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The discrete difference equations may then be solved iteratively to calculate a price for the option. [4] The approach arises since the evolution of the option value can be modelled via a partial differential equation (PDE), as a function of (at least) time and price of underlying; see for example the Black–Scholes PDE. Once in this form, a ...
A long iron butterfly will attain maximum losses when the stock price falls at or below the lower strike price of the put or rises above or equal to the higher strike of the call purchased. The difference in strike price between the calls or puts subtracted by the premium received when entering the trade is the maximum loss accepted.
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.
(Note that the alternative valuation approach, arbitrage-free pricing, yields identical results; see “delta-hedging”.) This result is the "Binomial Value". It represents the fair price of the derivative at a particular point in time (i.e. at each node), given the evolution in the price of the underlying to that point.
A condor is also known as a "stretched butterfly", as its maximum profit is reached on a wider range of underlying prices compared to a butterfly. [6] Both butterflies and condors are known as "wingspreads". [1] The condor is so named because of its payoff diagram's perceived resemblance to a large bird such as a condor. [6]
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Brian K. Boonstra: Model For Pricing ESOs (Excel spreadsheet and VBA code) Joseph A. D’Urso: Valuing Employee Stock Options (Excel spreadsheet) Thomas Ho: Employee Stock Option Model Archived 2016-03-04 at the Wayback Machine (Excel spreadsheet) John Hull: software based on the article: How to Value Employee Stock Options (Excel spreadsheet)
where is the continuously compounded risk free rate of return, and T is the time to maturity. The intuition behind this result is that given you want to own the asset at time T , there should be no difference in a perfect capital market between buying the asset today and holding it and buying the forward contract and taking delivery.