Learn about time switch options, and get a pricing spreadsheet.
The payout of time switch call options increases with how long the stock price is greater than strike price (and vice-versa for put options). The difference is checked every time step Δt. For an option that expires in one year, the time step is usually 1/250 (i.e. the reciprocal of the number of trading days).
In effect, the payout for each time step the stock price is greater than the strike price is A Δt, where A is an accumulated amount. The total is paid at maturity.
These exotic options were studied by Pechtl (1995). He developed these equations to describe the price of discrete time switch options.
- c and p are the price of call and put options
- A is the acumulated amount
- m is the number of fulfilled units
- σ is the volatility
- r is the risk-free rate
- b is the cost of carry
- S is the spot price
- T is the time to expiry
- Δt is the time step
- n is equal to T/Δt
This Excel spreadsheet uses the equations given by Pechtl (1995). The VBA can be viewed and edited.