A learner-centered approach to design a Computational Finance module in higher education

In this paper, we describe our design of ACM30070 “Computational Finance”, a core module in the BSc in Financial Mathematics in the School of Mathematics and Statistics. The over-arching purpose of this module is to help students to develop mathematical, statistical and coding skills, along with significant knowledge and critical thinking, that allows them to effectively construct, manipulate and visualize financial datasets and to build financial mathematical models. The use of computation and a FinTech software (FinCad Analytics) are pointed out as essential to facilitate sensemaking in computational finance. More broadly, we discuss the education-research based rationale behind the “learning by doing” and “flipped classroom” institutional models that we have chosen for ACM30070, and we show how the modern “inclusive” definition of computation has been embedded into the learning activities. An accurate description of the design principles and implementation is also presented. At the end of the paper, we briefly introduce a discipline-based education research that will follow from this module design.

Forward start options under Heston affine jump-diffusions and stochastic interest rate

This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].

The sum of two independent polynomially-modified hyperbolic secant random variables with application in computational finance

In this paper, by reshaping the hyperbolic secant distribution using Hermite polynomial, we devise a polynomially-modified hyperbolic secant distribution which is more flexible than secant distribution to capture the skewness, heavy-tailedness and kurtosis of data. As a portfolio possibly consists of multiple assets, the distribution of the sum of independent polynomially-modified hyperbolic secant random variables is derived. In exceptional cases, we evaluate risk measures such as value at risk and expected shortfall (ES) for the sum of two independent polynomially-modified hyperbolic secant random variables. Finally, using real datasets from four international computers stocks, such as Adobe Systems, Microsoft, Nvidia and Symantec Corporations, the effectiveness of the proposed model is shown by the goodness of Gram–Charlier-like expansion of hyperbolic secant law, for performance of value at risk and ES estimation, both in and out of the sample period.

Implementing de-biased estimators using mixed sequences

We describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.

Computational Finance

The field of computational finance is evolving ever faster. This book collects a number of novel contributions on the use of computational methods and techniques for modelling financial asset prices, returns, and volatility, and on the use of numerical methods for pricing, hedging, and risk management of financial instruments.