## Delta & Probability Question

This is a discussion on Delta & Probability Question within the Futures & Options forums, part of the Markets category; Hello, I've been reading about the Greeks, and have a question for the option crowd here. In my readings on ...

 Jan 23, 2010, 4:12am #1 Joined Jan 2010 Delta & Probability Question Hello, I've been reading about the Greeks, and have a question for the option crowd here. In my readings on Deltas, it is said that when an underlying is exactly ATM, its Delta should be .50, which basically says that the underlying has a 50/50 chance of either going ITM or OTM. I could agree with that premise in a completely directionless market, but what if the overall trend is bullish or bearish? If the underlying is biased towards one direction or the other, its probability should be greater that 50% of going one way or the other. Unless the Delta calculation already takes the market's bias into account. Agree? Disagree?
 Jan 23, 2010, 10:22am #2 Joined Feb 2009 Re: Delta & Probability Question A theoretical concept, such as the Black-Scholes delta, doesn't take particular mkt conditions into account. Why should it? In certain cases, this means that using simple B-S for delta calcs is not a good idea and you need to refine the model. However, this is normally the case for deep OTM options. In the case you have given, the above doesn't apply. Delta of an ATM option is always arnd 1/2 (not exactly that for puts, but close enough), regardless of your personal opinion of which way the mkt is going. Unless you somehow have a rigorous way to prove the existence of trends/biases and forecast direction? If you do, why would you worry about deltas and the rest of this malarkey. If you know which way the trend is, just buy/sell outright and forget options. __________________ "Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
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 Feb 11, 2010, 4:18pm #3 Joined Jun 2009 Re: Delta & Probability Question Does anyone actually knows the maths behind this,ive heard on other forums that's its wrong to think of D1 os the prob of finishing ITM?
 Feb 11, 2010, 4:31pm #4 Joined Feb 2009 Re: Delta & Probability Question It's not wrong, per se. It's just the risk-neutral probability, which is a special beast. __________________ "Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
 Feb 16, 2010, 1:59pm #5 Joined Jan 2009 Re: Delta & Probability Question One of the assumptions of B-S is that the underlying's price follows a Markov process, so that you can't determine what the next move is going to be from the past history. Whether this is actually the case or not is a different matter.
 Feb 16, 2010, 2:48pm #6 Joined Sep 2004 Re: Delta & Probability Question Highlander...Read up on smile and skew to give you a better understanding of how all this stuff interrelates. If I see a good link I'll post. GJ __________________ "That which doesn't kill me makes me stronger"
 Feb 16, 2010, 9:44pm #7 Joined Jan 2009 Re: Delta & Probability Question Indeed, the presence of a smile would suggest a trend, as a lognormal distribution of returns of asset price shouldn't give rise to one. If you define an ATM option as one whose strike is at the CURRENT spot price, then the delta will be someway off from 0.5, depending on the maturity of the option. You need to consider the underlying's price when the option expires and look at the ATM Forward.
Feb 18, 2010, 8:04pm   #8
Joined Dec 2008
Re: Delta & Probability Question

Quote:
 Originally Posted by Scouser76 Indeed, the presence of a smile would suggest a trend, as a lognormal distribution of returns of asset price shouldn't give rise to one. If you define an ATM option as one whose strike is at the CURRENT spot price, then the delta will be someway off from 0.5, depending on the maturity of the option. You need to consider the underlying's price when the option expires and look at the ATM Forward.
Don't make any sense. A smile does not suggest a trend at all. If an index is trading 3000 and you have a 3000 strike call/put IT WILL have a delta of 50%, simple as that.

 Feb 23, 2010, 7:29pm #9 Joined Jan 2009 Re: Delta & Probability Question A smile (and here I include asymmetric skews too) implies that the distribution of underlying price returns (change in price / price) is NOT normally distributed. That is, there is a degree of kurtosis in the price distribution and there are (usually)' fatter tails. That being the case, it means some prices are more likely than a simple 'random' Wiener process would suggest. That generally means there is some 'extra' expectation of those prices. Options with strikes at those prices are more expensive (assuming +ve skew) than they should be. There are other explanations for the general presence of skew (e.g. insurance against crash for stock market 'smirk'), but when the smile changes rapidly, that's saying something to me. The delta of an ATM is generally NOT exactly 50% (see Martinghoul's earlier reply regarding puts), although I believe that as you get closer to expiry, it generally will be. http://www.wilmott.com/messageview.c...threadid=54099
 May 16, 2010, 12:22pm #10 Joined Feb 2008 Re: Delta & Probability Question Technically I dont know, and who cares really. Thats why Traders dont like Economists, lol. Practical Applications is all that matters in trading. But Practical Implementation, Yes you can view Delta's as a Percents/Probabilities measure. __________________ "Trading is a percentage business. Some trades will fail but it is absolutely vital that losses are kept to a minimum." --Mr. Charts
 May 16, 2010, 4:05pm #11 Joined Dec 2008 Re: Delta & Probability Question you got to remember, the options market is different from the underlying, even though the options market may be implying a greater probability of a fall, which the equity market vol curve tends to suggest, this does not mean the underlying will follow. Options volume does not drive the underlying, it is those directly buying the cash market, (i.e the actual stock) who drive indices higher or lower and therefore are the creaters of trends, not the options buyers or sellers
May 18, 2010, 3:35pm   #12
Joined May 2010
Re: Delta & Probability Question

Quote:
 Originally Posted by Highlander1 Hello, I've been reading about the Greeks, and have a question for the option crowd here. In my readings on Deltas, it is said that when an underlying is exactly ATM, its Delta should be .50, which basically says that the underlying has a 50/50 chance of either going ITM or OTM. I could agree with that premise in a completely directionless market, but what if the overall trend is bullish or bearish? If the underlying is biased towards one direction or the other, its probability should be greater that 50% of going one way or the other. Unless the Delta calculation already takes the market's bias into account. Agree? Disagree?
Delta as a proxy for probability of being ITM at expiration only works for ATM options.
After that it is bunk. The reason for this is that Delta is a the value of a definite integral whose limits are around a different question: how much the option is acting like a stock. This is why Delta tells you how much the option is acting like the underlying and thus why delta hedging makes sense.

Luckily that N[d_2] term in black scholes does give you the probability of ending ITM.