Black Scholes failing to solve near expiration

[Adam G]

I am trying to calculate the implied volatility of equity options on expiration day. However, sometimes the iteration never converges on a solution. This occurs even when I manually set the starting guess close to the actual IV. I have tried Newton's and Halley's method and the same behavior occurs.

I was wondering if this behavior could be caused by the convergence method or just from the fact that it is difficult to price options close to expiration.

 

[bob]

Run your code in whatever debugger you have. Near expiry the price of the option will be very close to intrinsic; your iteration is probably hitting a negative vol.

Use boundary checking, or use a method such a false position that keeps the iteration on a specified interval.