# Why does volatility increase the expense of delta-hedging?

Consider someone that writes a call, and wishes to delta-hedge against it to remain delta neutral. For this to be profitable, the price they sell this option for should be greater than or equal to the cost of delta-hedging it. (From this question answer: "An option price is equal to the cost of delta-hedging")

I understand the option writer has to use capital to delta-hedge, which would imply some risk-free cost to borrow. However, I do not understand how volatility increases the overall expense of delta-hedging.

The option writer could do the following, continuously: For each theoretical price point, compute what delta would be, and place a limit buy or sell order at that theoretical price that would result in their position matching that delta. This would result in them having a ladder of orders up and down the order book, which would slowly change over time. Notice: this is entirely agnostic of the actual volatility.

What am I missing here? Given that options' IVs correlate with historical volatilies there must be some real cost or risk associated with delta-hedging more volatile stocks. However, that cost and/or risk eludes me.

• Regarding buy high/sell low: When delta-hedging, do you not buy and sell the same amounts at the same price? That is, if "on the way up" you bought 1 share at \$1.00, and 1 share at \$1.01, if the price goes back down, you'll also sell 1 share at \$1.01, and 1 share at \$1.00. Where's the loss? Jul 21, 2021 at 12:58