In a finance world, you usually derive a set of discount factors based on a set of market quotes (bootstrapping) and then you interpolate the discount factors using log-linear interpolation so in fact you use linear interpolation between zero rates.

Thanks @Confounded! Good point :)

I found the same article on XVA but on arxive.org: arxiv.org/pdf/2107.10377.pdf

Thanks for your input!

@dm63 I think your formula is incorrect. It should be rather $\int_{K}^{+\infty}(z-K)^{2}f(z)dz$ where $f(z)$ is a pdf of $L(t_{1};t_{1},t_{2})$. Note that, your formula is a price at time $0$ and $L(t_{1};t_{1},t_{2})$ is a random variable at time $0$, so it does not make any sense, does it?

I like your solution. Very elegant and therefore better than mine. :)

This would not take into account the dollar volume weights.

Thanks! In the case of the second question shall one compute the cumulative dollar volume, calculate 25% of this amount and then find the interest rate associated with this dollar volume?