Historical or implied?

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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Don't trust a model

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

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Exposures are not additive: case in point

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

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Counterparty risk calculation guide

This paper by S.  Zhu and M. Pykhtin provides a blueprint for counterparty risk modelling framework.

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Exposure at default calculation

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.

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Implied density of the underlying

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.
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Why I use Black formula rather than Black-Scholes

When I need to price a European option, I use Black formula rather than Black-Scholes. Although both formulas give the same result when applied correctly, I think that Black formula is a bit more general. Let me show why.

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