# MoCaX leverages from a blend of state-of-the-art mathematics and software optimisation techniques

It delivers a very special technologyMoCaX can increase Monte Carlo simulation speed by orders of magnitude. For example, with MoCaX Intelligence we can do **Monte Carlo within Monte Carlo**, ultrafast; this was meant to be quasi-impossible, until now.

The graphs below show exposure profiles for an European option (left panels) and American options (right panels), both uncollateralised (top panels) and collaterised (bottom panels). Each graph shows the profiles obtained using standard pricing functions (solid lines) and MoCaX Intelligence (dotted lines)*.

Taking the American option as an example, a classic exposure profile requires to price the derivative around one million times in each simulation (e.g., 10,000 scenarios, 100 time steps). That is, one million Monte Carlo simulations within the exposure Monte Carlo simulation. Using standard pricing techniques for this this job took 7 hours. However, we switched on MoCaX Intelligence and **computation time went from 7 hours to only 59 seconds**.

For example, here you can see the Black-Scholes function (top left panel), a zoom to it (top right panel) and the error that a linear Lattice method produces compared to MoCaX (bottom left panel).

With only 10 calls to the Black-Scholes function, **MoCaX’s accuracy** (red) is so good that it cannot be distinguished from the original function. However, a Lattice method error (blue) is obvious, large and biased.

Lattice methods may be good when they are all we have, but they are dangerous: they produce large, uncontrolled and biased errors. This is sub-optimal for accurate pricing and hedging, and the last thing regulators want these days.

The graph bellow shows a Black-Scholes pricer (left panel) and the error, in log scale, that MoCaX delivers compared to Lattice methods (right panel). **MoCaX achieves with only 10 anchor points* what a Lattice can only deliver with thousands of them**. Equivalent results can be obtained for any pricing function.

For example, in a Black-Scholes pricer, with only 10 anchor points, MoCaX achieves a precision of 0.000001, while that precision is only 0.01 with Lattice methods. Furthermore, with only 20 anchor points, **MoCaX is 100,000,000 more precise than standard Lattice methods**.

MoCaX convergence is so fast that we would need many thousand of anchor points in a Lattice method to achieve what MoCaX can do with only 10 or 20 of them.

**Have you ever seen anything like this?**

(*) Anchor points: points where the original function is called.

MoCaX applies **state-of-the-art research** in mathematics and software optimisation techniques to deliver an unparalleled product.

The result shown here for a Black-Scholes function is only one example. MoCaX technology **works with any pricing function**.

MoCaX provides an **outstanding technical edge** to be applied to any function that needs to be called repeatedly in a numerical simulation.

(*) Same results are obtained. Differences are due to numerical noise.