Model de prețuri cu opțiuni reale is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. 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.
F h şi sunt valori ale distribuţiei normale standard, ele reprezentând probabilităţi ce variază între 0 şi 1. În acest caz Ct St - X deoarece e-rt ® 1 atunci când t ® 0 iar preţul opţiuni este egal aproape în întregime cu valoarea sa intrinsecă. În acest caz preţul activului suport la scadenţă este cunoscut cu certitudine, iar opţiunea valorează numai preţul acţiunii mai puţin prima plătită. Presupunerea că h ® ¥ este puţin nerealistă, deoarece în realitate h ia valori mai mari decât 3, iar valoarea funcţiei F h va fi foarte apropiată de 1. Aceasta arată că, dacă preţul acţiunii este mare în raport cu preţul de exerciţiu al opţiunii, dacă opţiunea se apropie de scadenţă sau dacă dispersia activului suport tinde către zero atunci valoarea unei opţiuni va fi Ct St - X.
Being relatively simple, the model is readily implementable in computer software including a spreadsheet. Although computationally slower than gradul liniei de tendință 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.
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Monte Carlo methods in finance. However, the worst-case runtime of BOPM will be O 2nwhere 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.
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. 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.
Types of real options[ edit ] Simple Examples Investment This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example". Consider a firm that has the option to invest in a new factory.