Gap options are an example of exotic options. Their payoff depends on trigger price and strike price. The trigger price determines whether the gap option will have a nonzero payoff. The amount of payoff however depends on the strike price and the price of the underlying asset. The payoff can also be negative. Gap options are divided into gap call options and gap put options and they can be European or American. We can calculate the premium of a European gap option using the Black-Scholes formula for gap options. In order to use this formula, we must however know all market parameters. The relation between the premiums of the gap call option and the gap put option is known as put-call parity for gap call and put options. For European gap options, we can also calculate their Greeks as partial derivatives of the Black-Scholes formula with respect to market parameters. They can help us create a portfolio, with a value that is less susceptible to the changes of some market parameters.
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