Stochastic Interpolation

[jerome]

Stochastic Interpolation

[Anonymous]

Hi,

My question is concerned with the implemented/proposed approach of doing the interpolation on the risk factors. To explain in a bit more detail, the number of the dates for which the exposures are computed is usually fixed on a portfolio (i.e. not trade-by- trade basis) level. Given that it would be costly to generate these factors on every single trade date, this means we do not have the values of the risk factors on some of the fixing or exercise dates which in turn implies we need to have some method of the interpolation of some of the stochastic variables. Obviously, this can have a large impact especially for callable trades. One of the approaches proposed in the literature can be found in the book Modelling, Pricing, and Hedging Counterparty Credit Exposure (Cesari, G., Aquilina, J., Charpillon, N., Filipovic, Z., Lee, G., Manda, I.), page 122 – Martingale Interpolation. The other approach I have seen in the literature is using the Brownian Bridge technique. My question is which approach are you using or intend to use in the future? If you have any other suggestions/comments on the topic, it would be more than welcome.

Thanks,
Miro

[Peter Caspers]

Hi Miro,

in ORE we work around these issues by a) interpolating fixings backward flat between simulation dates and b) moving exercise dates effectively to the next simulation date. If you are interested in the details you can look at

a) https://github.com/OpenSourceRisk/Engine/blob/master/OREAnalytics/orea/simulation/fixingmanager.cpp
b) https://github.com/OpenSourceRisk/Engine/blob/master/OREData/ored/portfolio/optionwrapper.cpp

Of course this method introduces a bias in both cases, and the simulation grid has to be fine enough to control the resulting error. In the context of exposure simulation using regression techniques (a.k.a. American Monte Carlo) which you will probably resort to for callable exotics exposure simulation anyway, interpolation using a Brownian Bridge seems to be the most straightforward approach. However we do not provide our AMC engine as part of the open source libraries.

Best Regards
Peter

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