Efficient and accurate simulation of the stochastic-alpha-beta-rho model

ArXiv ID: 2408.01898 “View on arXiv”

Authors: Unknown

Abstract

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and integrated variance. For the first sampling procedure, we sample the conditional integrated variance using the moment-matched shifted lognormal approximation. For the second sampling procedure, we approximate the conditional terminal forward price as a constant-elasticity-of-variance (CEV) distribution. Our CEV approximation preserves the martingale condition and precludes arbitrage, which is a key advantage over Islah’s approximation used in most SABR simulation schemes in the literature. We then adopt the exact sampling method of the CEV distribution based on the shifted-Poisson mixture Gamma random variable. Our enhanced procedures avoid the tedious Laplace inversion algorithm for sampling integrated variance and non-efficient inverse transform sampling of the forward price in some of the earlier simulation schemes. Numerical results demonstrate our simulation scheme to be highly efficient, accurate, and reliable.

Keywords: SABR model, Simulation, Constant-elasticity-of-variance (CEV), Moment-matched shifted lognormal, Integrated variance, Equity (Derivatives)

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents advanced mathematical derivations for moment matching and CEV sampling, but focuses on theoretical simulation methodology rather than providing backtest-ready results, code, or extensive empirical validation.

  flowchart TD
    A["Research Goal: Efficient & Accurate SABR Simulation"] --> B{"Data/Input: Market Parameters"};
    B --> C["Method: Sample Integrated Variance<br/>Moment-Matched Shifted Lognormal"];
    C --> D["Method: Sample Terminal Forward Price<br/>CEV Distribution Approximation"];
    D --> E["Compute: Exact Sampling via<br/>Shifted-Poisson Mixture Gamma"];
    E --> F["Key Findings: Arbitrage-Free & Highly Efficient<br/>& Reliable Scheme"];