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This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point.
Informatica 23 11 2020
As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time.
Being relatively simple, the model is readily implementable in computer software including a spreadsheet.
This article's tone or style may not reflect the encyclopedic tone used on Wikipedia. See Wikipedia's guide to writing better articles for suggestions. From the partial differential equation in the model, known as the Black—Scholes equationone can deduce the Black—Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the modelul valorii opțiunii of the security and its expected return instead replacing the security's expected return with the risk-neutral rate. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. Merton was the first to publish a modelul valorii opțiunii expanding the mathematical understanding of the options pricing model, and coined the term "Black—Scholes options pricing model".
Although computationally slower than the Black—Scholes formulait is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets.
When simulating a small number of time steps Monte Carlo simulation will be more computationally time-consuming than BOPM cf. Monte Carlo methods in finance. Modelul valorii opțiunii, the worst-case runtime of BOPM will be O 2nmodelul valorii opțiunii n is the number of time steps in the simulation.
Monte Carlo simulations will generally have a polynomial time complexityand will be faster for large numbers of simulation steps. Monte Carlo simulations are also less susceptible to sampling errors, since binomial techniques use discrete time units.
Sunteți pe pagina 1din 14 Căutați în document Există două modele de evaluare a opţiunilor: modelul Black - Scholes şi modelul binomial. Cele doua tipuri de modele se bazează pe raţionamente de arbitraj şi hedging şi pornesc de la premisa că piaţa nu permite operaţiuni de arbitraj.
This becomes more true the smaller the discrete units become. This is done by means of a binomial lattice treefor a number of time steps between the valuation and expiration dates.
Each node in the lattice represents a possible price of the underlying at a given point in time.
Mai jos poate fi vizualizat un extras din document aprox. Arhiva contine 1 fisier doc de 7 pagini. Ai nevoie de doar 4 puncte. Descarcă acum Extras din document O optiune de vânzare PUT cumparare CALL reprezinta dreptul de a cumpara sau de a vinde un portofoliu de active suport la un pret determinat înainte sau la o data determinata.
Valuation is performed iteratively, starting at each of the final nodes those that may be reached at the time of expirationand then working backwards through the tree towards the first node valuation date. The value computed at each stage is the value of the option at that point in time.
Option valuation using this method is, as described, a three-step process: price tree generation, calculation of option value at each final node, sequential calculation of the option value at each preceding node.
Step 1: Create the binomial price tree[ edit ] The tree of prices is produced by working forward from valuation date to expiration.
At each step, it is assumed that the underlying instrument will move up or down by a specific factor u.