Category Archives: Finance

A crash course in CVA calculation

Recently I was asked by a student to give some guidance on using Monte Carlo method for CVA calculation. Here is what I came up with.

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CVA calculation example

Let’s calculate CVA (credit value adjustment) analytically. We will see that analytical CVA calculation is quite complex even for a fairly simple transaction (a vanilla swap). A few shortcuts will help us simplify the calculation.

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The dreadful 40-60 rule

When we have to calculate exposure at default (EAD) on a particular trade, we seldom have to compute it analytically (e.g. as shown here). More often we just take the current MtM of the trade and add the so-called add-on. … Continue reading

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Historical or implied?

To calculate counterparty exposure, we need to calibrate our scenario generator to historical data. However, for CVA calculations, we need scenarios based on implied volatilities of the underlying risk factors. Continue reading

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Exposures are not additive: case in point

Potential exposure is not additive: the total exposure on two trades can be very different than the sum of potential exposures on each trade. 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

Exposure at default calculation for one contract can be done analytically, but for a big portfolio one has to resort to Monte-Carlo simulation. Continue reading

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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. Continue reading

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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. Continue reading

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Pricing interest rate swaps

To price an interest rate swap (e.g. fixed versus 6 months LIBOR paid semi-annually), one needs to use 2 zero-rate curves: a discount curve and a prediction curve (a.k.a. forecast curve). This article by Bruce Tuckman and Pedro Porfirio gives … Continue reading

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