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[1] If the options are purchased, the position is known as a long strangle, while if the options are sold, it is known as a short strangle. A strangle is similar to a straddle position; the difference is that in a straddle, the two options have the same strike price. Given the same underlying security, strangle positions can be constructed with ...
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.
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.
As above, the PDE is expressed in a discretized form, using finite differences, and the evolution in the option price is then modelled using a lattice with corresponding dimensions: time runs from 0 to maturity; and price runs from 0 to a "high" value, such that the option is deeply in or out of the money. The option is then valued as follows: [5]
[1] [3] [4] A long call ladder consists of buying a call at one strike price and selling a call at each of two higher strike prices, while a long put ladder consists of buying a put at one strike price and selling a put at each of two lower strike prices. [1] A short ladder is the opposite position, in which one option is sold and the other two ...
Box spreads' name derives from the fact that the prices for the underlying options form a rectangular box in two columns of a quotation. An alternate name is "alligator spread," derived from the large number of trades required to open and close them "eating" one's profit via commission fees.