When I wrote my letter for the previous issue of The Journal of Computational Finance, I could not have imagined the world in which we now find ourselves. At this point, with many of us in physical isolation of an unpredictable duration, it is harder still to foresee the longer-term societal and economic consequences of the current crisis.
Robust mathematical and statistical modeling is now more important than ever. Our community – with its wealth of expertise in stochastic modeling, risk estimation, statistical data analysis and, not least, computational methods – is exceptionally well placed to predict and mitigate the effects of Covid-19, and to plan for similar outbreaks moving forward. I applaud everyone on the front line who is helping us to get through the present crisis, while more fundamental research develops methods that will play a vital role in the future.
Our first two papers in the present issue both consider derivative pricing with finite-difference schemes derived in a nonstandard way.
To begin, in “Option pricing in exponential Levy models with transaction costs”, Nicola Cantarutti, Manuel Guerra, Joao Guerra and Maria do Rosario Grossinho consider option pricing under transaction costs. They introduce a Markov chain approximation to the underlying jump model and formulate a dynamic programming prob- lem, ultimately demonstrating convergence and showing that the proposed method performs well numerically.
Next, in “Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode”, Reza Mollapourasl, Majid Haghi and Alfa Heryudono study in detail the application of a finite-difference scheme generated by radial basis functions to partial differential equations in option pricing.
Our third and fourth papers are devoted to Monte Carlo schemes for options with barrier features.
In “Monte Carlo pathwise sensitivities for barrier options”, Thomas Gerstner, Bastian Harrach and Daniel Roth derive pathwise sensitivities in Monte Carlo methods for options with discretely observed barriers. They specifically focus on the discontinuities of this payoff.
Finally, in “An adaptive Monte Carlo approach for pricing Parisian options with general boundaries”, Sercan Guur uses explicit hitting time distributions for the simulation of Parisian option payoffs with general boundaries, where the estimation is enhanced by an adaptive control variate strategy.
I hope that you are well and safe while reading the papers in this issue, and that the next time I write to you it will be under better circumstances.
University of Oxford
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.
In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions.
We present an approach for pricing European call options in the presence of proportional transaction costs, when the stock price follows a general exponential Lévy process.
This paper proposes a new, flexible framework using Monte Carlo methods to price Parisian options not only with constant boundaries but also with general curved boundaries.