Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.
In this article, we generalize the results of Markovian Projection onto a Heston model to a wider class of approximating models, a Heston model with displaced volatility. As an important application, we derive an effective approximation for FX/EQ options for the Heston model, coupled with correlated Gaussian interest rates. The main technical result is an option evaluation for correlated Heston/Lognormal processes.
Unlike the case of exactly solvable (affine) zero correlation or its uncorrelated displacement generalization, considered by Andreasen, non-trivial correlations destroy affine structure and exact solvability. Using the powerful technique of Markovian Projection onto a Heston model with displaced volatility, we produce an effective approximation and present its numerical confirmation.

Authors: A. Antonov, M. Arneguy and N. Audet

Download Numerix Research Paper

Complete the form below to download this complimentary research paper.

Select Form: 

Form #5: Research

Keep me informed of future research from Numerix:

Sign me up to receive "Thinking Derivatively" monthly newsletter by Numerix:

* Required fields
content collection

Numerix Quant Tech Resource Hub

on-demand webinar

SRP Europe Conference 2021: Optimizing Financial Valuations to Improve Investor Experience

on-demand webinar

QuantMinds 2020: Modelling Energy Curves for XVA


QuantMinds in Focus

on-demand webinar

Quantitative R&D Innovations Update

on-demand webinar

Neural Networks with Asymptotics Control

quantitative research

Machine Learning: Deep Asymptotics

quantitative research

Multi-curve Cheyette-style models with lower bounds on tenor basis spreads

written blog

Leading Numerix Through the Pandemic: Taking Action that Makes a Difference

next 2020 session video

Numerix Quantitative Research and Development Roundtable Discussion

written blog

How to Make the Smart Investment in FinTech

industry conference

QuantMinds International 2020