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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.
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.
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. "payoff") of the option for each path. (3) These payoffs are then averaged and (4) discounted to today.
For example, for stock RST and a long straddle consisting of a purchased call option with a price of $1.50 and a purchased put option with a price of $2.00 with a strike price of $50. Assume the initial price of RST is $50, and at option expiration, the price of RST is $55. % Return = [|55-50| - (1.5+2.0)]/(1.5+2.0) = 42.9%
A typical option strategy involves the purchase / selling of at least 2-3 different options (with different strikes and / or time to expiry), and the value of such portfolio may change in a very complex way. One very useful way to analyze and understand the behavior of a certain option strategy is by drawing its Profit graph.
[2] [3]: 180 In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option. [4]
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In finance, a price (premium) is paid or received for purchasing or selling options.This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.