In the past several years, leading quant teams have been utilizing Algorithmic Differentiation (AD) to accelerate their valuation and risk management calculations. While AD has only been applied in financial markets recently, the methodology is several decades old. For many years, this technique has been successfully applied to a variety of fields including Oceanography, Physics, Geology, Meteorology, Engineering, and many others.
But despite the proven advantages of using AD, such as staggering speed and accuracy improvements, for most financial firms, finite difference methods (known less formally as bumping) to calculate greeks and other sensitivities continues to be the status quo. The biggest problem with bumping is that it’s slow. As slow as a turtle one might analogize. An entire portfolio valuation is required for every sensitivity calculation. This means that firms have to sacrifice intra-day risk reporting and pre-trade risk and rely on overnight snapshots of their exposure.
Teams with complex multi-asset, multi-currency portfolios that need to bump, will often cut corners for overnight runs to reduce run-time. Typically they will elect to not bump every quote or bump curves using a parallel shift, twist, or other aggregate bump.
So with that said, if you can’t afford to bump every quote, then what should you bump? In other words, which risk factors matter most? Determining this, from a risk management perspective, is like trying to navigate a dark and dangerous landscape with a small flashlight. On the other hand, with AD, you don’t have to decide which quote you want to calculate portfolio sensitivities on. You see everything. Essentially, you trade your flashlight for a floodlight, yielding a complete view of the risk landscape. Sensitivities to every relevant quote – including intermediate ones – are available for a fraction of the cost.
I also cannot neglect to highlight the dramatic speed improvements with AD, which, for most firms, are in the realm of 100x – 1000x. Thus, managing exposure is no longer an overnight activity, but a pre-trade one.
There are a variety of tangible use cases for AD including the ability to hedge every exposure in your portfolio, reproject risk to form an alternative view of your exposure, and knowing how your risk profile changes under different market scenarios. The first and last use-cases are fairly well known, so for the purpose of this blog, I’d like to focus on risk re-projection.
With risk re-projection, you can transform sensitivities from one set of instruments into equivalent sensitivities for another set of instruments. Imagine you’re managing a long-only fund and you want to control your rate exposure but your mandate prohibits the use of contingent liabilities like swaps. You can measure your interest rate exposure with a model built from the swap market (Libor, OIS, etc.), but what you really need is to calculate exposure with respect to the medium-term notes that you’re actually allowed to trade.
The solution here is to use AD, which will allow you to transform your sensitivities to swap quotes into another set of sensitivities for medium-term note yields. This will enable you to build an effective interest rate hedge.
While AD is widely known for its speed enhancements in calculating risk, accuracy is another big area where the method excels. Bumping is an approximate technique and therefore subject to numerical noise. Among many questions, you’re faced with deciding how big a bump should be; whether a basis point is sufficient and whether it should be relative or absolute.
With AD, this fine-tuning goes away. What was once approximate now becomes exact and you get true analytic sensitivity. Additionally, when AD is used within calibration, things become more stable. The need to modify risk calculations is eliminated. Therefore, your quants are freed up to move onto more productive activities, saving your firm valuable time and resources.
For more information on AD, including FINCAD’s own patented implementation of the methodology known as Universal Algorithm Differentiation (UAD), download our eBook: Improving Risk Performance with Algorithmic Differentiation.
