So I'm reading through Dynamic Hedging to start trying to learn option theory better. I hit Chapter 8 on Delta and am completely lost on a certain example he gives.
The example is from Page 119 and is labeled "A Misleading Delta" - He posits the following scenario -
A trader has the following position, yield curve is flat and forward is same as spot. European options with one month maturity:
Long 1M 96x calls delta of 82.4
Short 1M 104x calls delta of 198
Net delta is 62.6
Taleb says that the trader "could hedge it by selling $626,000 of forward" which makes it unclear whether or not this is included in the position (though it makes even less sense if it isn't included).
He then posts a table which shows a flat delta and P&L at 100 (so assuming position was put on at 100 and delta hedged). However, it also shows the delta increasing for price movements in either direction. A graph is also shown that shows the position as hedged to some extent around 100 (the origin) i.e. flat P&L, with positive P&L accruing with higher prices and losses at lower prices.
How is this possible? My limited understanding suggests that this would result in the opposite exposure - decreasing P&L to the upside and gains to the downside as the delta of the net option position would be near or at its max at 100 and decreasing in either direction. So due to the forward hedge, you'd have a net short position.
In fact, from what I can tell the data output provided in the book shows the opposite position - long 104 put, short 96 put, long ~$626,000 fwd.
Can anyone help me understand what I'm missing?