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Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
The risk-free rate is also a required input in financial calculations, such as the Black–Scholes formula for pricing stock options and the Sharpe ratio. Note that some finance and economic theories assume that market participants can borrow at the risk-free rate; in practice, very few (if any) borrowers have access to finance at the risk free ...
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the process of determining spot rate model inputs from observable bond market data.
Volatility and interest rate risk: Without regular interest payments to cushion price fluctuations, zero-coupon bonds are more volatile than short-term bonds. In general, the current value of any ...
Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates. Investment banks or dealers may separate coupons from the principal of coupon bonds, which is known as the residue, so that different investors may receive the principal and each of the coupon payments.
Short rate models are often classified as endogenous and exogenous. Endogenous short rate models are short rate models where the term structure of interest rates, or of zero-coupon bond prices (,), is an output of the model, so it is "inside the model" (endogenous) and is determined by the model parameters. Exogenous short rate models are ...
The zero-coupon bond will have the highest sensitivity, changing at a rate of 9.76% per 100bp change in yield. This means that if yields go up from 5% to 5.01% (a rise of 1bp) the price should fall by roughly 0.0976% or a change in price from $61.0271 per $100 notional to roughly $60.968.
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