What I did was:
StDev = StDev(253 daily prices)/Average(253 daily prices)
Goldman Sachs for example has a StDev of 15.71%, when I plug the relevant data into my Black Scholes model (I know the model is right because I checked it against a few different BS models).
My inputs are...
Stock Price = $112.40
StDev = 15.71%
RF Rate = 3%
Strike Price = $100
Time to Maturity = .5 (Apr 09)
My model has the call option priced at $14.57, mkt has it priced at $29.70
Is Black Scholes typically that inaccurate to mkt pricing? Am I doing something wrong? Is it just bcause of the current volatility in the market? Is black-scholes pricing typically closer in line with the mkt under normal conditions?
Prob just market craziness right now...
when genius (Black scholes) failed
Wouldn't your calculated call price be for a European Option, not an American one?
This is what I'm thinking too...Black-Scholes was made for European Options, not American Options. Perhaps that's your issue?
American v. European pricing differences should be negligible. The VIX is trading at 70+, why would anyone in their right mind sell options close to historic vol? The inputs to black-scholes are mindless, your volatility estimation is the key.
The input into black scholes to price is implied volatility, which is the future view of what the standard deviation is going to be.
So is that to say I may be better off inputting the option price and backing into the implied volatility the market is pricing into the option? And maybe keep that implied volatility constant as the underlying price fluctuates and see what the option value is with that constant Expected Implied Volatility assumption?
Also, my sensitivity tables are running haywire... are there any known issues in Excel sensitivity tables when running more complicated calculations?
ATM european call theoretically the same price as american call. Check using that.
Elan - mind if I ask what you are using this for - are you looking at buying GS calls or just trying to understand B-S/option pricing. Also, what is your data source for listed option prices? Note that the bid/ask is extremely wide on most screens right now, a caveat getting back to what you are using this for.
Killer Mike - how would you respond to the statement that buying vol is paying up for theta?
You mean being long vega/gamma short theta? The cost of buying vol/options is that you bleed away value every second
Also elan, your method works only if you assume that implied volatility is constant across strikes. That's not true and especially for equities and especially now you'll see a pretty large downside skew.
Have you tried using the STD Dev for the past, say, month or two as your inputted vol? I think historical yearly vols have been thrown out the window. It may give you a an answer closer to the implied. Let me know. Also have you tried solving for vol given the other inputs and price of the option? It may be interesting to see what the implied is.
Yeah, I figured I should be using the last 30 or 60 days st dev.
Just back testing the last couple of weeks of mkt activity to a trading strategy.
Not necessarily GS, or calls, it was just for the example.
Black-Scholes Equation vs. Model/Formula (Originally Posted: 04/22/2015)
What are the different applications and uses for each of the two? Where would one use the equation instead of the formula? What are the uses of solving the BS-Equation? I know they're related but they are different things: one is a differential equation and the other is a bunch of templates from which inputs yield outputs.
This doesn't seem to make any sense to me. The Black-Scholes equation is by definition the Black-Scholes formula, assuming formula = equation........
Google DerivaGem template
Black-Scholes is only applicable to European style options.....Binary models need to be implemented to value American or certain Exotic derivatives
Equation: http://www.subjectmoney.com/Black%20Scholes%20Equation.jpg Formula: http://upload.wikimedia.org/math/6/6/c/66c077aa44cab1df32603df78b81057e…
n(d1) black scholes model (Originally Posted: 03/29/2014)
derivation of N(d1)
Isn't it just the delta of the option? Pretty sure one of the N(d) terms is but could be mistaken...
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