Options prices are often based upon the volatility of a stock. I'm left to wonder how we might estimate volatility. Let:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]r[/tex] is the yearly expected rate of return

[tex]\sigma_r[/tex] is the uncertainty in the yearly expected rate of return.

[tex]\sigma_y[/tex] the daily volatility.

Then we might model the current price as follows:

[tex]y(n)=\sum_{i=1}^{\infty} w_i (r+\sigma_{r,i})^{(i-n)/365}(y(n-i)+\sigma_{y,i})[/tex]

where:

[tex]w_i[/tex] is how much weight we use each past value to determine the future value

and

[tex]1=\sum_{i=1}^{\infty} w_i[/tex]

Once the [tex]w_i[/tex]'s are chosen then [tex]r[/tex], [tex]\sigma_r[/tex] and [tex]\sigma_y[/tex] are chosen so that they minimize:

[tex]E \left[\left( y(n)-\hat{y}(n) \right)^2\right][/tex]

where:

[tex]\hat{y}(n)=\sum_{i=1}^{\infty} w_i E\left[(r+\sigma_{r,i})^{(i-n)/365}\right]y(n-i)[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Volatility in Stocks

**Physics Forums | Science Articles, Homework Help, Discussion**