FIN 550- Module 8 - Call Option Price

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1 | P a g e Call Option Price What effect does Stock Price have on call option price? “A call option gives its owner the right to buy a share of stock at a fixed price, which is called the strike price (sometimes called the exercise price because it is the price at which you exercise the option” (Ehrhardt& Brigham, 2019). The stock price is one of the main factors that determines if the price of the call option will increase or decrease. The price of a call option usually increases as the stock price increases. A higher stock price increases the probability of the option being profitable for the holder, leading to a higher option premium. For example: “assume you bought an option on 100 shares of a stock, with an option strike price of $30. Before your option expires, the price of the stock rises from $28 to $40. Then you could exercise your right to buy 100 shares of the stock at $30, immediately giving you a $10 per share profit. Your net profit would be 100 shares, times $10 a share, minus whatever purchase price you paid for the option. In this example, if you had paid $200 for the call option, then your net profit would be $800 (100 shares x $10 per share – $200 = $800).” (CFI Team, 2023) On the other hand, a decrease in the stock price will cause the call option to lose its value. The reason for the decrease in value is connected to the intrinsic value of the call option. The intrinsic value of the call option is the difference between the stock price and the strike price. If the stock price is below the strike price, the call option has no intrinsic value. As the stock price decreases, the intrinsic value of the call option decreases or becomes negative. What effect does Time expiration have on call option price? According to Ehrhardt and Brigham, “the 1-year call option always has a greater value than the 6-month call option, which always has a greater value than the 3-month call option.” As illustrated in figure 8-4 below. In other words, the longer a call option has until expiration, the

2 | P a g e greater its value will be. The longer period to the expiration date allows the stock price to increase well above the strike price. At the same time, we can also argue that a longer period until the expiration date increases the possibility of the stock price falling far below the strike price. “But there is a big difference in payoffs for being well in-the-money versus far out-of-the- money. Every dollar that the stock price is above the strike price means an extra dollar of payoff, but no matter how far the stock price is below the strike price, the payoff is zero. When it comes to a call option, the gain in value due to the chance of finishing well in-the-money with a big payoff more than compensates for the loss in value due to the chance of being far out-of-the money.” (Ehrhardt& Brigham, 2019).

3 | P a g e What effect does Risk-free rate have on call option price? “The risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. The risk-free rate is commonly considered to be equal to the interest paid on a 10-year highly rated government Treasury note, generally the safest investment an investor can make. The risk-free rate is a theoretical number since technically all investments carry some form of risk” (Vipond, 2023) Changes in risk-free interest rates can impact the pricing of options, including call options. The impact that the risk-free rate has on call options can be understood through the lens of the Black-Scholes option pricing model. According to the Black-Scholes model, an increase in the risk-free interest rate tends to increase the price of call options. This is because the present value of the option's potential future payoff is discounted at the risk-free rate. As the risk-free rate increases, the present value of future cash flows decreases, leading to an increase in the option price. However, according to Ehrhardt and Brigham “Option prices in general are not very sensitive to interest rate changes, at least not to changes within the ranges normally encountered” (Ehrhardt& Brigham, 2019). What effect does Standard Deviation of Stock returns have on call option price? “The Black-Scholes option pricing model (OPM), developed in 1973, helped give rise to the rapid growth in options trading. The variables used in the Black-Scholes model are the stock’s price, the risk-free rate, the option’s time to expiration, the strike price, and the standard deviation of the underlying stock”. The standard deviation of stock returns, also referred to as the volatility of the stock, has a significant impact on call option prices. An increase in the stock's standard deviation (a stock with higher volatility) leads to an increase in the price of the call option. This is because higher volatility increases the potential for large stock price movements, making the option more valuable. On the other hand, a decrease in volatility tends to decrease the

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4 | P a g e price of a call option. Volatility is a key component in option pricing models, and higher volatility is associated with higher option premiums . (Ehrhardt& Brigham, 2019)

5 | P a g e References: Ehrhardt, M. C., & Brigham, E. F. (2019). Corporate Finance: A Focused Approach (7th ed.). Cengage Learning US. https://mbsdirect.vitalsource.com/books/9781337910231 Fernando, J. (2023, August). What is a call option and how to use it with example20. Investopedia. https://www.investopedia.com/terms/c/calloption.asp#:~:text=Suppose%20you %20purchase%20a%20call,plus%20the%20stock’s%20purchase%20price . CFI Team. (2023, May 8). Call option. Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/derivatives/call-option/ Johnson, R. S., Zuber, R., & Gandar, J. (2007). Pricing Stock Options under Expected Increasing and Decreasing Price Cases Vipond, T. (2023, September 27). Risk-free rate. Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/valuation/risk-free-rate/