What will happen to the value of the option if the underlying stock price changes to $34.50? Why?

If the underlying stock price changes to $34.50, the option’s value will depend on whether it is a call or put option and if it is in-the-money or out-of-the money. For example, if the option is a call with a strike price of $32 and the underlying stock price increases to $34.50, the option would be in-the money since its intrinsic value (difference between strike price and current stock price) would be $2.50. This means that it has some intrinsic value which will increase its overall worth as long as it stays in-the-money; thus, increasing its value from what was originally paid for it when purchased (premium). On the other hand, if the same call option had an initial underlying stock price of $30 but then increased to 34.50, then this puts it out of money since there would no longer be any intrinsic value associated with owning this particular call due to its difference between strike prices ($2), meaning at most you could only sell/buy back your option for whatever premiums were initially paid when purchasing.

In contrast, if we look at a put option with a strike price of 34.50 at an underlying stock price of 30$, this puts us in-the money so that now there is an intrinsic value associated with owning a put due to being able to exercise our right to sell our security at a higher market rate than what we bought them for ($4). Thus, now by changing our underlying stockprice from 30$ up to 34$, not only do we have 4$ more inherent political advantage though exercising rights compared before but also see appreciation or increase in values for our options as well depending on how much premium was paid when purchasing those securities initially.