can someone summarize this simple and clean?
My understanding is the impact on put option price is larger when the underlying equity is declining and smaller when the underlying is increasing
for call the impact on call option price is larger when the underlying is increasing and smaller when the call is decreasing?
when will this be asked and is this why we need to be aware of convexity issue when hedging (duration not enough)?
Gamma is sensitivity of delta to changes in price of underlying. So if you’ve written a put at $ 50 and stock suddenly falls to $45, the risk to you increases. But if the stock suddenly rises to 55, your risk isn't that high, because 50 is the strike price. The risk and reward is not symmetric for an equal move in either direction.
I think by duration you mean delta of options. Also be aware of the risk of Gamma, which is rate of change in delta. Gamma is highest when option is at the money and close to expiration. As an option writer if on the last day there is a large movement in underlying and option is at the money, the dealer may not find it easy to delta hedge. The risk ( and hence losses ) can rise significantly.