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OPT-6 Exotics

Range Forward

Contract to buy/sell an asset at a future date for a price within some range, . The portfolio is constructed by longing a call with strike and shorting a put with strike . If , this is a regular forward.
Range Forward, composition and payoffs
Range Forward, composition and payoffs

Forward Start Options

Option starts at a future date, . It is commonly used in employee stock option plans. Strike price is determined at start date in reference to stock price at that time.
notion image
Forwar start option value is

Binary Options

Cash-or-Nothing
Pays if at time , otherwise pays 0.
Value = , where
Asset-or-Nothing
Pays is at time , otherwise pays 0.
Value = , where
Displaced Strike Call
Pays if at time , otherwise pays 0.
A package:
  • Long Asset-or-Nothing option
  • Short Cash-or-Nothing option
Value =
notion image

Lookback Options

Lookback call pays at time , allowing buyer to buy stock at lowest observed price in some interval of time.
Lookback put pays at time , allowing buyer to sell stock at highest observed price in some interval of time.

Asian Options

Payoff is related to average stock price,
  • Average Price options pay:
    • call:
    • put:
  • Average Strike options pay:
    • call:
    • put:

Rainbow Options

Rainbow options involve multiple securities, e.g. an option that pays
at time .

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