Does a higher exercise price increase the value of a call option?

No, just the opposite. It decreases the value.

Options have two "Prices" associated with the financial instrument. STRIKE PRICE and PREMIUM PRICE. When you use the term "Excercise Price" you are referring to the "STRIKE PRICE."

A CALL option is the right to BUY a specific instrument at a specific price. So having the "RIGHT TO BUY LOWER" is always worth more than the right to buy higher.

To clarify, if your company offers you 3,000 options at an excercise price of $2, those are worth vastly less than the same options with an excercise price of ZERO. Here's why:

An options "Value" is known as the Option Premium (OP). OP is what the option is worth.

Time Value + Intrinsic Value = Option Premium

So if the market value of ABC Company is $5 and your options strike price is $0 you can cash those in for $5 a share right now.

However, if your Option Strike Price is $4 in the same market (ABC stock price is $5) then you only get a dollar on exercision.

Who gets the other $4? The company.

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"Higher exercise price" (traders would say "higher strike price") means nothing in and of itself. The big question is, what is the difference between the strike price and the stock price at the time you bought the call? Or, in trader's lingo, how far out of the money is the option?

People who sell ("write") options are gambling, and the thing they are most hoping for is the price of the stock staying below the strike price. If this happens the option expires worthless and the writer keeps the premium. That's the ideal.

The closer the two numbers are, the more likely the option will be exercised and, therefore, the more likely you're going to have to cough up either cash or stock. SO...the more likely the option is to be exercised, the more expensive it will be.

Let's take two options priced at $340.50 per share. That is a ton of money so obviously the premium should be pretty low, right? Not if you're buying calls on Apple--$340.50 was the Friday, May 13 closing price so this call would be at-the-money and therefore very expensive. As in 10 percent, or more, expensive.

OTOH, if you were buying $340.50 Caterpillar calls, assuming anyone would sell you a $300-plus call on a $106 stock, you could get into those for about a quarter per share.