Choosing a Minimum Volatility for Bjerksund–Stensland Implied Volatility

Summary

The note discusses numerical instability when using the Bjerksund–Stensland 2006 option pricing model at very low volatility, especially when solving for implied volatility on out-of-the-money options. It offers a practical parameter choice: use a minimum volatility of 0.005 as a lower bound for the calculation.

The recommendation is based on testing reported by the answer author. The floor is described as low enough to serve as a reasonable starting point while avoiding numerical problems. The document gives no test details, error measurements, market examples, or analysis of how the choice depends on option inputs or implementation, so the value should be treated as a heuristic rather than a generally validated threshold.

Key ideas

• A low volatility input can cause numerical problems in Bjerksund–Stensland implied volatility calculations.
• The answer recommends a minimum volatility of 0.005, based on the author's testing.
• The stated motivation is to avoid instability for out-of-the-money options while retaining a low starting value.
• The document does not provide test methodology or evidence that the same floor suits every implementation.

Tags

# Bjerksund and Stensland model, reasonable minimum value for Volatility?


# Bjerksund and Stensland model, reasonable minimum value for Volatility?












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?

## Answer by Franchesca (score 1, accepted)

https://quant.stackexchange.com/a/45773

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.