XYZ is trading at 100 on January 1, 2009. A 24-month 150 call option is trading at $3 and a 24-month 50 put is trading at $3. A trader is long 1 each of these options on Jan 1st. If the next day the market gaps open $50 to 150, or gaps down $50 to $50, how much more extrinsic value is possible for each option on top of the $5000 minimum intrinsic value it accrued from the gap in either direction.
On 1/2/2009, assuming IV stays the same, I show a profit of about $1650 if at 150. And a profit of about $650 if at 50. This is just a simple b-s model and I could have interest rates wrong, but I think the numbers are close. Since you start so far OTM (at $100) and only go to ATM, you don't instantly just get $5K.
What intrinsic value? In your scenario, your option went from being OTM (no intrinsic value) to ATM (still no intrinsic value). There won't be any intrinsic value until it goes ITM - that is, until your stock drops below 50 or goes above 150. To have $5000 intrinsic value, your stock would have to drop to zero or go up to 200. As for extrinsic value (also known as time value, etc.), if your stock drops $50, you can be certain IV will soar. Hard to say how much. There is no theoretical maximum - your option will be worth whatever someone is willing to pay for it. But using history as a guide I can't recall seeing IV's much over 500% - although during the '87 crash some individual stock options may well have been trading higher than that.
As pointed out by others, there's no intrinsic involved. Nor will IV stay the same. But if it did, you could simply look at the current option chain to see what the gains would be. If the stock jumped 50 pts, the 150c would be ATM (at the money). If the stock dropped 50 pts, the 50 put would be ATM. With the stock at 100 today, today's 100 strike ATM prices would be what the 50p and 150c would worth in your scenario.