Calibration of Local Correlation Models. Notice to Skeptics of Particle Methods: With the Diffusion Implied Kernel, You Will Have No More Excuses!

In this paper we compare three ways of taking into account the basket skew by using a LVLC (Local Volatility Local Correlation) model. The two first methods were already presented in Langnau (2009) and Guyon and Henry-Labordère (2012). The third method, which is the main result of this paper, reduces the number of used particles by a factor of 10 and was inspired from Muguruza (2019).

This article is organized as follows. After a paragraph where we introduce the hypothesis and notations, we briefly present the final objective of the calibration. We then propose 3 solutions which are special cases of the (Guyon, 2017) framework:

• Method 1 does not require a conditional expectation calculation (and therefore has no calibration phase) is presented here for comparison

• Method 2 is based on the classical calculation of conditional expectations by choosing a Kernel and a bandwidth parameter

• Method 3 calculates the conditional expectations required by method 2 using the diffusion implied kernel

Then we move on to numerical results paragraph where we present honestly the benefits of the alternative method followed by the appendices where we provide the proofs of the propositions and the details of the calculations allowing to easily implement the diffusion implied kernel.