How to calculate the standard deviation of stock returns?

I’m trying to learn the the Black–Scholes option pricing formula and one of the elements of that formula (according to http://bradley.bradley.edu/~arr/bsm/pg04.html) is the “standard deviation of stock returns”.

I know if I download a CSV file of historical prices from Yahoo! and open up Excel and execute STDDEV(column with prices), I can get the “standard deviation of stock PRICES”. But that is not what I need. I need the “standard deviation of stock RETURNS”.

Does anyone know how I can calculate this in Excel? Or even better yet, if someone can provide a implementation in code showing how to do it?

Some of the questions that came up in my head when thinking about how to approach this include “how much historical data to use? (how far back to we go when downloading the CSV file from Yahoo!)” and “what kind of stock returns are we supposed to be calculating? Annual stock returns? Daily returns?”

Can the Delta be used to calculate the option premium given a certain target?

I’m struggling for a while now with a question about options, namely ‘which is the best option to buy?’. I have various books on options, but I’m not an mathematician and don’t have (yet) any extensive hands-on experience with options.

According to Cohen (Options Made Easy, 2nd Edition), the Delta of an option is the “change in option price relative to the change in underlying asset price”. He goes on to give an example of an option with an Delta of 0.5 which moves $1, in which case the premium of the option will increase with 0.50 (call) or decrease with 0.50 (put).

Even though Delta’s of options are changing with each change to the various components which make up an option premium, I’m wondering if a Delta can be used to determine the premium of an option given a certain target.

For example, let’s say stock XYZ trades at 50 dollar and we have an price target of +10% (so the share price of XYZ increases to 55 dollar; +$5). Let’s say an option’s current premium is 2.00, with an Delta of 0.40. Can the option premium at the target of 55 dollar be calculated with the following formula?

Current option premium + ( (share price target - current share price)
* current delta of the option) = Approximated option premium at the price target

So, with the example figures this option will be worth..
2.00 + ( (55 – 50) * 0.20) = 3.00
…at the price target?

Besides this, I’m wondering:

  • Isn’t the gamma (that is, the change
    in delta relative to the change in de
    underlying asset) needed for such an
    calculation?
  • If we have a time period
    in which to achieve this price target
    of $55, can the Theta (time decay) be
    incorporated in the calculation of
    the approximate value at the price
    target?
  • And, above all, requires this
    really so much calculation or can the
    approximated value be more easily and
    better be derived from something
    else? (like, say, the same strike of
    the option at and different
    expiration month, correcting for time
    value?)

Edit:
My original angle to my question was more in wondering if there was a sort of ‘rule of thumb’ which an investor could use, in trying to choose between different strike of options. The underlying idea to my question was that, if somehow the option premiums could be guessed given the target for the stock, then the investor would be able to select the ‘best’ option for his outlook (i.e. the one with the highest potential return). With the same ‘rule of thumb’ an investor could calculated the potential downside, given his stoploss on the stock.

I agree with DumbCoder that an option model (like the Black and Scholes model; see https://secure.wikimedia.org/wikipedia/en/wiki/Black%E2%80%93Scholes#Mathematical_model) has the potential to answer this question, even though I don’t (yet) understand this model.

Any more insights would be highly welcomed,

Regards,

How to calculate Black-Scholes using Google Sheets?

I’d like to calculate Black-Scholes using Google Sheets based on this formula: https://www.erieri.com/blackscholes.

Here are the parameters I’m using in the form:

Stock price = 60.89
Option strike price = 40
Maturity = .27
Risk-free rate = .02
Volatility = .59

European Put result is 0.5631.

The Black-Scholes formula can be found on the same page below the form in the definitions section.

Here’s the formula I’m using in Google Sheets:

d1 = ((ln(60.89/40)+((0.02*0.5*0.59^2)*0.27))/(0.59*SQRT(0.27))) = 1.3766
d2 = d1-0.59*SQRT(0.27) = 1.06709
C = 60.89*NORMDIST(d1)-40*2.718^(0.02*0.27)*NORMDIST(d2) = error

Here’s the error details:

Error
Wrong number of arguments to NORMDIST. Expected 4 arguments, but got 1
arguments.

How should NORMDIST be used?

Implied or historical volatility to calculate theoretical options price with black scholes?

According to the black scholes model, volatility is one of the variables to calculate the fair price of an option. However, it doesn’t specify which volatility should I use. Should I take the annualized standard deviation or should I use the implied volatility?

How do I calculate the Forte number from the Prime form?

How do I calculate the Forte number from the prime form of a set? For Example: I have the prime form (0,1,5,8)… How would I determine the Forte number from this set? Or would I use a different form of the pitch class set to figure this out? I have been trying to figure this out for weeks but can’t seem to know how to figure this out myself without using a calculator.

How do I calculate Forte number from Prime form

How do I calculate the Forte number from the prime form of a set? For Example: I have the prime form (0,1,5,8)… How would I determine the Forte number from this set? Or would I use a different form of the pitch class set to figure this out? I have been trying to figure this out for weeks but can’t seem to know how to figure this out myself without using a calculator.