Adjoint Delta for Monte-Carlo

In an earlier post, I have been quickly exploring adjoint differentiation in the context of analytical Black-Scholes. Today, I tried to mix it in a simple Black-Scholes Monte-Carlo as described in L. Capriotti paper, and measured the performance to compute delta compared to a numerical single sided finite difference delta.

I was a bit surprised that even on a single underlying, without any real optimization, adjoint delta was faster by a factor of nearly 40%. I suspect this is mostly due to exp evaluations being /2.

On a basket of 4 assets, the adjoint method was 3.25x faster.

It’s quick to have such results on basic payoffs: it took me a few hours and worked on the first run, even though my Monte-Carlo is slightly different from the Capriotti paper. It is much more challenging to have it working across a wide variety of payoffs, and to automatize some of it.

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