I purchase 1 IBM March 120 put contract for premium of $10. The Max profit I could gain is?

The max you could make is $11,000 (assuming zero cost in commission)

If IBM stock drops to zero, your you can sell for a price of $120*100=$12,000 (one option contract covers 100 shares of the underlying stock) Since you paid a $10 premium (that is $10 per share that the contract covers) you paid $1,000 for the position ($10*100=$1,000).

Since you could sell the position for $12,000 (if IBM stock drops to zero)and you paid $1,000 your max profit is $11,000.

Not to split hairs, but an options time value (a component of the options potential total value) drops as it gets closer to expiration.

$11,000

It drops to zero (where you get 100 shares). You are able to sell it for $12,000 (120 * 100 shares). From that your $1000 ($10 * 100 shares) Premium must be subtracted.

In a more likely scenario it drops to 100 and your profit is $1,000. (120 - 100 = 20. $20 per contract * 100 shares / contract = $2,000 profit. $2,000 - $1000 premium = $1,000)

I stand corrected on the premium costs. My bad.

Options decrease in value as you get closer to the expiration date. Theoretically, the MOST you could make is $110/share which is the difference between the strike price (120) and 0, assuming IBM stock becomes worthless. There is a complex mathematical model which takes into account the time remaining on the contract, the premium and the current trading price.