# Diamonds and forward variance models

@inproceedings{Friz2022DiamondsAF, title={Diamonds and forward variance models}, author={Peter K. Friz and Jim Gatheral}, year={2022} }

In this non-technical introduction to diamond trees and forests, we focus on their application to computation in stochastic volatility models written in forward variance form, rough volatility models in particular.

## References

SHOWING 1-10 OF 18 REFERENCES

### Option Valuation under Stochastic Volatility

- Economics
- 2000

This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other…

### Option valuation using the fast Fourier transform

- Business
- 1999

This paper shows how the fast Fourier Transform may be used to value options when the characteristic function of the return is known analytically.

### Exponentiation of conditional expectations under stochastic volatility

- MathematicsQuantitative Finance
- 2019

We use the Itô Decomposition Formula (see Alòs [A decomposition formula for option prices in the Heston model and applications to option pricing approximation. Finance Stoch., 2012, 16(3), 403–422])…

### Pricing under rough volatility

- Mathematics
- 2015

From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance…

### VOLATILITY DERIVATIVES AND MODEL-FREE IMPLIED LEVERAGE

- Economics
- 2014

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract…

### The characteristic function of rough Heston models

- Mathematics
- 2016

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to…

### The Volatility Surface: A Practitioner's Guide

- Economics
- 2006

List of Figures. List of Tables. Foreword. Preface. Acknowledgments. Chapter 1: Stochastic Volatility and Local Volatility. Stochastic Volatility. Derivation of the Valuation Equation, Local…

### Rational Approximation of the Rough Heston Solution

- Computer Science
- 2019

A simple rational approximation to the solution of the rough Heston Riccati equation valid in a region of its domain relevant to option valuation is presented and pricing using this approximation is both fast and very accurate.

### Affine forward variance models

- MathematicsFinance and Stochastics
- 2019

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterised…

### Affine Volterra processes

- MathematicsThe Annals of Applied Probability
- 2019

We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine…