# Delta Hedge

If you sold options and bought stock to delta hedge then If stock prices are increasing you will be overhedged, and if stock prices decreasing you will be underhedged. Reason is for every \$ incr in stock prices, call options will decrease by less Is this correct?

if the underlying increases by a \$1 then almost always the option price will increase less than \$1 (this assumes a call option of course). now, a deep in the money option with little time to expiry coul dhav ea delta of 0.99 but an at the money option with lots of time to expierly will have a delta significantly closer to 0 than 1. so if stock prices go up your delta will change as well and to determine your hedging position use the stock*delta = -options forumla to figure out what to do.

for call option, if stock prices are increasing, it’s more likely the buyer of the call will exercise so the delta will increase. So as a hedger, you need to buy more stock to hedge. So they make the market more volatile.

atpr Wrote: ------------------------------------------------------- > If you sold options and bought stock to delta > hedge then If stock prices are increasing you will > be overhedged, and if stock prices decreasing you > will be underhedged. Reason is for every \$ incr > in stock prices, call options will decrease by > less > > Is this correct? First, whether this is correct or not depends on whether you’re hedging a put or call (it looks like you’re trying to hedge a call, since hedging a put would require shorting the stock, I think). Here’s what you remember: 1) # shares stock per option = hedge ratio = option delta. It’s all the same thing. (thank you David Hetherington for pointing this out at L2) 2) Delta is also the slope of the option price curve at different prices for the underlying. For a call, it is an upward sloping curve that sort of “evaporates” as the option gets closer to expiration and gets closer and closer to the hockey stick pattern that shows the option’s intrinsic value (i.e. it’s value at expiration for different underlying prices) So… in a call… if the underlying goes up, you are at a steeper part of that price curve, and so Delta is bigger. This means that the hedge ratio is bigger - you need more stock per option to be hedged. This would mean that you are underhedged (not overhedged as you asked) unless you buy more stock to rebalance the hedge. The number of shares would be: (Delta@newUnderlying - Delta@oldUnderlying) * (# options) Multiply by the price of new shares to figure out how much to buy.

Just remember that if stock price goes up, delta goes up too. Assuming the number of call options remains unchanged, you need to buy more shares to maintain the hedging position (No. of options * delta = - No. of shares).

I saw a q related to this…where investor had # of shares and wanted to hedge. We were provided only delta