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Table of contents [ Hide ]. For a call put the terminal price is greater than less than the exercise price, the call put expires worthless. The exercise price is never paid. Instead, the value of the asset relative to the exercise price determines whether or not the option returns a payoff. The value of an asset-or-nothing call put option is the present value of the asset multiplied by the probability that the terminal price will be greater than less than the exercise price.
The option price is calculated analytically according to Cox and Rubinstein These options represents a contingent claim on a fraction of the underlying portfolio. The contingency is that the value of the portfolio must lie between a lower and an upper bound at expiration. If the value lies within these boundaries, the supershare is worth a proportion of the assets underlying the portfolio, else the supershare expires worthless.
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A supershare has a payoff that is basically like a spread of two asset-or-nothing calls, in which the owner of a supershare purchases an asset-or-nothing call with an strike price of the lower strike and sells an asset-or-nothing call with an strike price of the upper strike. The option price is calculated analytically according to Hakansson These options combine characteristics of both binary and barrier options.
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They are path dependent with a discontinuous payoff. Similar to barrier options, the payoff depends on whether or not the asset price crosses a predetermined barrier.
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There are 28 different types of binary barrier options, which can be divided into two main categories: Cash-or-nothing and Asset-or-nothing barrier options. Cash-or-nothing barrier options pay out a predetermined cash amount or nothing, depending on whether the asset price has hit the barrier. Asset-or-nothing barrier options pay out the value of the asset or nothing, depending on whether the asset price has crossed the barrier.
The barrier monitoring frequency can be adjusted to account for discrete monitoring using an approximation developed by Broadie, Glasserman, and Kou Binary-barrier options can be priced analytically using a model introduced by Reiner and Rubinstein Cox J. Hakkansson N. Haug E. Reiner E.