Market value and intrinsic value are broad terms used to define several different things in the financial world. They are most commonly used to describe the implicit and explicit valuation of publicly-traded companies, but can also be used to describe the valuation of stock options.
Market Value for Stocks
The market value of a security is what anyone is willing to pay for it in the open market. Depending on broader market conditions and the popular opinion of investors at any given time, a company's market value can either be much higher or lower than its fundamental and intrinsic value.
Intrinsic Value for Stocks
Intrinsic value is a somewhat more nebulous, subjective term than market value. It typically refers to the value of a company's intellectual property like copyrights, trademarks and patents or other intangible things like business models, personal contacts and complex proprietary technology that may be difficult to properly value in the open market.
Prominent investors like Benjamin Graham and Warren Buffett made some of their greatest profits by purchasing fundamentally-sound, well-run companies when their market value was running at a substantial discount to their intrinsic value. They were able to look past the near-term problems and bad news affecting the firms and realize that once ephemeral issues were taken care of, they would be viable, profitable enterprises.
Market Value for Stock Options
Like with stocks, the market value of an option is simply the price anybody is willing to pay for it in the open market. This price is influenced by four core variables: the strike price of the option, how much time it has left until expiration, whether or not it has any intrinsic value and the volatility of the underlying stock.
Intrinsic Value for Stock Options
In options pricing, intrinsic value is the amount by which options are in the money. For a call option, the underlying stock has to be trading above it in order for it to have any intrinsic value, while a put option is just the opposite, only retaining intrinsic value if it's below the stock price. For example, if a call option has a strike price of $50, and the underlying stock is trading at $51, that option has $1 of intrinsic value. Conversely, if the stock were trading at $49, the call option would have $0 of intrinsic value, and be comprised entirely of time value.