On calibration of stochastic and fractional stochastic volatility models

Mrázek, Milan; Pospı́šil, J.; Sobotka, Tomáš

doi:10.1016/j.ejor.2016.04.033

Cited by 26 publications

(34 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Mrázek, Pospíšil, and Sobotka (2016) studied the calibration task for FSV model and compared it to the Heston case with respect to in-and out-of-sample errors on equity index data sets. Our study confirms that the approximative fractional model can outperform other studied SV models (see Table 1).…”

Section: Resultsmentioning

confidence: 99%

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

2018

Self Cite

View full text Add to dashboard Cite

In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the jump part in the underlying model dynamics. Also an impact of the long memory parameter is measured for the approximative fractional SV model. For the first time, the robustness of calibrated models is measured using bootstrapping methods on market data and Monte-Carlo filtering techniques. In contrast to several other sensitivity analysis approaches for SV models, the newly proposed methodology does not require independence of calibrated parameters -an assumption that is typically not satisfied in practice. Empirical study is performed on data sets of Apple Inc. equity options traded in April and May 2015.

show abstract

Section: Resultsmentioning

confidence: 99%

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…the calibration is now 4.3 times faster than the calibration procedure presented in [14]. In fact, the speed-up is even bigger, since in [14] the GA was run for more iterations than 10 and with population size 100, but to provide the meaningful comparison, in both tests we fixed the number of iterations in the first step of the calibration to be 10 and the population size to be 50 which seems to be sufficient for problems with five variables.…”

Section: Speed-up Using Approximationsmentioning

confidence: 99%

“…Following the methodology and results obtained by the authors in [13,14], we describe in more details the behaviour of all optimization techniques. We consider functions from MATLAB's Optimization Toolbox, genetic algorithm (GA) and simulated annealing (SA) as well as MATLAB's lsqnonlin using trust-region-reflective algorithm.…”

Section: Considered Optimization Techniquesmentioning

confidence: 99%

“…The bigger the spread the less weight is put on the particular difference between the model price and the market price during the calibration process. In [14], it was shown that weights calculated from the Black-Scholes vega greeks (denoted by weights D) can be the least suitable and hence we abandoned their usage as well as we have not normalized the weights and omitted also the equal weights E.…”

Section: Considered Weightsmentioning

confidence: 99%

“…Calibration of the Heston model together with the recent approximative fractional stochastic volatility model is briefly described and compared also in the author's papers [13,14], where only calibration results are presented. In this paper we focus on the Heston model only, for which we deeply compare not only calibration techniques, but also several simulation methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calibration and simulation of Heston model

Mrázek

Pospı́šil

2017

Open Mathematics

Self Cite

View full text Add to dashboard Cite

Abstract:We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods.We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.

show abstract

Unifying pricing formula for several stochastic volatility models with jumps

Baustian

Mrázek

Pospı́šil

et al. 2017

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce a unifying approach to option pricing under continuous-time stochastic volatility models with jumps. For European style options, a new semi-closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro-differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log-normal and a log-uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yan and Hanson, respectively. The comparison of existing and newly proposed option pricing formulas with respect to time efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out-of-the money contracts.Appl. Stochastic Models Bus. Ind. 2017, 33 422-442 F. BAUSTIAN ET AL. allows to have correlated increments of the asset price and the volatility process (as opposed to Stein and Stein [3]), which can mimic a volatility leverage effect observed on many financial markets. However, the model lacks the ability to fit reasonably well-complex option price surfaces [5,6], especially the ones that involve both short-dated and long-dated contracts.To deal with the drawbacks of the first SV models, many modifications have been introduced since, including a dynamic Heston model that involves time-dependent parameters. The case of piece-wise constant parameters in time is studied in Mikhailov and Ngel [7], a linear time dependence in Elices [8] and a more general case is analysed in Benhamou et al. [9]. The latter result introduces only an approximation of the option price. However, Bayer et al. [5] suggest that the general overall shape of the volatility surface does not change in time, at least to a first approximation given by stochastic volatility inspired (SVI) models. Hence, it is desirable to model volatility as a time-homogeneous process. Other generalizations of the Heston model with time-constant parameters include jump processes in asset price, in volatility or in both (e.g. Duffie et al. [10]). As Gatheral [11] notes (and supports by empirical analyses of several authors), a model with jumps in both underlying and volatility, although having more parameter and degrees of freedom, might not provide significantly better market fit than its counterpart with jumps in underlying only. The first SVJD model introduced in [12] adds a log-normally distributed jumps to the diffusion dynamics of the Heston model. Several different jump-diffusion settings were proposed, for example, models postulated by Scott [13] and Yan and Hanson [14] among others.Another possibility to modify standard diffusion SV models is to use a Lévy subordinator as a driving noise of the volatility process. This idea was firstly developed by where both volatility and as...

show abstract

On calibration of stochastic and fractional stochastic volatility models

Cited by 26 publications

References 26 publications

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Calibration and simulation of Heston model

Unifying pricing formula for several stochastic volatility models with jumps

Contact Info

Product

Resources

About