Stephen Cooper

Option Pricing

roarflolo said: "How do you guys estimate option prices? I've tried some option pricing calculators online, usually the Black-Scholes model. What do you currently use for the risk-free rate? 91-day T-Bill rate adjusted for time to expiry? What do you use for volatility? In the TOS software I click on the option I want to get the volatility to show up. Is there a easier way? When estimating option price do you adjust the volatility? Say current stock price is 170, volatilty is 20% and expiration is 30 days away. I want to estimate the option price 10 days from now if the stock price drops to 165. Volatility goes up when price goes down, do I adjust for this? If so, any estimation methods for change in volatility based on change in stock price?"

drdan said: "I guess I do not try to estimate option prices for the future in specific terms, it can be like predicting the weather or predicitng market direction for any given day, for example in your case what is the market going to do on March 30th (about 10 days from now). The reason - too many variables, stock price is going to fluctuate and so is volatility. Also when first placing a trade I figure that with the popularity of options now that they are always fairly priced, there are no "mistakes" and getting undervalued or overvalued options is near impossible anymore. What I do is look at volatility charts and stock charts and generalize. I do not need to know or expect to know what the exact option price is going to be, even in straight plays."

RaymondKH said: "[QUOTE=roarflolo]What do you currently use for the risk-free rate? 91-day T-Bill rate adjusted for time to expiry? ... When estimating option price do you adjust the volatility? Say current stock price is 170, volatilty is 20% and expiration is 30 days away. I want to estimate the option price 10 days from now if the stock price drops to 165. Volatility goes up when price goes down, do I adjust for this? If so, any estimation methods for change in volatility based on change in stock price?[/QUOTE] Hi roarflolo, I am not sure if you are already aware of it, but implied volatility is actually not a strict "input" value that goes into the pricing of an option. Meaning that one always has to solve Black-Scholes backwards to find the IV from the current option prices. In a way of looking at it, we solve for the IV after we gather all the other parameters (S, K, t and i). Numerous algorithms exist to estimate the IV based on all the other parameters, such as bisection and Newton-Rhapson, but they all involve some work to calculate. So if you can just click on an option and get the IV, I think that's as easy as it gets. :-) One place I go for to find a good benchmark of the Risk-free interest rate is the [URL="http://www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/yield.shtml"]US Treasury[/URL]. It's not too hard to curve-fit from the various periods and extrapolate the rate at, say, 10 days out. I believe iVolatility.com also goes to the Treasury to get their daily reference interest rates. So back to your last question regarding whether one should adjust the IV when modelling a future option price, I'm not sure if it's practical / possible. Since the IV is solved backwards (i.e. after you already know the option price), you would have no idea what the IV would be when the underlying is trading at $165 and 20 days from expiration, which means you will have 2 unknowns (option price and IV). You would need to fix one in order to solve for the other. In most cases, you can assume the IV to stay relatively close to current values if you are only looking at 10 days away (assuming there are no major events happening in the next 10 days. In addition, the IV for most options trading at 30 days from expiration or less usually have artificially inflated values anyway. Assuming you are still trading options at nickel increments (though penny increments are available in some markets), the few percent difference in IV estimation might not even have that much impact on the estimated option price after all. Just my 2 cents' worth. Hope this helps. - R."

Rickster said: "That looks like more than 2 cents worth to me. :)"

Rbreb13 said: "[QUOTE=Rickster]That looks like more than 2 cents worth to me. :)[/QUOTE]LOL, no doubt! :laugh:"

drdan said: "See I knew I wanted to keep it simple! LOL"

holzie said: "Lol, he is exactly right. The only thing you can do with IV is to see if you are buying higher volatility than normal, which is a BAD thing and you should implement strategy that will allow you to sell the high IV. On the other hand, if you see the IV is on the low end of the yearly average, than it is always better to implement strategy that will buy the low IV. As it was said, there is no such thing as undervalued or overvalued options anymore -- they are priced exactly relevant to risk, delta and theta (mostly) but that doesn't mean you can't make good money, it just means you won't find bargains. Most option pricing models just adjust for the delta (increase or decrease in the stock price) and recalculate the option price based on the other unchanged greeks, which is why it should not be your only guidance. Holz."

roarflolo said: "Thanks everyone, this is good info. I'm not trying to get exact option pricing, just a ballpark figure so I can run through a few what-if scenarios. With time I hope I will get a 'feel' for pricing changes."