Can someone please explain to me, in explicit terms, why a delta hedged call is the same as a straddleThanks.

huh is it? if the underlying doesn't move at all, payoff is zero in both cases, but you've spent twice more for the straddle no ?

Yea, i agree with you. Beats me too. That's what a trader told me. I can't figure it out as well. Anyone with other ideas?

The p&l of the two will be equal if gamma-weighted realized volatility ends up equalling the implied volatility, and if by some magical relationship between rates and div yields makes the financing costs the same (or offset each other).The difference quantstudent mentioned is that on a delta-hedge, you are effectively paying floating volatility, while when you buy the other option you have paid fixed for volatility. So if volatility is 0, you lose big by paying fixed, but if vol ends up being 5 times the implied, you'd wish you bought the straddle as an option. In a Black-Scholes world, the two are idealized to the same payoff diagram.

QuoteOriginally posted by: quantstudent19huh is it? if the underlying doesn't move at all, payoff is zero in both cases, but you've spent twice more for the straddle no ? wrong. buying the ATM call delta hedged is the same as buying half the volume in the straddle.puts are calls especially in futures markets and other instruments without carry or real interest effects. synthetics are very important in tradingif u do a straddle and a delta hedged call, u payoff diagram will be equal as well.

the delta hedge means a cost (or gain), but thats not an upfront cost.if the underlying does not move, you wont delta hedge at allif it moves exactly as expected, the delta hedge costs the initial value of the put, then yes, straddle = delta hedged ATM call edit: after re-reading exotiq's post, i think thats actually what he meantsorry for cross post

quantstudent19>if the underlying doesn't move at all, payoff is zero in both cases, but you've spent twice more for the straddle This assumes you hold the position to expiration.If the options started with a low implied volatility, and if IV increased the value of option faster than theta decreased the value, then even if the underlying did not move outside the breakeven point, then you could potentially close the position prior to expiration for a profit.

QuoteOriginally posted by: kc11415quantstudent19>if the underlying doesn't move at all, payoff is zero in both cases, but you've spent twice more for the straddle This assumes you hold the position to expiration.If the options started with a low implied volatility, and if IV increased the value of option faster than theta decreased the value, then even if the underlying did not move outside the breakeven point, then you could potentially close the position prior to expiration for a profit.i cant really imagine a situation where IV would move up that much while realized volatility is zero

quantstudent19> i cant really imagine a situation where IV would move up that much while realized volatility is zeroLet's assume for the sake of argument that the above is true. HV can move within the range of the upside & downside breakeven points without crossing outside. If such a position is held to expiration then it would expire worthless. However, if such movement within that range caused IV to increase more quickly than theta pushed the payoff curve towards the expiration shape (i.e. perhaps before the knee in the theta curve about 100 days out), then liquidating the position prior to expiration could result in gain.Next, as for the issue of IV depending closely and exclusively upon HV, I'd be grateful to be referred to literature which helps to reinforce this dependancy. I realize that B-S assumes they are closely related, but is not the relation rather imperfect in practice?For classes of underlyings in which options are primarily used to maintain some sort of hedge for the life of the position, perhaps it might be reasonable to assume that the relation between IV & HV tends to mean revert in a tighter manner? (just speculating)However, consider classes of underlyings in which options are often used for other than continuous hedging of the underlying:*) putting on a hedge as a substitute for liquidating an underlying position (i.e. costless collars), when such liquidation would be problematic (i.e. SEC reporting of insider transactions, or restricted/locked-up shares);*) as a means of quickly monetizing an iceberg order, with the options position undone gradually as the iceberg is worked;*) for creating synthetic futures;*) for speculative purchases of naked options by investors.The point of these examples is to ask whether it might be reasonable for supply/demand of options to move in a manner which occasionally drifts out of the usual correlation with the supply/demand of the underlying?For which categories of underlyings do you tend to monitor the correlation between IV & HV, where you observe that it tends to be rather tight? When I run the BB HIVG function on US equities indices, the correlation between IV & HV does not appear to be quite so strict. I do see some mean reversion there, but it does not seem to be quite so immediate.

P.S. perhaps of some relevance to this discussion....http://www.wilmott.com/detail.cfm?articleID=194The Relationship Between Implied and Realized Volatility of SP500 Index: Wilmott Magazine Article Jinghong Shu & Jin E. Zhang Views: 2424 Posted: 02/05/2004 This paper studies the relationship between implied and realized volatility by using daily S&P 500 index option prices over the period between January 1995 and December 1999. In particular, we want to test the how different measurement errors affect the stability of this relationship.---------------------------------------------------------

here is something pretty clear from Mr Dermanpage 10

I saw a term sheet for a straddle. It says probability of recovering the premium is 99%. How do I test this?

in very simple terms: assume a delta of 0,5, so you would sell one stock for every second call you own. as long call + short stock = long put you end up owning puts and calls in the same quantity, a straddle

50 strads or 100 calls are approximately the same thing. the straddle will have a little more delta normally depending on how u calculate it.