Window Barrier Options
This page demonstrates pricing of Window Barrier Options by solving corresponding partial differencial equations using finite difference method.
A barrier option is an exotic option on an underlying asset whose existence depends upon the underlying asset's price reaching pre-set barrier level:
the derivative either springs into existence (knock-in) or, if the option already exists, expires (knock-out).
Where the option springs into existence upon the underlying asset's price reaching the barrier level, it may be called an up and in, knock-in, or down and in option.
Where the option is terminated upon the underlying asset's price reaching the barrier level, it may be called an up and out, knock-out, or down and out option.
A barrier option has a lower premium than a similar option without a barrier. Barrier options were created to provide the hedge of an option at a lower premium than a conventional option.
A window barrier option is a type of barrier option for which the barrier strike is only active for a specific period during the option’s life.
That means the barrier commences at a particular date after starting the contract and terminates at a particular date before expiration.
If the underlying price breaches the barrier during the monitoring period (the window), then the option either knocks in or knocks out. Otherwise, it will terminate as an
ordinary option and expire at maturity. Holders of window barrier options can reign in the effect of volatility during the “window”, and hence hedge their views on the range of volatility showed by movement in the underlying’s price within a specific period.
| In/Out |
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| European/American |
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| Call/Put |
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| Spot |
\( S = \) |
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Please enter a value in range [0.01, 99999]
The input cannot be empty
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| Maturity (years) |
\( T = \) |
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Please enter a value in range [0.001, 150]
The input cannot be empty
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| Strike |
\( K = \) |
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Please enter a value in range [0.01, 99999]
The input cannot be empty
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| Interest rate |
\( r = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Volatility |
\( \sigma = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Dividend |
\( \delta = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Mesh size in asset S |
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Please enter an integer in range [10, 1,000]
The input cannot be empty
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| Number of time steps |
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Please enter an integer in range [10, 10,000]
The input cannot be empty
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| Number of Barrier Windows |
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| Barrier |
| Window One |
| Window Two |
| Window Three |
Note: if it is a single barrier, then the barrier level is a single input and it is
specified in the row of "Lower Barrier". |
Important! This model is for online demonstration purposes only. Calculations can take a long time if the number of times steps, barrier windows and mesh size are high. The time-out for calculations has been set to 1 hour, after which the webpage will return an error. We suggest you start with low values and then increase them if better accuracy is needed.