Abstract:
Slow greeks for callable instruments The speed of greeks calculations for non-cleared callable exotics is important with recent initial margin rules (ISDA SIMM) requiring daily sensitivities for a large set of risk factors. Such callable deals are priced using American Monte Carlo (regression) which is known to be computationally intensive leading to very slow greeks, if done by a simple bump-and-reprice.
Adjoint Differentiation (AD) as alternative The fast alternative is the AD but its direct application to exotics is not straightforward because regressions introduce path interdependency (the standard AD is applied path-by-path). Here, we extend the traditional AD method to include the regressions. However, the AD “weakness” is related with its tape (information recorded during the backward pricing): it can introduce memory issues (due to large storage), adds coding and debugging difficulties, etc.
New method (Backward differentiation (BD)) as a tapeless alternative to the AD The BD is applied during the backward pricing procedure. Importantly, it completely avoids the tape and all of its related complications. On example of a Bermudan swaption we demonstrate the efficiency: for 50–100 greeks, the BD calculation time is only 2–6 times slower than a single pricing which leads to up 20 times acceleration with respect to the bump-and-reprice.