A call option with an exercise price substantially below the underlying stock's market price (deep in the money) or substantially above the market price (deep out of the money). Also put option with an exercise price substantially above the underlying stock's market price (deep in the money) or substantially below the underlying stock's market price (deep out of the money). Often substantially below is defined as more than one strike price below (for calls)/above (for puts) the current value of the underlying security.