How Bond Prices, Yields, Curves, and Market Trading Relate

# How is the price of a bond actually determined?


# 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?

## Answer by Helin (score 1)

https://quant.stackexchange.com/a/14084

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).

## Answer by Taran (score 0)

https://quant.stackexchange.com/a/14117

- 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.

- 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



$$ Price = \sum{CF_i*D(0,i)} $$ 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!