Research articles for the 2021-03-14

A closed-form approximation for pricing geometric Istanbul options
Mohamed Amine Kacef,Kamal Boukhetala

The Istanbul options were first introduced by Michel Jacques in 1997. These derivatives are considered as an extension of the Asian options. In this paper, we propose an analytical approximation formula for a geometric Istanbul call option (GIC) under the Black-Scholes model. Our approximate pricing formula is obtained in closed-form using a second-order Taylor expansion. We compare our theoretical results with those of Monte-Carlo simulations using the control variates method. Finally, we study the effects of changes in the price of the underlying asset on the value of GIC.

A machine learning approach to portfolio pricing and risk management for high-dimensional problems
Lucio Fernandez-Arjona,Damir Filipović

We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces. We show results based on polynomial and neural network bases. Both offer superior results to naive Monte Carlo methods and other existing methods like least-squares Monte Carlo and replicating portfolios.

A new method for identifying changing marital preferences for race and education level
Anna Naszodi

In this paper, I generalize the Naszodi-Mendonca method in order to identify changes in marital preferences over multiple dimensions, such as the partners' race and education level. Similar to the original Naszodi-Mendonca method, preferences are identified by the generalized method through estimating their effects on marriage patterns, in particular, on the share of inter-racial couples, and the share of educationally homogamous couples. This is not a simple task because marriage patterns are shaped not only by marital preferences, but also by the distribution of marriageable males and females by traits. The generalized Naszodi-Mendonca method is designed for constructing counterfactuals to perform the decomposition. I illustrate the application of the generalized Naszodi-Mendonca method by decomposing changes in the prevalence of racial and educational homogamy in the 1980s using US data from IPUMS.

Electricity intraday price modeling with marked Hawkes processes
Thomas Deschatre,Pierre Gruet

We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity, random jump sizes but above all microstructure noise through the signature plot. This last feature is of particular importance for practitioners and has not yet been modeled on those particular markets. We provide analytic formulas for first and second moments and for the signature plot, extending the classic results of Bacry et al. (2013) in the context of Hawkes processes with random jump sizes and time dependent baseline intensity. The tractable model we propose is estimated on German data and seems to fit the data well. We also provide a result about the convergence of the price process to a Brownian motion with increasing volatility at macroscopic scales, highlighting the Samuelson effect.

Equilibrium Price Formation with a Major Player and its Mean Field Limit
Masaaki Fujii,Akihiko Takahashi

In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit.

Modern risks of small businesses
A.R Baghirzade

An important area of anti-crisis public administration is the development of small businesses. They are an important part of the economy of developed and developing countries, provide employment for a significant part of the population and tax revenues to budgets, and contribute to increased competition and the development of entrepreneurial abilities of citizens. Therefore, the primary task of the state Federal and regional policy is to reduce administrative barriers and risks, time and resources spent on opening and developing small businesses, problems with small businesses ' access to Bank capital [8], etc. Despite the loud statements of officials, administrative barriers to the development of small businesses in trade and public catering are constantly increasing, including during the 2014-2016 crisis.

Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models
Maximilian Beikirch,Simon Cramer,Martin Frank,Philipp Otte,Emma Pabich,Torsten Trimborn

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy-Levy-Solomon model and the Franke-Westerhoff model. We derive time-continuous formulations of both models, and in particular we discuss the impact of the time-scaling on the model behavior for the Levy-Levy-Solomon model. For the Franke-Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic desciptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy-Levy-Solomon and Franke-Westerhoff model.