Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models
In this paper the authors derive stability and convergence of fully discrete approximation schemes of solutions to linear parabolic evolution equations governed by time-dependent coercive operators.
In this paper the authors formulate the one-dimensional RMQ and d-dimensional PMQ algorithms as standard vector quantization problems by deriving the density, distribution and lower partial expectation functions of the random variables to be quantized at…
This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance-reduction framework originally proposed by Heath and Platen.
This paper compares two methods to calibrate two popular models that are widely used for stochastic volatility modeling (ie, the SABR and Heston models) with the time series of options written on the Nasdaq 100 index to examine the regularization effect…
In this paper, the authors propose to approach the calibration problem of local volatility with Bayesian statistics to infer a conditional distribution over functions given observed data.
In this paper the authors show how the techniques introduced by Hurd and Zhou in 2010 can be used to derive a pricing framework for rainbow options by using the joint characteristic function of the logarithm of the underlying assets.
This paper looks at ways of solving (decoupled) forward–backward stochastic differential equations numerically using regression trees.
A new solution to calibrate derivatives with multiple strikes is proposed
This paper derives a new integral equation for American options under negative rates and shows how to solve this new equation through modifications to the modern and efficient algorithm of Andersen and Lake.
Expansion method for pricing foreign exchange options under stochastic volatility and interest rates
This paper applies the smart expansion method to the Heston–Hull–White model, which admits stochastic interest rates to enhance the model, and obtains the expansion formula for pricing options in the model up to second order.
The authors examine two potential routes to improve the outcome of option pricing: extracting the variance from futures prices instead of the underlying asset prices, and calculating the variance in different frequencies with intraday data instead of…
Convexity adjustments can be valued with an analytical formula, avoiding replication arguments
This work presents an efficient computational framework for pricing a general class of exotic and vanilla options under a versatile stochastic volatility model.
In this paper, the authors introduce two mixing fractions that can be controlled separately to apply impact to the volatility-of-volatility and the correlation in a lognormal LSV model.
New pricer for options with time-dependent barrier shown to be computationally efficient and stable
A new arbitrage-free volatility surface with closed-form valuation and local volatility is introduced
In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor-type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of…
Risk-neutral densities: advanced methods of estimating nonnormal options underlying asset prices and returns
This work expands the analysis in Cooper (1999) and Santos and Guerra (2014), and the performance of the nonstructural models in estimating the "true" RNDs was measured through a process that generates "true" RNDs that are closer to reality, due to the…
This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of convection–diffusion–reaction type.
Addressing model calibration and the issue of no-arbitrage in a deep learning approach
A variation of the rough volatility model is introduced by plugging in a different stochastic process
In this paper, the authors develop a new local correlation model that uses a generic function 'g' to describe the correlation between all asset–asset pairs for a basket of underlyings.
This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering.
This paper develops efficient importance sampling schemes for a class of jump–diffusion processes that are commonly used for modeling stock prices.