to the fact that the bond’s coupon rate differs from the prevailing market interest rate. When a bond’s coupon is higher than the market interest-rate the demand for the bond will increase which will drive its price up. Inversely, when the coupon is lower than the market interest-rate, investors will favor newly issued bonds paying higher coupons which will drive the price down.
Two-way bond prices advertised by dealers on electronic trading platforms are valid for immediate delivery. These prices are called spot prices. A client that wishes the security to be delivered at a particular date in the future will implicitly enter in a forward contract with the dealer. The forward price refers to the price of that contract. The term forward date refers to the date of that future purchase or sale. By convention, the forward price is quoted as a flat price. The invoice price of the transaction equals the forward price plus accrued interest at the forward date.
When working with Fixed Income trading systems we are often confronted with the requirement to implement a bond security Price/Yield conversion service. Many Finance textbooks describe the computation but the provided formulas are too academic and examples are provided only for the special case when the valuation date coincides with the coupon payment date. This post aims to provide a step-by-step explanation of the Price/Yield conversion used by market practitioners and valid for any valuation date.