# Time Switch Options

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.