Near term wave count - The sizable advance today should be wave (v) up. Last week's high is either a part of wave (iv) or a part of wave (v).
Chart 1 presents three probable counts for the current rally.
[blue] The least bullish count. The top is in once the advance from yesterday's low is over. See the squiggle count in Chart 2.
[orange] Moderately bullish count. This is the ED lovers' choice. It's too early to call an ED at this stage, but an ED would be very appropriate with respect to the larger structure if it turns out to be the case.
The three waves for wave c of (v) is likely complete at today's high (Chart 2). If so, wave iii is at 84% of wave i.
[green] The most bullish count. Today's rally is an incomplete wave iii of (v), to be followed by wave (iv)-down and then wave (v)-up.
Medium and long term wave structure -
It's informative to keep an eye on the larger picture.
As shown in Chart 3, an upward ABC structure which corrects the April-July decline is clearly visible.
Moreover, SPX is now touching the trend channel of this ABC structure - [a] and [c] have reached equality.
Finally, negative divergence has started showing up in the daily chart. Conditions are now ripe for a turn.
The long term profile (Chart 4) is equally revealing.
The red line connecting the 2007 and 2010 highs serves as working resistance for the current rally.
The green line connecting the 2007 high and the intermediate wave (2) [or (B)] during the last crash has acted as a successful support for the late August low.
Finally, one may consider raising the degree of the post-April waves as indicated in Chart 4, given how long these waves have been evolving, especially when compared to the first two intermediate waves (1)(2) or (A)(B) during the last crash in terms of time as well as magnitude (%). The implication is certainly the speed and the magnitude of the subsequent decline - if the larger count is on track.