Using limit orders or stop orders and gamma

Question

From Dynamic Hedging by Taleb:

Risk Management Rule: Option trader lore states that when long gamma, use limit orders. When short gamma, use stop orders.

I cannot understand why this is and the book gives no justification.

Answer 1

An important theme in N. Taleb's book(s) is that being short gamma is a dangerous situation, in the sense that you are subject to occasional very sharp losses, losses that could put you out of business or at least be very painful. You do make frequent small gains, but these are of less concern. (Recall that the P&L of an option when the underlying changes by $\Delta S$ can be approximated by a linear term $\delta \Delta S$ plus a quadratic term $\frac{1}{2} \gamma (\Delta S)^2$. This last term is important when $\Delta S$ is large and will be negative when gamma is negative, i.e. you are short the option). The author returns to this theme of dangerous gamma and illustrates it in many different ways.

For example, because when you are short gamma you are in a dangerous situation, you need to act quickly and decisively. When you put in a limit order [for the underying] it may take some time to execute (if at all), with a stop order you are able to get in/out decisively when the market turns unfavorable to you.

As you know, with a limit order you transact if the price becomes more favorable to you (comes in when you are a buyer). With a stop order, it is the opposite, you transact when the price becomes more unfavorable (gets away from you when you are a buyer).

In general stop orders are a risk control tool, limit order are a patient accumulation tool that saves money but does not guarantee execution. To give another example [of how these orders can be used for different purposes]: a trend follower would probably use stop orders (he wants to buy once the price begins to rise), a value investor would probably use a series of limit orders (he is trying to buy cheaply, whenever the price dips down).