Time Switch Options

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.

Pricing Time Switch Options

These exotic options were studied by Pechtl (1995). He developed these equations to describe the price of discrete time switch options.

Equations for the Payout of 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.

Download Excel Spreadsheet to Price Time Switch Options

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