Chooser option

In finance, a chooser option is a special type of option contract. It gives the purchaser a fixed period to decide whether the derivative will be a European call or put option.

In more detail, a chooser option has a specified decision time

      t
      
        1
      
    
  

{\displaystyle t_{1}}

, where the buyer has to make the decision described above. Finally, at the expiration time

      t
      
        2
      
    
  

{\displaystyle t_{2}}

the option expires. If the buyer has chosen that it should be a call option, the payout is

    max
    (
    S
    −
    K
    ,
    0
    )
  

{\displaystyle \max(S-K,0)}

. For the choice of a put option, the payout is

    max
    (
    K
    −
    S
    ,
    0
    )
  

{\displaystyle \max(K-S,0)}

. Here

    K
  

{\displaystyle K}

is the strike price of the option and

    S
  

{\displaystyle S}

is the stock price at expiry.

For stocks without dividend, the chooser option can be replicated using one call option with strike price

    K
  

{\displaystyle K}

and expiration time

      t
      
        2
      
    
  

{\displaystyle t_{2}}

, and one put option with strike price

    K
    
      e
      
        −
        r
        (
        
          t
          
            2
          
        
        −
        
          t
          
            1
          
        
        )
      
    
  

{\displaystyle Ke^{-r(t_{2}-t_{1})}}

and expiration time

      t
      
        1
      
    
  

{\displaystyle t_{1}}

;.

• Yue-Kuen Kwok, Compound options (from Derivatives Week and Encyclopedia of Financial Engineering and Risk Management) [1]

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