[1][2] To an option trader engaging in volatility arbitrage, an option contract is a way to speculate in the volatility of the underlying rather than a directional bet on the underlying's price.
If a trader buys options as part of a delta-neutral portfolio, he is said to be long volatility.
So long as the trading is done delta-neutral, buying an option is a bet that the underlying's future realized volatility will be high, while selling an option is a bet that future realized volatility will be low.
Because of the put–call parity, it doesn't matter if the options traded are calls or puts.
This is true because put-call parity posits a risk neutral equivalence relationship between a call, a put and some amount of the underlying.
Long Term Capital Management used a volatility arbitrage approach.
This is typically done by computing the historical daily returns for the underlying for a given past sample such as 252 days (the typical number of trading days in a year for the US stock market).
However, in practice, the only two inputs to the model that change during the day are the price of the underlying and the volatility.
For example, assume a call option is trading at $1.90 with the underlying's price at $45.50 and is yielding an implied volatility of 17.5%.
A short time later, the same option might trade at $2.50 with the underlying's price at $46.36 and be yielding an implied volatility of 16.5%.
This is because the trader can sell stock needed to hedge the long call at a higher price.
In the first case, the trader buys the option and hedges with the underlying to make a delta neutral portfolio.
Over the holding period, the trader will realize a profit on the trade if the underlying's realized volatility is closer to his forecast than it is to the market's forecast (i.e. the implied volatility).
The profit is extracted from the trade through the continuous re-hedging required to keep the portfolio delta-neutral.