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On the White Board - July 2009
Jul 15, 2009
Stressing Skew
Like most option markets, swaptions and caps/floors exhibit a pronounced skew. Modeling this skew is important for pricing, but in order to generate effective stress tests, it is critical to also capture the dynamics of this skew. A common model that does this is SABR.
The skew in an options market can be represented graphically by plotting the implied volatility of a set of options against their strikes. If the market priced these assuming the future distribution of the underlying was log-normal, then this graph would be a horizontal line. In reality, this graph is usually a curved line. The accompanying figure illustrates this for Euro swaptions. The black dots represent the state of the market on June 9, 2009. One model that is often used for rates is termed the SABR model and the result of fitting this model to the market is shown as a solid black line. The vertical line shows the underlying (in this case a forward swap rate.)
The blue dots show the state of the market exactly one month later. The curved blue line is the result of adjusting only the forward rate to the new forward rate in the market. As can be seen, the model captures the new general shape of the skew. In practical terms, this means that if one is stressing LIBOR, one can expect the model to automatically generate realistic changes in the shape of the entire skew.
Aside from the shape the skew, the level of volatility may change in an unpredictable manner. Thus a refinement to a scenario that moves just rates, is one that also adjusts the ATM volatilities. Such a scenario might be generated explicitly by a stress test. An important source of such scenarios is simulation in order to compute historical or Monte Carlo VaR. In this case we want the model to capture the level of volatilities in each scenario. A natural way to accomplish this is to partially recalibrate the model to match the scenario ATM volatilities.