Theta of a long OTM put as the stock rises

A stock is at $S_0 = 35$ and you have bought a put struck at $33$. If the stock price goes up, what happens to the theta of your position?

Reply $1$ if it goes up, $0$ if it is unchanged, or $-1$ if it goes down.

$1$ (theta increases). A long put has negative theta, largest in size near the money. The put is already out of the money, so a higher stock price moves it further away from the strike and shrinks the time decay; a negative number moving toward zero is an increase.