Weak Markovian Approximations of Rough Heston

ArXiv ID: 2309.07023 “View on arXiv”

Authors: Unknown

Abstract

The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use Markovian approximations of the model. Several previous works have shown that these approximations can be very accurate even when the number of additional factors is very low. Existing error analysis is largely based on the strong error, corresponding to the $L^2$ distance between the kernels. Extending earlier results by [“Abi Jaber and El Euch, SIAM Journal on Financial Mathematics 10(2):309–349, 2019”], we show that the weak error of the Markovian approximations can be bounded using the $L^1$-error in the kernel approximation for general classes of payoff functions for European style options. Moreover, we give specific Markovian approximations which converge super-polynomially in the number of dimensions, and illustrate their numerical superiority in option pricing compared to previously existing approximations. The new approximations also work for the hyper-rough case $H > -1/2$.

Keywords: Rough Heston Model, Markovian Approximation, Option Pricing, Kernel Approximation, Stochastic Volatility, Derivatives (Options)

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper is heavily mathematical, focusing on theoretical error bounds using advanced stochastic calculus, fractional calculus, and PDE/Riccati equations for weak error analysis, with almost no mention of backtesting or implementation details.
  flowchart TD
    A["Research Goal: Analyze Weak Error of Markovian Approximations for Rough Heston"] --> B["Methodology: L^1 Kernel Error Analysis"]
    A --> C["Input: General Class of European Option Payoffs"]
    B --> D["Computation: Bound Weak Error via L^1 Distance"]
    C --> D
    D --> E["Computation: Construct New Super-Polynomial Approximations"]
    E --> F["Outcome: Accurate Option Pricing for H > -1/2"]