# The mathematical finance app store

Lorella Fatone, Dipartimento di Matematica e Informatica, Università di Camerino, Camerino, Italy,
Francesca Mariani, Dipartimento di Scienze Economiche, Università di Verona, Verona, Italy,
Maria Cristina Recchioni, Dipartimento di Management, Università Politecnica delle Marche, Ancona, Italy,
Francesco Zirilli, Dipartimento di Matematica G. Castelnuovo, Università di Roma "La Sapienza ", Roma, Italy.

This website contains a library of apps based on the research work in mathematical finance of the authors. The apps run on devices using the Android software system. The app library is organized as follows: each Mathematical Finance App (MFA) is characterized by a progressive number and by a title and can be freely downloaded clicking the corresponding button. A general reference to the work of the authors and of their coauthors in mathematical finance is the website http://www.econ.univpm.it/recchioni/finance.

The mathematical finance app store presentation VIDEO 2:20

MFA 1.    Moments Hull and White model

Content: This app computes the first two moments of the asset price variable in the Hull and White model. The moments are computed using two different approaches: explicit formulae and Monte Carlo method. The explicit formulae used in the app have been obtained in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, Some Explicit Formulae for the Hull and White Stochastic Volatility Model, International Journal of Modern Nonlinear Theory and Application 2, (2013), 14-33.

MFA 2.    Moments SABR model

Content: This app computes the m-th moment (0 < m ≤ 5) of the forward prices/rates variable in the SABR model with b Î (0,1). The moments are computed using two different approaches: explicit formulae and Monte Carlo method. The explicit formulae used in the app have been obtained in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, The SABR model: explicit formulae of the moments of the forward prices/rates variable, and series expansions of the transition probability density and of the option prices, Journal of Applied Mathematics and Physics, 2, 2014, 540-568.

Website:

MFA 3.    Optimal trading execution strategy

Content: This app is based on a model that describes the behaviour of a big trader and of a multitude of retail traders operating on the shares of a risky asset. The big trader wants to execute a liquidation order in a given time interval. The app computes the optimal trading execution strategy of the big trader, the mean value of the trading execution strategy of the retail traders and the asset price dynamics. The previous quantities are computed using explicit formulae obtained in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, A trading execution model based on mean field games and optimal control, Applied Mathematics, 5(19), 2014, 3091-3116

Website:

MFA 4.    American option prices and free boundaries

Content: This app evaluates the price and the free boundary of an American call or put option in the Black Scholes framework using a perturbation expansion that has the Barone-Adesi, Whaley formula as zero-th order term. The Barone-Adesi, Whaley formula, the first order approximation and the second order approximation resulting from the perturbation expansion of the price and of the free boundary of the American option considered are computed. The app is based on formulae that have been deduced in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, The Barone-Adesi Whaley formula to price American options revisited, Applied Mathematics, 6, 2015, 382-402.

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MFA 5.    A Dynamical Model of a Banking System

Content: This app shows the trajectories of a stochastic dynamical system describing an homogeneous population of banks. The trajectories represent the log-monetary reserves of the banks as a function of time. Two distinct mechanisms are used in the banking system model to describe the cooperation between banks and the cooperation between banks and monetary authority. These cooperation mechanisms produce a “swarming effect” in the trajectories of the log-monetary reserves of the banks. The banking system model used in this app has been introduced and studied in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, Systemic risk governance in a dynamical model of a banking system, submitted.

Website:

MFA 6.    Moments of the Stein-stein model

Content:This app computes the m-th moment (0 ≤ m ≤ 2) of the log-price variable of the Stein-Stein model. The moments are computed using two different approaches: explicit formulae and Monte Carlo method. The explicit formulae used in the app have been deduced in the paper:

Paper:  L. Fatone, F. Mariani, M.C. Recchioni, F. Zirilli, The Stein-Stein stochastic volatility model: transition probability density function, moment formulae, option pricing, implied volatility, calibration, submitted.

Website:

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