Journal of Computational Finance

Christoph Reisinger
University of Oxford

I am delighted to introduce this issue of The Journal of Computational Finance. The three papers herein provide novel insights on the themes of numerical option pricing and hedging, approximation and arbitrage.

In our first paper, “Option pricing under the normal stochastic alpha–beta–rho model with Gaussian quadratures”, Jaehyuk Choi and Byoung Ki Seo consider accurate and arbitrage-free numerical schemes for the classical SABR model. Based on analytical transition densities, their quadrature scheme gives option prices and deltas to within a single basis point and percentage point, respectively, for a small number of nodes. This avoids traditional closed-form approximations that may introduce arbitrage.

Staying on the theme of stochastic volatility models, Song-Ping Zhu and Chun- Yang Liu take a partial differential equations (PDEs) perspective in their paper “On the boundary conditions adopted in stochastic volatility option pricing models”. Their paper aims to fill a gap in the literature by investigating the effect of posing conditions on the boundaries of the computational domain, as required in the implementation of numerical PDE schemes. The authors first conduct a comprehensive review of the literature on various boundary conditions used in the past and then carry out comprehensive numerical tests. In particular, they suggest appropriate boundary conditions that should be adopted for pricing European- and American-style options under the Heston model.

In the issue’s third and final paper, “Multiperiod static hedging of European options”, Purba Banerjee, Srikanth Iyer and Shashi Jain consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework and offer an extension of Carr and Wu’s well-known static hedging approach to short-dated hedging options with multiple maturities. Moreover, they provide a practical implementation using a realistic number of hedges based on Gaussian quadrature to determine the hedging error, and they then test this against Black–Scholes and Merton jump-diffusion benchmark models.

I hope you will find these papers enjoyable, and I also hope that you will find that their novel methodologies stimulate ideas for further research and applications.