Alluve on A crash course in CVA cal… Alluve on CVA calculation example Alluve on Exposures are not additive: ca… govind pratap chand on Exposures are not additive: ca… Nina Nadia Q. Narvan… on A crash course in CVA cal…
Recently I was asked: “Are you not afraid of over-reliance on numerical methods in finance?”
Indeed, if I had to rely on numerical results in finance, I would be afraid. Continue reading
If we have a portfolio of vanilla trades (say, swaps), we can calculate EAD on each trade individually (an example is discussed here). Naturally, it is tempting to say that the exposure on the portfolio is the sum of the exposures on individual trades. That’s very wrong because exposures are not additive. Continue reading
This paper by S. Zhu and M. Pykhtin provides a blueprint for counterparty risk modelling framework.
Many believe that the calculation of exposure at default (EAD) on derivative contracts is fairly straightforward, so it can easily be done analytically. In many cases it is true, but not always.
Let us consider an easy case when EAD can be calculated analytically. By looking at how we do that, we will discover under which circumstances the method would not work.
If we know call option prices for every strike (underlying and expiry date being the same for all of the options), and the option price is a twice differentiable function of the strike, then we can calculate the probability density of the underlying on the expiry date. This density is implied by the option prices.
If C(K) is the price of the option with strike K, then the implied density of the underlying on expiry date is C”(K). Remarkably, this does not imply any particular model for the underlying process. This fact is well known, but I could not find a proof of it anywhere in the literature. To me, the following informal reasoning sounds pretty convincing.