January 20th, 2015, 9:12 pm
QuoteOriginally posted by: AlanIn my experience, the trickiest cases are those when the option value is in a legal range, and so aniv > 0 exists, but the price is extremely small. This happens frequently when the option price comes,not from the market, but from a model and you want to convert it to an iv.To take a simple example, suppose [$]S=100, \quad K =150, \quad T=1[$], and [$]\sigma = 0.04 = 4\%[$].The Black-Scholes call price [$]C \approx 9.01 \times 10^{-25}[$].Now, given that option price, try your iv routine. How did it do? Full disclosure: my 'robust iv routine' which I previously described, will also fail with this onebecause it is too simple and working at machine precision. However, with a little more work, you could writea `more robust iv routine' that will also work in this case, and using only machine precision.As another initial check, I ran this on my DE on the least squares formulation. I get sig == 0.039999 Letting K get bigger 120,130, 200 etc.... in double precision the machine precision is reached at ~ K = 135 (data falls off the radar). After that the solver gives incorrect results. Have not considered multiple precision. Maybe TT and Alan have some input. From all this I would tend to provisionally conclude that the DE is fine if we have enough machine bits. Apples and oranges.
Last edited by
Cuchulainn on January 19th, 2015, 11:00 pm, edited 1 time in total.