An increase in the price of the underlying increases delta, so the size of delta hedge call position should be decreased. True or false, and why? Thanks.

Call delta increases when underlying asset increases and delta hedge is devised as the 1/delta, means that hedge ratio decreases, so means you should sell some of your calls in the portfolio to rebalance and maintain an effective hedge.

True, assuming the number of shares doesn’t change. Look at an out-of-the-money call option, as the u/l price moves up the option’s closer to being at-the-money. So the option price will increase at a faster rate, i.e. higher delta. If the delta increases, the number of options has to decrease… because the formula is (# of options) / (#of u/l shares) = -1/delta, or delta*(# of options) = -(# of u/l shares) … so as the delta goes up, # of options goes down.

Thanks. Why call delta increases when underlying asset increases? Delta = Change in option price / Change in stock price. If stock price increases, the denominator increases, then shouldn’t delta decrease?

No, because delta measures the relative rates of change in the option and underlying prices - not absolute change in underlying price

sleepybird Wrote: ------------------------------------------------------- > Thanks. Why call delta increases when underlying > asset increases? > Delta = Change in option price / Change in stock > price. > > If stock price increases, the denominator > increases, then shouldn’t delta decrease? If you were to graph the relationship between the underlying price and the option price, you would see that it is not a linear relationship As a result, as the underlying price moves up or down, the slope of the curved line changes. So at any given point along that curved line, the slope (delta), will change. See exhibit 4 on page 308 of CFAi Volume 5… its shows this graphically. Delta is a similar concept to elasticity in econ. Someone PLEASE tell me if I’m wrong so I can learn it right!!

Thanks. I think I got it. When stock price go up, the denominator goes up, but the numerator also go up at a higher pace. This is because when stock price increase, the value of the calls increases, so does the premium. So overall delta increases. CF-AHHHHHHH Exhibit 4 on page 308 is for delta hedging currency with puts in relation to exchange rate. It looks to me when the underlying exchange rate increase, the slope decreases (flatten), so delta decreases in this case.

Yeah, because a put will react in the opposite direction as a call. The principles of delta remain the same, however. I just thought Exhibit 4 was a good visual aid for the concept… not necessarily your specific question as it pertained to calls.

Is hedge ratio = -1/delta TRUE for both put and call option hedges? The difference is that delta is negative for puts and positive for calls? (put option delta hedge is covered in currency risk hedging)

this kind of questions always get me, because i am always overthinking. for a call option, you need to have positive gamma to have delta and price go the same direction. if they don’t specifically say gamma is positive, i will think the first part of the statement is wrong. i guess cfa pre-assumes it w/o even mention it. but in reality it is not always true. this is why we can do strategies like delta neutral gamma scalping.

lenchik, thats the formula that popped into my head when i saw this question and would have made me answer true… I know for a fact the negative sign represents that you are buying puts, i have assumed up until now if it was positive it means you should buy calls. Not 100% of that last call part tho.

Guys This is pure level II stuff. put delta = call delta -1 for the same strike price, same expiration. - Call delta: 0 for far out of money,1 for far in the money. It moves from 0 to 1 when stock price increases. - Put delta: 0 for far out of money, -1 for far in the money. Moves from -1 to 0 when stock price increases. The hedge ratio = -1/delta applies both call and put. As delta increases for call when stock price up --> 1/delta decreases --> less call needed for hedge. As delta decreases for call when stock price up --> 1/delta increases --> more call needed for hedge. Dust off your level II book, if you are still in doubt.

come on. delta hedge is simply -1/delta. delta up call down. i believe everybody gets this part. what really gets me is underlying price is not relevant here. or i should say not directly related to the hedge. i don’t need it to rebalance a delta hedge. why they throw it in? by saying “An increase in the price of the underlying increases delta, so …” are they implying price increase will definitely lead to delta increase? that’s surely wrong.

Boris_7 Wrote: ------------------------------------------------------- > come on. delta hedge is simply -1/delta. delta up > call down. i believe everybody gets this part. > what really gets me is underlying price is not > relevant here. or i should say not directly > related to the hedge. i don’t need it to rebalance > a delta hedge. why they throw it in? by saying > “An increase in the price of the underlying > increases delta, so …” Again, not sure it is appropriate to write a long post about this since it is a pure level II stuff which level III candidates are supposed to know all about, but since you insist. > are they implying price increase will definitely > lead to delta increase? that’s surely wrong. Yes, option 101: price increases --> call price increases, thus delta ratio increases --> less number of call to hedge. Say you are long 200 stocks. You want to delta hedge. You find out at a particular option has delta = .2 so you need to buy -1/.2 or short 5 calls for each stock you own --> short 1000 calls now to delta hedge the 200 stocks. Say again, stock price up 4%. Your stock is up by 4% but it is upset by (approx for small % change) same decrease in call position. Now, you find that the delta of the options you are already shorting is now up,say .25 instead .2 --> now hedge ratio -1/.25 = 4 calls per stock, so you need only to short 800 calls --> you adjust by buying 200 calls so that your net call position is now (-1000+200)= -800 calls for the same 200 stocks. I urgently urge you to dust off your level II book and take a refresh. It is all in there.

Ok, here is what i get, correct? Underlying Price Increases Calls: Hedge ratio decreases (-1/delta)-> less calls needed to hedge -> buy calls Puts: Hedge ratio increases (-1/delta) -> more puts needed to hedge - > buy puts Underlying Price Decreases Calls: Hedge ratio increases->more calls needed to hedge -> sell calls Puts: Hedge ratio decreases->less puts needed to hedge->sell puts

as i pointed out earlier above, delta change is driven by gamma. you need to have positive gamma to make delta and price go the same direction. will gamma always positive even if it is a single leg option hedge? option 201 class will tell you it is not. for example, there is a stock up for fda. implied volatility will be extremely high, which makes the calls extremely expensive. after the fda, stock goes up a little bit, but not as expected by the market, close to money calls may have small movement either way, while out of money calls will surely go down. again i think it is beyond cfa. if i get this type of question on june 5, i will have to pray.

lenchik101 Wrote: ------------------------------------------------------- > Ok, here is what i get, correct? > > Underlying Price Increases > > Calls: Hedge ratio decreases (-1/delta)-> less > calls needed to hedge -> buy calls > > Puts: Hedge ratio increases (-1/delta) -> more > puts needed to hedge - > buy puts > > Underlying Price Decreases > > Calls: Hedge ratio increases->more calls needed to > hedge -> sell calls > > Puts: Hedge ratio decreases->less puts needed to > hedge->sell puts You’ve got it. Boris_7 wrote >As i pointed out earlier above, delta change is driven by gamma. you need to have positive gamma to make delta and price go the same direction Gamma is ALWAYS positive for long call and long put, i.e. the option curve is always convex.

i need to make myself clear. gamma is positive for single leg. what i really mean is we need a good positive gamma reading to make sure delta goes with price. price goes up, all calls with delta greater than 0 will go up, but not necessarily delta itself. (delta could equal to zero, so those calls will not move.) the original delta hedge is designed as if delta never changes. and anytime delta changes, you need to rebalance otherwise the hedge will be ineffective. option price curve is convex, but not delta. gamma derives from delta.

Boris_7 Wrote: ------------------------------------------------------- > i need to make myself clear. gamma is positive for > single leg. what i really mean is we need a good > positive gamma reading to make sure delta goes > with price. > > price goes up, all calls with delta greater than 0 > will go up, but not necessarily delta itself. > (delta could equal to zero, so those calls will > not move.) > the original delta hedge is designed as if delta > never changes. and anytime delta changes, you need > to rebalance otherwise the hedge will be > ineffective. > > option price curve is convex, but not delta. gamma > derives from delta. Dude. Not want to waste time on this, since not sure you know what you are talking about or what you are asking. Take “all calls with delta greater than 0” calls ALWAYS have delta >0 unless stock price =0!!! The rest of your comment is way above my limited intelligence or knowledge about options to comment on. Anyway, good luck my friend, since you seem to be quite confident about your knowledge of this stuff.

Lenchick and ElCfa, don’t you mean: Underlying Price Increases Calls: Hedge ratio decreases (-1/delta)-> less calls needed to hedge -> SELL calls (Because delta increases) Puts: Hedge ratio increases (-1/delta) -> more puts needed to hedge - > buy puts (Because delta decreases) Underlying Price Decreases Calls: Hedge ratio increases->more calls needed to hedge -> BUY calls (because delta decreases) Puts: Hedge ratio decreases->less puts needed to hedge->sell puts (because delta increases) I don’t get one thing though. Don’t puts have negative delta? So, if price of stock decreases, then put delta moves towards 0 from a negative number and so don’t you need to BUY more puts? For example: if put delta is currently -.5, therefore hedge ratio is -1/-.5 = 2 If price falls, put delta would be -.2, and therefore hedge ratio is -1/-.2 = 5 and hence BUY puts??? Sorry if I am making this more complicated. Thanks Thanks for the clarifications.