(Whereas these options are more commonly valued using lattice based models, as above, for path dependent interest rate derivatives – such as CMOs – simulation is the primary technique employed. The same approach is used in valuing swaptions, where the value of the underlying swap is also a function of the evolving interest rate. Here, for each randomly generated yield curve we observe a different resultant bond price on the option's exercise date this bond price is then the input for the determination of the option's payoff. For example, for bond options the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. In other cases, the source of uncertainty may be at a remove.More generally though, simulation is employed for path dependent exotic derivatives, such as Asian options. Since the underlying random process is the same, for enough price paths, the value of a european option here should be the same as under Black–Scholes. Here the price of the underlying instrument S t is found via a random sampling from a normal distribution see further under Black–Scholes. An option on equity may be modelled with one source of uncertainty: the price of the underlying stock in question.This approach, although relatively straightforward, allows for increasing complexity: (3) These payoffs are then averaged and (4) discounted to today. The technique applied then, is (1) to generate a large number of possible, but random, price paths for the underlying (or underlyings) via simulation, and (2) to then calculate the associated exercise value (i.e. Here the price of the option is its discounted expected value see risk neutrality and rational pricing. In terms of theory, Monte Carlo valuation relies on risk neutral valuation. An important development was the introduction in 1996 by Carriere of Monte Carlo methods for options with early exercise features.
REAL OPTIONS VALUATION HOW TO
Glasserman showed how to price Asian options by Monte Carlo.
The first application to option pricing was by Phelim Boyle in 1977 (for European options). In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features.
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