To calculate counterparty exposure, we need to know the volatility of our risk factors (interest rates, stock prices, etc.) in the future. Continue reading

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To calculate counterparty exposure, we need to know the volatility of our risk factors (interest rates, stock prices, etc.) in the future. Continue reading
Recently I was asked: “Are you not afraid of overreliance 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.
Continue reading
When I need to price a European option, I use Black formula rather than BlackScholes. Although both formulas give the same result when applied correctly, I think that Black formula is a bit more general. Let me show why.