Wilmott – Automatic Differentiation for the Greeks

By: Julia Computing, Inc.

Re-posted from: http://juliacomputing.com/blog/2017/04/26/Wilmott-AD-Greeks.html

Online quantitative finance magazine Wilmott featured Julia yet again.

Julia Computing’s Dr. Simon Byrne and Dr. Andrew Greenwell engage the magazine readers in a solution they built in Julia, that uses Automatic Differentiation (AD) to calculate price sensitivities, also known as the Greeks.

Fast and accurate calculation of these price sensitivities is extremely crucial in understanding the risk of an option position, and using AD in Julia achieves precisely that.

Traditionally, the world is familiar with using finite-difference approximation for the same calculations. Simon and Andrew go on to argue how that solution is numerically unstable, and how their solution will not only shoot up numerical accuracy, but will also eliminate computational overheads.

To put that in context, there are C++ libraries that assist in these calculations too, QuantLib being one of them. However, a simple implementation of a Cox–Ross–Rubinstein tree (for pricing an American put) with AD in Julia fared 3x times faster than with the C++ library. The code for this example is available here.You can also read the article to know more.

At Julia Computing, we curate all this and much more as part of JuliaFin, a suite of Julia packages that simplify the workflow for quantitative finance, including storage, retrieval, analysis and action.

Julia is already solving a variety of use cases. BlackRock, the
Federal Reserve Bank of New
York
, Nobel
Laureate Thomas J.
Sargent
,
and the world’s largest investment banks,
insurers,
risk managers, fund
managers
, asset
managers, foreign exchange
analysts
, energy
traders, commodity traders and others are all using Julia to solve some of their very complex and challenging quantitive computational problems.