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  2. Monte Carlo methods for option pricing - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_methods_for...

    The first application to option pricing was by Phelim Boyle in 1977 (for European options). In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. An important development was the introduction in 1996 by Carriere of Monte Carlo methods for options with early exercise features.

  3. Binomial options pricing model - Wikipedia

    en.wikipedia.org/wiki/Binomial_options_pricing_model

    In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" ( lattice based ) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting.

  4. Trinomial tree - Wikipedia

    en.wikipedia.org/wiki/Trinomial_Tree

    The trinomial tree is a lattice-based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option ...

  5. Black's approximation - Wikipedia

    en.wikipedia.org/wiki/Black's_approximation

    One such approximation is described here. See also Black–Scholes model#American options. The method essentially entails using the BS formula to compute the value of two European call options: (1) A European call with the same maturity as the American call being valued, but with the stock price reduced by the present value of the dividend, and

  6. Black–Scholes model - Wikipedia

    en.wikipedia.org/wiki/Black–Scholes_model

    In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put—the binary options are easier to analyze, and correspond to the two terms in the Black–Scholes formula.

  7. Margrabe's formula - Wikipedia

    en.wikipedia.org/wiki/Margrabe's_formula

    The payoff of the option, repriced under this change of numeraire, is max(0, S 1 (T)/S 2 (T) - 1). So the original option has become a call option on the first asset (with its numeraire pricing) with a strike of 1 unit of the riskless asset. Note the dividend rate q 1 of the first asset remains the same even with change of pricing.

  8. Lattice model (finance) - Wikipedia

    en.wikipedia.org/wiki/Lattice_model_(finance)

    Here, options with differing strikes will return differing implied volatilities, and the tree may then be calibrated to the volatility smile, by a "judicious choice" [21] of parameter values. For pricing American options, the valuation will be on an R-IBT as combined with the calibrated maturity distribution.

  9. Option style - Wikipedia

    en.wikipedia.org/wiki/Option_style

    If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black–Scholes price of a European option that is equivalent to the American option (except for the exercise dates). The difference between the two prices can then be used to calibrate the more complex American option model.

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