# Can you use the Svensson model to fit a smoothed curve for yields on coupon paying bonds rather than spot rates?

i've been struggling to find an answer to this question online, I know most applications of the model are used on zero (aka spot) rates. But could you use yields from a sovereign yield curve (i.e coupon paying bonds) to find a smoothed curve?

thanks,

• As a smooth interpolator, you can use the model for whatever you want, eg to interpolate yield rates. But if you want to interpret it‘s fit as a zero curve, you need to plug the correct data into it. – Kermittfrog Apr 16 at 19:26

Recall that the zero coupon rates under the Svensson model can be calculated from $$y(t) = \beta_0 + \beta_1 \frac{1 - \exp(-t/\tau_1)}{t/\tau_1} + \beta_2 \left( \frac{1 - \exp(-t/\tau_1)}{t/\tau_1} - \exp(-t/\tau_1) \right) + \beta_3 \left( \frac{1 - \exp(-t/\tau_2)}{t/\tau_2} - \exp(-t/\tau_2) \right),$$ where $$\beta_0$$, $$\beta_1$$, $$\beta_2$$, $$\beta_3$$, $$\tau_1$$, and $$\tau_2$$ are the model parameters, and $$t$$ is time to maturity. The discount factor for time $$t$$ is then $$d(t) = \exp(-t\cdot y(t)).$$ In other words, given the model parameters, you can calculate discount factor corresponding to any future cash flow.
In a typical curve fitting exercise, you have a large collection of bonds, whose theoretical prices, or prices as determined by the Svensson model, can be obtained as $$P_i^\text{theoretical} = \sum c_i(t) \cdot d(t),$$ where $$c_i(t)$$ is the cashflow at time $$t$$ for bond $$i$$ (coupon payments and principal payments). From this $$P_i^\text{theoretical}$$, you can use the standard price-yield formula to calculate the theoretical yield, $$y_i^\text{theoretical}$$.
Our objective is then to find the model parameters (i.e., the $$\beta$$'s and $$\tau$$'s), such that the yield errors across all bonds are minimized (typically in a least squares sense): $$\min \sum_i \left(y_i^\text{quoted} - y_i^\text{theroetical}\right)^2.$$