Tuesday, June 23, 2009

Variable Delta and Risk Graphs

I kicked off my series on delta hedging by exploring the intricacies of delta and risk graphs. If you missed it, you can find it here. In the first installment we explored the difference between fixed and variable delta, focusing on how the former plays out on a risk graph. Today we'll focus on the latter.

There are 2 types of Delta: Fixed and Variable
Stocks have fixed delta, Options have variable delta

Remember, delta ranges between 0 and 100.

ITM options have delta >50
ATM options have delta = 50
OTM options have delta <50

Variable Delta: If I were to buy an at-the-money call option, my position delta would be around +50. This means if the underlying stock were to increase $1, my call option would increase $50. As the call moves in-the-money, the delta increases; as the call moves out-of-the-money, the delta decreases. Thus we could say that variable delta is in a constant state of flux. For option positions the delta fluctuates as the underlying stock price changes.

What's it look like on a risk graph?
Long ATM call option

What can we glean from the risk graph?
1.Whereas a fixed delta risk graph is a straight line, a variable delta risk graph curves (this is why gamma is often called the curvature of an option).
2. When the call is ATM, it's delta = 50. As it moves ITM the delta approaches +100, and as it moves OTM the delta approaches 0. Notice the effect that these delta changes have on the slope of the line.
2. The long call risk graph changes closer to a 45 degree line (sloping from bottom left to top right) as delta approaches +100, and changes closer to a horizontal line as delta approaches "0". Put another way, the steeper the line, the higher the position delta; the flatter the line, the lower the position delta. Understanding this becomes important when looking at more complex option trades.
Long ATM put option
What can we glean from the risk graph?
1. A put options delta is variable as well, thus its risk graph curves.
2. When the put is ATM, it's delta = -50. As it moves ITM the delta approaches -100, and as it moves OTM the delta approaches 0. Notice the effect that these delta changes have on the slope of the line.
2. The long put risk graph changes closer to a 45 degree line (sloping from bottom right to top left) as delta approaches -100, and changes closer to a horizontal line as delta approaches 0.

Long Straddle Position
What can we glean from the risk graph?

1. The straddle starts off delta neutral (the risk graph is horizontal in the middle)
2. When the straddle is ATM, it's delta = 0. As the stock price increases (calls move ITM, puts move OTM) the position delta approaches +100, and as the stock price decreases (calls move OTM, puts move ITM) the position delta approaches -100. Notice the effect that these delta changes have on the slope of the line.
2. A rise in the stock price causes the risk graph to change closer to an upward sloping 45 degree line (bottom left to top right). Conversely a fall in the stock price causes the risk graph to change closer to an upward sloping 45 degree line (bottom right to top left).

The fact that options possess variable delta results in a certain degree of complexity when trying to delta hedge. Because delta is in a constant state of flux it requires constant monitoring and adjusting when trying to keep a position delta neutral (or close to).

Now that we're all squared away on variable & fixed delta we can start to delve into delta hedging various option strategies.

On a related note, Condor Options had a very nice post today on Why Delta Hedging Matters. Take a look if you haven't seen it, as it sheds some insight on delta hedging.

Stay tuned...

Tyler-

3 comments:

Bill Luby said...

I know I've said this before, but you are doing some excellent work on this blog and this post is an excellent example.

Kudos,

-Bill

Tyler Craig said...

I really appreciate that Bill.

Tyler-

QUALITY STOCKS UNDER 5 DOLLARS said...

Interesting graphs