Mário Marinato

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visits member for 2 years, 3 months
seen Jun 12 '12 at 12:00

Apr
24
comment What precision do I need to calculate implied volatility?
In-the-money and at-the-money options are calculated without those ranges. @SRKX answer helped me discover what I was doing wrong. Thanks for you kind attention.
Apr
24
comment What precision do I need to calculate implied volatility?
Thanks, @SRKX! In fact, it was not a matter of reducing ϵ, but it led me to the real problem: my B&S formula was rounding the result returned to two fraction digits. To out-of-the-money options, the results were almost always below 0.01, in which cases the formula would return 0.01 as the fair price. Thus, based on the example values I gave on a comment above, to every volatility from 10% to 80%, the fair price would be 0.01, leading to my confusion. I changed the B&S formula to not round the results and my implicit volatility discovery method worked as I expected.
Apr
24
comment What precision do I need to calculate implied volatility?
An example: underlying stock price is 21.19. Option strike price is 35.50. Time to expire is 27 days (which I divide by 365 and use as 0.0740. Interest rate: 9.75. Current option market price: 0.01. Then, as I said on my first comment, the first try is the historical volatility, which is 31.27%, and B&S gives me 0.01 as the fair price. Again: great! But I discovered that, with those same parameter values, the volatilities 10% and 80% also give me the same 0.01 as fair price.
Apr
24
comment What precision do I need to calculate implied volatility?
My parameters are the ones the B&S formula requires: - Underlying stock current price. - Option strike price. - Time to expire. - Interest rate. - Volatility. The four first ones are known to me, and I want to discover the last one, given an option market price. I start by trying it with the historical volatility and, by trial-and-error, adjust it until the result is the same as option market price. When it comes to out-of-the-money call options, the historical volatility usually is a valid answer, but, as I said before, it is a fraction of a wide range of valid answers.