An investigation of model risk in a market with jumps and stochastic volatility

Coqueret, Guillaume; Tavin, Bertrand

doi:10.1016/j.ejor.2016.03.018

Cited by 18 publications

(14 citation statements)

References 34 publications

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“…However, it is shown in the literature that stochastic volatility effects can be added by means of time changes (see Carr and Wu, 2007, for example); the extension to the multidimensional case is though subject of current research. Further research concerning applications of the model proposed in this paper could be the analysis of model risk, with respect to the distributions corresponding to the processes indicated in Table 1, in the context of capturing the joint dynamics of FX rates and other securities, as well as pricing multinames FX derivative contracts in the spirit of Barrieu and Scandolo (2015); Coqueret and Tavin (2016).…”

Section: Discussionmentioning

confidence: 99%

Multivariate FX models with jumps: Triangles, Quantos and implied correlation

Ballotta

Deelstra

Rayée

2017

European Journal of Operational Research

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We propose an integrated model of the joint dynamics of FX rates and asset prices for the pricing of FX derivatives, including Quanto products; the model is based on a multivariate construction for Lévy processes which proves to be analytically tractable. The approach allows for simultaneous calibration to market volatility surfaces of currency triangles, and also gives access to market consistent information on dependence between the relevant variables. A successful joint calibration to real market data is presented for the particular case of the Variance Gamma process.

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Section: Discussionmentioning

confidence: 99%

Multivariate FX models with jumps: Triangles, Quantos and implied correlation

Ballotta

Deelstra

Rayée

2017

European Journal of Operational Research

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“…We use the FDHestonMEM, the characteristic function (13), and Formula (24) (COSbased method) to evaluate European puts. To test the effectiveness of the pricing method, we take the numerical integration method as a benchmark and set 64 points in Formula ( 24) and L = 10 in Formula (25).…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In fact, in a setting driven by standard Brownian motions, the studies in [10][11][12] by real data suggest the real asset price is not a continuous process but jumps occasionally. Moreover, extensive empirical studies [13][14][15] show that jumps and stochastic volatilities exist in the asset price. On the one hand, compared to the other jump distribution, the mixed-exponential jump [12] is more general in approximating asset return distributions; on the other hand, the double Heston model [16] exhibits good performance in fitting the long-term "volatility smile" and "volatility clustering".…”

Section: Introductionmentioning

confidence: 99%

Option Pricing with Fractional Stochastic Volatilities and Jumps

Zhang,

Yong,

Xiao

2023

Fractal Fract

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Empirical studies suggest that asset price fluctuations exhibit “long memory”, “volatility smile”, “volatility clustering” and asset prices present “jump”. To fit the above empirical characteristics of the market, this paper proposes a fractional stochastic volatility jump-diffusion model by combining two fractional stochastic volatilities with mixed-exponential jumps. The characteristic function of the log-return is expressed in terms of the solution of two-dimensional fractional Riccati equations of which closed-form solution does not exist. To obtain the explicit characteristic function, we approximate the pricing model by a semimartingale and convert fractional Riccati equations into a classic PDE. By the multi-dimensional Feynman-Kac theorem and the affine structure of the approximate model, we obtain the solution of the PDE with which the explicit characteristic function and its cumulants are derived. Based on the derived characteristic function and Fourier cosine series expansion, we obtain approximate European options prices. By differential evolution algorithm, we calibrate our approximate model and its two nested models to S&P 500 index options and obtain optimal parameter estimates of these models. Numerical results demonstrate the pricing method is fast and accurate. Empirical results demonstrate our approximate model fits the market best among the three models.

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“…They show that uncertainty in the portfolio's dependence is a source of huge model risk. Coqueret & Tavin (2016) investigate model risk for variance swaps and forward start options in a market with jumps and stochastic volatility and measured model risk based on the worst case risk measure.…”

Section: Introductionmentioning

confidence: 99%

Measuring Model Risk in Financial Risk Management and Pricing

Jokhadze

Schmidt

2020

Int. J. Theor. Appl. Finan.

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Risk measurement and pricing of financial positions are based on modeling assumptions, which are common assumptions on the probability distribution of the position’s outcomes. We associate a model with a probability measure and investigate model risk by considering a model space. First, we incorporate model risk into market risk measures by introducing model weighted and superposed market risk measures. Second, we quantify model risk itself and propose axioms for model risk measures. We introduce superposed model risk measures that quantify model risk relative to a reference model, which is the financial institution’s model of choice. Several risk measures that we propose require a probability distribution on the model space, which can be obtained from data by applying Bayesian analysis. Examples and a case study illustrate our approaches.

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An investigation of model risk in a market with jumps and stochastic volatility

Cited by 18 publications

References 34 publications

Multivariate FX models with jumps: Triangles, Quantos and implied correlation

Multivariate FX models with jumps: Triangles, Quantos and implied correlation

Option Pricing with Fractional Stochastic Volatilities and Jumps

Measuring Model Risk in Financial Risk Management and Pricing

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