> But I doubt whether my calculation is precise enoughWell, you could try central differences on points (t-dt, t+dt) to estimate f(t) and you could try higher order estimates, like Richardson extrapolation, on (t-2*dt, t-dt, t+dt, t+2*dt), but I think that would be a waste of time. The error in each of your discount factors will limit how accurate you can get with f(t).Tell me why you think your calculation might not be precise enough. Also, how did you get your daily discount factors? There isn't enough market information to get a discount factor for every day. You have to have a model to extrapolate from a smaller set of points. It seems to me that your outputs can only have as much accuracy as what you put in.