برآورد قیمت گذاری انتخاب موانع در یک سناریوی اینترنت اشیا Pricing estimation of a barrier option in an IoT scenario

1. Introduction In this paper we extend the methodology of [1] to the case of European barrier options. More precisely, we consider an IoT scenario1 extracting and managing very huge data and describe a mobile app which makes use of this information to estimate the no-arbitrage price of this kind of option. In IoT scenarios very sophisticated and efficient tools are able to infer, classify and store data coming from different types of sources (an example of a IoT financial data flow is presented in [3]). The advantages of this kind of approach is investors are updated about the conditions of the financial world and of new markets (for IoT we refer to [4,5]). Iot frameworks already find applications in different sectors: (i) monitoring of drivers’ performance in insurance (see [6]); (ii) creation of apps to improve trades, as Mobile Location Confirmation, Alfa-Bank Sense, Groceries by MasterCard; (iii) management of data in cultural heritage (see [7–9]). European barrier options are a very old and simple example of exotic options, and they can be defined as a vanilla (or basic) option to which some mathematical constraints, named barriers, are added. More precisely, as basic options, an investor is provided with the right to buy (Call) or to sell (Put) a quantity of a good (underlying) in a future date (maturity) by paying a further amount (strike price): the great difference consists in the presence of the barriers, which determines the beginning of the option (knock-in) or the end (knock-out). From a classification point of view, we distinguish different kinds of barrier options: (i) up (the initial value of the underlying is below the barriers) or down (the initial value of the underlying is above the barriers); (ii) discrete (the barriers are represented by a numerable set of values) or continuous (the barriers are a real regular function); (iii) single (the barrier is a real half-line) or double (the barrier is a delimited real interval). In this paper we focus our attention on single discrete down knock-out barrier options. Pricing a barrier option is a very complex, involving many sophisticated mathematical tool. In simple cases it is possible to achieve a closed for barrier option price: in the case of barrier options with continuous monitoring of the barrier (see [10]), or in the case of discrete barrier options by using the continuous barrier formulas with a correction (see [11]). In general, this topic can only be analyzed by using numerical techniques, in particular binomial and trinomial lattices [12], finite differences schemes [13] and integration [14], or statistical methodologies, in particular Monte Carlo methods [15,16]. The paper is organized in the following way. In Section 3 we introduce the analytical model we focus our attention on numerical issues and we present a numerical example; in Section 4 we draw the conclusions.