Regime Switching Rough Heston Model

Pricing Exotic Derivatives for Cryptocurrency Assets—A Monte Carlo Perspective

“…Rough volatility has lower price compare to the other models. This agrees with finding by [16] that rough volatility model prices are lower in general. Figure 5 shows implied volatility for all three models.…”

Inhomogeneous affine Volterra processes

“…Third, in Section 3, assuming a convolution kernel K(t, s) = K(t − s) we show existence of a solution to (1) and under the affine assumption (3) we prove that the conditional Fourier-Laplace functional is exponential-affine in the past path (X s ) s∈[0,t] . Finally, in Section 4, we apply our results to extend the rough Heston model introduced and studied by El Euch & Rosenbaum in [20] and [21] to the inhomogeneous case, which is used in mathematical finance, cf., e.g., Alfeus, Overbeck & Schlögl [10] and Alfeus, Nikitopoulos & Overbeck [9]. In the homogeneous case, comparable results can be found in Abi Jaber, Larsson & Pulido [8], which serves as our basic reference.…”

“…Recent research shows that these rough phenomena are important to give a more realistic description of the priced and observed volatility, cf., e.g., [7,6,1,21,19,26,35,20,13,27,25,32,34,10,9]. Time-inhomogeneous parameters in volatility modelling are considered in El Euch & Rosenbaum [20] where the conditional characteristic function of a rough Heston model with time-inhomogeneous mean-reversion level is studied, in Alfeus, Overbeck & Schlögl [10] where this is applied to a regime switching model and in Alfeus, Nikitopoulos & Overbeck [9] where a rough Heston model with time-dependent volatility is required. The analytic requirements of those models can be handled by our results in Section 4 on the inhomogeneous rough Heston model.…”

Power‐type derivatives for rough volatility with jumps

“…On the other hand, under the so‐called “rough Heston model” with a stationary power‐type kernel that belongs to the family of affine Volterra processes discussed in Jaber et al (2019) (see also Gatheral & Keller‐Ressel, 2019), characteristic function‐based pricing methods were developed in El Euch and Rosenbaum (2019), which depend, partially, on solving a fractional Riccati equation and whose applicability was also demonstrated by calibrating the S&P500 implied volatility surfaces; the paper El Euch and Rosenbaum (2018) considered from a theoretical standpoint similar hedging problems, after being able to write the characteristic function of the log‐asset price in terms of a function of its corresponding forward variance curve. We also notice the up‐to‐date work of Horvath et al (2020), which adopted a martingale framework using forward variance curves with the goal of studying volatility options, Xi and Wong (2021), which investigated the valuation of discrete variance swaps, and Alfeus et al (2019), which advanced the rough Heston model to include regime switching. It is worth mentioning that these recent works have universally emphasized the role of a Brownian motion, having paid little attention to jumps in asset prices and their volatility.…”