## Monte Carlo methods for option pricing - Wikipedia

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Conversely, however, if an analytical technique for valuing the option exists—or even a numeric technique , such as a (modified) pricing tree [9] —Monte Carlo methods will usually be too slow to be competitive. They are, in a sense, a method of last resort; [9] see further under Monte Carlo methods in finance . With faster computing capability this computational constraint is less of a concern.

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Assume there are * n* assets in a basket and hence * n* correlated simulation
paths must be generated.
Hence at each time step in the simulation * n* correlated random numbers are
required.
Using the following notation,

Monte-Carlo methods differentiate themselves from other option pricing techniques in the way that potential future asset prices are generated. The following Simulating Asset Paths section describes how these paths may be generated for a standard log-normal model of equity asset prices. However, the technique may be applied to any asset that follows any stochastic process (where an associated random distibution exists from which samples may be obtained).

Main Drivers of an Option's Price

Let's start with the primary drivers of the price of an option: current stock price, intrinsic value, time to expiration or time value, and volatility. The current stock price is fairly obvious. The movement of the price of the stock up or down has a direct - although not equal - effect on the price of the option. As the price of a stock rises, the more likely the price of a call option will rise and the price of a put option will fall. If the stock price goes down, then the reverse will most likely happen to the price of the calls and puts . (For related reading, see ESOs: Using The Black-Scholes Model .)

Exchange traded options trading strategy evaluation tool & pricing calculators. Black-Scholes and the binomial model are used for option pricing . Pay-off ...

The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (tree), for 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.

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ITM stands for in-the-money and means if the option could be executed now, there would be a payoff. Thus for a call option the strike price is below the current price and for a put option it is above.