Put option

The no-arbitrage condition is violated at option expiry when the value of an in-the-money:

  1. put option is below its exercise price.
  2. put option is below its exercise value.
  3. call option is below the price of its underlying.
    solution: 2
    Can someone explain, whats the diff between price and value and how option 2 is correct ?

An option has an exercise price (also known as strike price).
For a call option, if the exercise price is 100, you exercise the option if the stock price is greater than 100, but not if it is 100 or less.
The exercise value is the amount you receive if you exercise the option.
For a call option with an exercise price of 100, if the stock price is 110, when you exercise the call option you will receive 110-100=10.
Similarly, for a put option with an exercise price of 100, if the stock price is 90, when you exercise the put option, you will receive 100-90=10

Generally, if the exercise price is X and the stock price is S,
when you exercise a call option, you receive max[S-X,0]
when you exercise a put option, you receive max[X-S,0]

The no-arbitrage condition at option expiry:

in (1), the value of the put option is below its exercise price X. But the payoff is max[X-S,0] so the payoff is always going to be less than X provided the stock is not zero

in (3), the value of the call option is below the price of the underlying S. But the payoff is max[S-X,0]
so the payoff is always going to less than S

So: not (1) and not (3)

(2) if the put option is below it’s exercise value
You are told it is in the money, which for a put option means S<X so the payoff is positive X-S.
If you bought the option and then exercised it, you would come out ahead as the value of the option is less than you get for exercising it