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In the Black–Scholes model, the price of the option can be found by the formulas below. [27] 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 ...
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, which in general does not exist for the BOPM.
The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price.
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.
The most common form of a prediction market is a binary option market, which will expire at the price of 0 or 100%. Prediction markets can be thought of as belonging to the more general concept of crowdsourcing which is specially designed to aggregate information on particular topics of interest.
A range accrual can be seen as a strip of binary options, with a decreasing lag between fixing date and payment date. For this reason, it is important the valuation model is well calibrated to the volatility term structure of the underlying, at least at the strikes implied by the range.
A compound option is an option on another option, and as such presents the holder with two separate exercise dates and decisions. If the first exercise date arrives and the 'inner' option's market price is below the agreed strike the first option will be exercised (European style), giving the holder a further option at final maturity.
An option is path-independent if its value depends only on the final price of the underlying instrument. Path-dependent options depend not only on the final price of the underlying instrument, but also on all the prices leading to the final price. An exotic option could have one or more of the following features: