Parameters Recovery via Calibration in the Heston Model: A Comprehensive Review

Abstract

Numerous publications take a perfect recovery of the actual parameters during a calibration of stochastic volatility models, such as the Heston model and other continuous option pricing models, for granted. However, we show that this is a misleading assumption and that a high accuracy in capturing the true model parameters is not guaranteed for standard calibration approaches as they are commonly utilized in the financial industry. Having conducted several thousand model calibrations within an artificial testing environment, we are able to identify three factors that influence the resulting calibrated parameters strongly. These are the number of calibration instruments (i.e., option prices or implied Black-Scholes volatilities) available for the calibration, the error measure selected for the calibration, as well as the choice of initial values (particularly their distance to the known true model parameters). Using synthetic, yet generic, data instead of market observed data, we are able to avoid model risk and contribute purely to the literature on calibration risk. We quantify the impact of these factors on the calibration performance by measuring the calibration error (i.e., the distance between the calibrated and known true model parameters). Based on our numerical results, we are able to derive conclusions which can be useful for academics and practitioners alike. We further specify a calibration setup which does not assure, but significantly increases, the probability of a perfect or near-perfect model calibration.

Robust Product Markovian Quantization

“…where F is the objective or error function and Θ = {y 0 , β, ν, ρ} is the parameter set for the SABR model. In Escobar and Gschnaidtner (2016) the relative squared volatility error (RSVE) is recommended as the objective function for calibrating the Heston model, and it is adopted here. It is defined as…”

Political risk modelling and measurement from stochastic volatility models

“…Whilst it is possible to calibrate the Heston model to real world market data, which would provide risk measurement results related to real market data, we restrict our analysis to the specified model values. The reader is referred to papers such as (Cui et al, 2017a), or (Escobar and Gschnaidtner, 2016), for more information on calibrating the Heston model to real world market data. In Figure 1, we illustrate the conditional transition densities of the volatility process for a model with n = 40 Markov states.…”