It is my pleasure to introduce the latest issue of The Journal of Computational Finance. A focus of this issue is simulation and pricing under different stochastic volatility models.
In the issue’s first paper, “Simulating the Cox–Ingersoll–Ross and Heston processes: matching the first four moments”, Ostap Okhrin, Michael Rockinger, and Manuel Schmid investigate to what extent common simulation schemes for the Heston model accurately reproduce the moments of the distribution, with a focus on return skewness and kurtosis. Through the use of extensive experiments they reveal challenges, especially in parameter regimes where the Feller condition is not satisfied.
In “Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model”, our second paper, Florian Bourgey and Stefano De Marco provide a multilevel estimator for the integrated forward variance in the VIX formula. This results in optimal sampling complexity in spite of the need to evaluate a quadrature formula.
The third paper in the issue is “Pricing the correlation skew with normal mean– variance mixture copulas” by Ignacio Luján. Here, the author establishes semianalytical formulas for basket-type options in a mixture model. He demonstrates the model’s ability to fit market smiles – particularly correlation smiles – in a variety of market applications.
In our fourth and final paper, “Adjoint differentiation for generic matrix functions”, Andrei Goloubentsev, Dmitri Goloubentsev and Evgeny Lakshtanov derive an expression for the adjoint of matrix functions, which can be used as an essential building block in adjoint differentiation methods. They give illustrative examples, such as applications to the search for the nearest correlation matrix search and to regression regularization.
As ever, I wish you an interesting read.
This paper investigates various techniques for the CIR and Heston models.
The authors consider the pricing of the Chicago Board options Exchange VIX, demonstrating experiments highlighting the efficiency of a multilevel approach in pricing of VIX options.
The author puts forward a pricing methodology for European multi-asset derivatives that consists of a flexible copula-based method that can reproduce the correlation skew and is efficient enough for use with large baskets.
The authors develop and apply a formula to derive closed-form expressions in particular quantitative finance cases.