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I am looking at an implementation of Bjerksund and Stensland (2006), and notice that it doesn't work well for very small volatilities. What is a reasonable minimum volatility to use in an algorithm for calculating the implied volatility?

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  • $\begingroup$ In what way does it not work that well? Are there problems in the limits for the numerical implementation of the normal distribution? Or are the problems specific to details of the Bjerksund and Stensland model? $\endgroup$ – Mats Lind May 24 at 8:17
  • $\begingroup$ From what I saw when debugging, the issue is related to practical considerations when implementing in software. Putting a very small value for volatility can lead to very large values for phi that don't fit in a "double" value. $\endgroup$ – Franchesca May 24 at 9:12
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After some testing, it is clear that a value of 0.005 is the most reasonable minimum volatility to use with this model.

It is small enough to be a reasonable starting point (extremely unlikely that the real volatility of an option will be lower than this), while still being sufficiently high enough to avoid numerical issues when calculating implied volatility for out of the money options.

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