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For parity, the profit should be zero. Otherwise, there is a certain profit to be had by creating either a long box-spread if the profit is positive or a short box-spread if the profit is negative. [Normally, the discounted payoff would differ little from the net premium, and any nominal profit would be consumed by transaction costs.]
Margrabe's model of the market assumes only the existence of the two risky assets, whose prices, as usual, are assumed to follow a geometric Brownian motion.The volatilities of these Brownian motions do not need to be constant, but it is important that the volatility of S 1 /S 2, σ, is constant.
Using put–call parity a long butterfly can also be created as follows: Long 1 put with a strike price of (X + a) Short 2 puts with a strike price of X; Long 1 put with a strike price of (X − a) where X = the spot price and a > 0. All the options have the same expiration date. At expiration the value (but not the profit) of the butterfly ...
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For example, the delta of an option is the value an option changes due to a $1 move in the underlying commodity or equity/stock. See Risk factor (finance) § Financial risks for the market . To calculate 'impact of prices' the formula is: Impact of prices = option delta × price move; so if the price moves $100 and the option's delta is 0.05% ...
A call option is in the money when the strike price is below the spot price. A put option is in the money when the strike price is above the spot price. With an "in the money" call stock option, the current share price is greater than the strike price so exercising the option will give the owner of that option a profit.
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 ...
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