# Comparing Implied Vol. to Historical Vol. using intraday data

I'm interested in estimating what my profit/loss would be for continuously gamma scalping a delta hedged option over the course of one day, using historical intra-day price data.

I found an equation for calculating the profit and loss for a delta hedged option from. "option Trading Volatility: Trading Volatility, Correlation, Term Structure and Skew"Apr 24 2014 by Colin Bennett

the equation is P/L = 1/2 * GAMMA * (REALIZED^2 - IMPLIED^2)

For use in this equation, I am interested in calculating realized volatility over the course of a day, I have historical intra-day tick data mined from bloomberg to help obtain it.

I have read that traditional/classical standard deviation formulas are not accurate measures of intra-day realized volatility, because volatility changes significantly over the course of day. How can you take changing intra-day volatility into an account to get a more accurate calculation?

Once I have the intra-day historical volatility from a more advanced method, can the number I obtain still be used in the equation at the start of my post? Can I compare it to the Implied Vol. for an option, obtained from bloomberg?

Am new to these ideas, so I'd appreciate answers given low assumptions about my knowledge base. Read a couple options books + bachelors level knowledge in mathematics/stats. Links/Books recommendations are also appreciated.

## 1 Answer

It's been a long time but just in case someone else happens on this question, see:

DOES ANYTHING BEAT 5-MINUTE RV? A COMPARISON OF REALIZED MEASURES ACROSS MULTIPLE ASSET CLASSES