Partial differential equation (PDE)
On the boundary conditions adopted in stochastic volatility option pricing models
The authors recommend boundary conditions that should be adopted when pricing European- and American-style options under the Heston model.
Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model
Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear partial differential equation (PDE). The authors propose numerical methods for…
Solving final value problems with deep learning
Pricing vanilla and exotic options with a deep learning approach for PDEs
Neural networks for option pricing and hedging: a literature review
This paper provides a comprehensive review of the field of neural networks, comparing articles in terms of input features, output variables, benchmark models, performance measures, data partition methods and underlying assets. Related work and…
The SABR forward smile
Thomas Roos presents the expressions for the implied volatilities of European and forward starting options
The homotopy analysis method for derivatives pricing under wrong-way risk
Derivatives pricing is approximated with a computationally efficient homotopy-based application that accounts for WWR
ADOL: Markovian approximation of a rough lognormal model
A variation of the rough volatility model is introduced by plugging in a different stochastic process
Efficient conservative second-order central-upwind schemes for option-pricing problems
In this paper, the authors propose improvements to the approach of Ramírez-Espinoza and Ehrhardt (2013) for option-pricing PDEs formulated in the conservative form.
Could machine learning improve CVA and IM calculations?
Banks have built ways to calculate CVA more quickly, but neural networks could offer more accurate method
CVA and IM: welcome to the machine
Henry-Labordere proposes a neural networks-based technique to price counterparty risk and initial margin
Pricing multidimensional financial derivatives with stochastic volatilities using the dimensional-adaptive combination technique
In this paper, the authors present a new and general approach to price derivatives based on the Black–Scholes partial differential equation (BS-PDE) in a multidimensional setting.
Quantitative finance still needs mathematicians
Quants develop model that fixes a longstanding problem with pricing American options
Local volatility from American options
De Marco and Henry-Labordère provide an approximation of American options in terms of the local volatility function
A new nonlinear partial differential equation in finance and a method of its solution
In this paper, the author considers a special type of nonlinear PDE that arises by applying optimization to some financial problems.
Bounding Bermudans
Thomas Roos derives model-independent bounds for amortising and accreting Bermudan swaptions
New execution algos show complexity is not to be feared
Quants develop method to include both market impact and limit orders in optimal trade execution
A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing
The authors introduce an RB space–time variational approach for parametric PPDEs with coefficient parameters and a variable initial condition.
A mixed Monte Carlo and partial differential equation variance reduction method for foreign exchange options under the Heston–Cox–Ingersoll–Ross model
The paper concerns a hybrid pricing method build upon a combination of Monte Carlo and PDE approach for FX options under the four-factor Heston-CIR model.
Pricing swing options in electricity markets with two stochastic factors using a partial differential equation approach
This paper considers the numerical valuation of swing options in electricity markets based on a two-factor model.
Time to gear up for MVA
Banks must be prepared for the looming rise of non-cleared margin requirements
MVA transfer pricing
Wujiang Lou extends liability-side pricing theory to initial margin