Properties of Stock Options and Time to Expiry

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Properties of Stock Options

Financial Risk Manager (FRM®), Part 1 of the FRM Exam covers the fundamental tools and techniques used in risk management and the theories that underlie their use.

Properties of Stock Options

Welcome to the 31st session in your preparation for the FRM Part 1 Exam. In this session, we will learn about the properties of stock options. Our main focus will be discovering the relationship between the upper and the lower bounds for options, and the factors that affect the option prices. You have already learned about the basics of options and their payoffs in previous sessions. In this session, we will learn the properties of options in more detail. In the next session, we will learn to combine various options and trade strategically.


The prime agenda of our discussion will be learning about the relationship between the factors affecting the option prices. We will begin by focusing on the factors that affect the option prices, such as stock price, strike price, risk-free rate, volatility, time to expiry and dividends. We will then determine the relationship between the upper and the lower bounds of European and American options. We will also discover an important put-call parity relation which can be used for making a synthetic call or put. Finally, we will end our session with discussion on the effect of dividends on option prices.

Let us start by discussing the factors that affect the option price. The first factor is the stock price. The option derives its price from the stock. As the price of stock increases, the option to purchase the stock will also increase; i.e., the call price increases while the put price decreases.

The second factor is the strike price. The higher price is the strike price; the lower price is the cost to purchase an option to buy the stock at the higher strike price. As such, the call price decreases while the put price increases with the strike price.

The third factor is the volatility. Whenever the markets are volatile, the option’s prices fluctuate even more, and as such, there is a greater chance for the exercise of the option. Therefore, the prices of both calls and puts increase with increasing volatility.

The fourth factor is the time to expiry. The longer the time to the expiry is, the greater the chance is for the option to expire in money. Hence, the prices of both calls and puts increase as the time to expiry increases. Correspondingly, as time to expiry decreases, call/put prices decrease.

The fifth factor is the risk-free rate. Whenever the risk-free rate rises, traders tend to purchase call options instead of purchasing the stock, which requires immediate cash outlay. Hence, the prices of call options increase while the prices of put options decrease with a rising risk-free rate.

The last factor is the dividend. Only holders of stocks are eligible to get dividends; hence, the price of call options decreases when dividends increase while the price of put options increases.