# How is the price of a bond actually determined?

How the price of a bond is actually determined? Is it the supply-demand that determines the price first and then the YTM is calculated on the back of this for that bond. Or is it that the changes to interest rate curve comes first and then the bond is priced using the typical discounting method and that becomes the price in stock market?

varies from market to market and from company to company... The methodology differs even for the US Treasury market (the most largest & most liquid govt bond market). Generally speaking, the benchmark bonds (2y, 3y, 5y, 7y, 10y, and 30y on-the-runs) are traded very very heavily and readily available. Their prices are driven by supply-demand. Non benchmark issues are priced using spreads to the benchmarks. Some firms (but not all) use a spline (smoothed curve) to price non-benchmark issues, but that's still just one input. Market microstructure information is paramount in eventual quoting.

At the end of the day, it's all supply-demand. As an example, this is the US Treasury yield curve from 2008... You can see having a discount curve model isn't really going to help you much...

Edit: Btw, price or yield first is strictly a convention. For example, US Treasuries are quoted on a price basis, but Australian bonds are quoted on a yield basis (if i remember correctly).

• Hello Hagline, Thanks for your input. Your answer prompts another question for non-benchmark bonds' spread. What determines their spread. I know about the Z-spread curve which is a fixed basis points above the benchmark curve. What determines the spread itself, for a given credit rating. Is the spread determined by demand-supply? Jul 21, 2014 at 6:44
• For govt's, yes, it's supply-demand. I don't know much about credit products, but my impression is that those guys use a matrix of spreads. A few points in the matrix might be marked based on market quotes, but most others are interpolated. Jul 25, 2014 at 3:04
• I don't know whether this is how traders mark credits, but this is how Barclays's Credit Index is priced: "Spreads are captured from pricing runs (~1000). Many of the spreads captured populate a set of issuer curves. The spreads captured also drive a spread matrix. The securities that are not driven by the issuer curves are marked using this matrix, driven by sector, quality and duration. This is seeded with the daily OAS percentage changes of the active trader marks. The spread with the updated Treasury curve is used to obtain dollar prices." (Source: Barcap Index Group publication) Jul 25, 2014 at 4:08
1. First of all bonds are not traded in the stock market. Bonds are traded in over-the-counter (OTC) markets (given they are already issued earlier) where buyers meet sellers and determine the price. This price is driven by the expectations of buyers and seller i.e. demand and supply.

2. YTM is linked to the price. A simple way to look at YTM is as the internal rate of return (IRR) on the bond investment since there will be cash flows on coupons (for coupon bond) and principal payment at maturity. The price can be determined by discount function (see next point) + credit risk + liquidity risk etc linked to the bond in question. So supply-demand -> Price and YTM

3. Pricing a bond: To keep things simple say you have a default-free bond i.e. there is no credit risk in the investment and all promised coupons will be paid on time. To compute the price of this bond you need the discount function for each tenor of the coupon. Discount function is the price of on-the-run treasury zero-coupon bonds/strips which pay $1 at maturity. Treasury strips are basically zero coupon bonds engineered from coupon treasury bonds and are very liquid instruments. So price of this bond will be given by: $$Price = \sum{CF_i*D(0,i)}$$ where$CF_i$is the cash flow from bond at time$i$and$D(0,i)$is the discount function i.e. present value of zero coupon treasury expiring at time$i$Since this "should" be the true price of the bond (we assumed default free bond) the no arbitrage principle will ensure market supply-demand keeps the price of the bond close to this value. Yield curve: Yield curve is basically a function of the$D(0,i)$. In the instance above we are using the spot yield curve since we are valuing a simple vanilla bond. In case you don't have values of$D(0,i)$for all$i$then people use interpolation methods to get the complete curve, which can include regression, cubic splines etc. for spot curve with yields quoted semi annually $$y_i = 2*(D(0,i)^{\frac{-1}{i}} - 1)$$ here$i$is the$i_{th}$cash flow so at time$t=0.5 yrs, i = 1$Cheers! • Thank Taran, for the reply. Can you tell me, how often does the yield curve change? Everyday, even by slight amount? Jul 22, 2014 at 6:17 • whenever the discount function moves the yield curves would move. As mentioned the discount function consist prices of zero-coupon highly liquid securities that pay$1 at maturity. So the YC would move after every tick in the market. If you like the answer please up vote it :) Jul 22, 2014 at 6:27
• Taran, Thanks for your reply. I think you got my question wrong. I am asking about the Yield-curve of US treasury bonds. I understand that this is interpolated across 11 keys rates and is used for constructing other curves by using adding a spread. So want to know weather these 11 keys rates are revised everyday? Jul 22, 2014 at 7:22
• Apologies if I got it wrong. So when you say key rates, you mean coupons or yields? Jul 22, 2014 at 7:31
• Well, key rates are the coupon rates of treasuries of certain standard maturities ( some 11 of them ). Jul 22, 2014 at 10:25