Radical Complexity

This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.

Quantum Arithmetic for Directly Embedded Arrays

We describe a general-purpose framework to implement quantum algorithms relying upon an efficient handling of arrays. The cornerstone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding hampering square roots. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient toolkit of basic quantum operations on arrays. We comment on strong and weak points of the proposed quantum manipulations, especially in relation to an effective exploitation of quantum parallelism. We describe in detail some general-purpose routines as well as their embedding in full algorithms. Their efficiency is critically discussed both locally, at the level of the routine, and globally, at the level of the full algorithm. Finally, we comment on some applications in the quantitative finance domain.

The Theory of Uncertaintism

The stock jumps of the underlying assets underpinning the Margrabe options have been studied by Cheang and Chiarella [Cheang, GH and Chiarella C (2011). Exchange options under jump-diffusion dynamics. Applied Mathematical Finance, 18(3), 245–276], Cheang and Garces [Cheang, GHL and Garces LPDM (2020). Representation of exchange option prices under stochastic volatility jump-diffusion dynamics. Quantitative Finance, 20(2), 291–310], Cufaro Petroni and Sabino [Cufaro Petroni, N and Sabino P (2020). Pricing exchange options with correlated jump diffusion processes. Quantitate Finance, 20(11), 1811–1823], and Ma et al. [Ma, Y, Pan D and Wang T (2020). Exchange options under clustered jump dynamics. Quantitative Finance, 20(6), 949–967]. Although the authors argue that they explored stock jumps under Hawkes processes, those processes are the Poisson process in their applications. Thus, they studied Hawkes processes in-between two assets while this study explores Hawkes process within any asset. Furthermore, the Poisson process can be flipped into Hawkes process and vice versa. In terms of hedging, this study uses specific Greeks (rho and phi) while some of the mentioned studies used other Greeks (Delta, Theta, Vega, and Gamma). Moreover, hedging is carried out under static and dynamic environments. The results illustrate that the jumpy Margrabe option can be extended to complex barrier option and waiting to invest option. In addition, hedging strategies are robust both under static and dynamic environments.

Estimation of the Bid-Ask Prices for the European Discrete Geometric Average and Arithmetic Average Asian Options

Conic finance is a new and exciting development in quantitative finance, which is widely applied to several topics in finance. The theory of conic finance extends the law of one price to the law of two prices, which yields closed forms for bid-ask prices of European options. In this paper, within the framework of conic finance, we derive effective, explicit, approximate formulas to estimate the bid-ask prices for the European discrete geometric average and arithmetic average Asian options. Finally, we give two examples to demonstrate and validate that the approximate closed-form solutions are efficient and accurate.

“What good is a volatility model?” A reexamination after 20 years

This article is primarily a replication study of Engle and Patton (2001, Quantitative Finance 1: 237–245), but it also serves as a demonstration of the time-series features introduced into Stata over the past two decades. The dataset used in the original study is extended from the end date of the original sample on 22 August 2000 to 1 August 2017 to examine the robustness of the models.

Cognitive User Interface for Portfolio Optimization

This paper describes the development of a chatbot as a cognitive user interface for portfolio optimization. The financial portfolio optimization chatbot is proposed to provide an easy-to-use interface for portfolio optimization, including a wide range of investment objectives and flexibility to include a variety of constraints representing investment preferences when compared to existing online automated portfolio advisory services. Additionally, the use of a chatbot interface allows investors lacking a background in quantitative finance and optimization to utilize optimization services. The chatbot is capable of extracting investment preferences from natural text inputs, handling these inputs with a backend financial optimization solver, analyzing the results, and communicating the characteristics of the optimized portfolio back to the user. The architecture and design of the chatbot are presented, along with an implementation using the IBM Cloud, SS&C Algorithmics Portfolio Optimizer, and Slack as an example of this approach. The design and implementation using cloud applications provides scalability, potential performance improvements, and could inspire future applications for financial optimization services.