When a delta neutral hedge has been established using call options, which of the following statements is most correct? As the price of the underlying stock: A) changes, no changes are needed in the number of call options purchased. B) increases, some option contracts would need to be repurchased in order to retain the delta neutral position. C) increases, some option contracts would need to be sold in order to retain the delta neutral position. The answer says: “As the stock price increases, the delta of the call option increases as well, requiring fewer option contracts to hedge against the underlying stock price movements.” Isn’t delta=change in call/change in stock price? Why does the delta of the call option increase when the stock price (the denominator) increases?
Imagine the call is DEEP in the money. If it is, the call price will move in just about the same amount of the stock (ratio would be close to 1).
heres my take, but i’m not sure. since we’re dealing with calls here, as the stock price goes up, the value of the option goes up to, but by a greater percentage. for ex. say the strike is 20 when the stock goes from 25 to 30, the value of the option goes from 5 to 10 which is a bigger percentae jump then the stock price, obviously. so that makes the delta increase.
gamma my friend
and leverage
Gamma measures how good or how bad the delta hedge performs. Thus in a volatile environment lot of rebalancing is needed to maintain the call ratio or delta-hedge if you like.
Ok, think about this way. lets use an example. say JAVA - the stock is ~6.60ish. so lets look at April 6 call which has a delta of .65 and compare it to an April 8c that has a delta of .20d On a basic level the intrepretation of delta is that if the stock moved up by one dollar. the April 6 call should be worth .65c more while the Apr 8 call would be worth .20 more. This is our hedge ratio then. But why doesn’t this hold. Lets say the stock stayed 6.60 and we fast forward to April 17 (expiration) and make the time 3:50 PM. 10 minutes before these options expire. The April 6 call which is in-the-money, would literally start to trade/be worth near parity (.60) while the out-of-the-money calls would be basically worthless. this implies then that the 6c is moving toward a 100d (stock)and the 8c is now zero delta (worthless). So as a stock moves higher, and a call gets more and more in the money, the more and more that call is going to act like the stock. so if you bought that 8c that was a .20d, and stock raced up to 15 cause IBM decided they love JAVA, then the delta of your calls moves higher as the stock moves higher and the intrinsic value increases. This is why gamma is important. because the delta isn’t stable. the amount of dollar change for your option is going to change as the stock moves. - if you got back to the JAVA example at expiration, then the option with the most gamma would therefor be an at-the-money option approaching expiration. (pin risk is beyond the scope, lucky for us!) So know then, that your delta hedge is good for SMALL changes in stock prices.
Delta is just like duration Gamma is just like convexity if that helps…
One way to look at delta is it’s the probability that the option will be in-the-money at expiration. The higher the stock goes, the more likely that call will be itm. Consider some extremes: You have a stock trading at $20 and a call with a strike price of $25. Delta would be around 40. Now, say the company gets taken over at $60 per share. Obviously, your $25-strike call is deep in the money, and would have a delta of 100. The rate of change of your delta on an option is gamma. Positive gamma means your option deltas get bigger as the stock goes higher (for calls. Deltas get smaller if the stock goes higher for puts.) As a good rule of thumb, if you’re net long options, you’re net long gamma. Hope that helps
It is better to refer to the graph, Sch P.271 Figure 11.
"One way to look at delta is it’s the probability that the option will be in-the-money at expiration. " This is technically not correct and you can get into trouble viewing it this way. View the Delta as your hedge ratio. The hedge ratio, which is your delta - the probability of the option finishing in-the-money are very different things, and if you go back above and look at your t/o situation that would actually be the mathematical proof. This relationship will only hold in a short term, low volatility, normalized situation. - In a longer term, potentially binary situation, the hedge ratio is different from the probability the stock will finish in the money. Additionally, the delta will only go to 100 as the call approaches expiration and time value approaches zero, ie, the put value approaches being actually worthless. (extreme situations where the call is $300 in the -money it will still only approach 100d, but the limit won’t hit 100 till expiration even though for all practical purposes it basically is stock at that point).
Sorry, wrong post.