*The Business Professor*, updated March 9, 2019, last accessed June 1, 2020, https://thebusinessprofessor.com/lesson/call-option-definition/.

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### Call Option Definition

A call option gives a buyer the right to purchase an asset in the future from the seller of the financial option at a pre-established price. The buyer doesn’t acquire the obligation but instead the right to buy an underlying asset, which is the basis for a derivative price, at a specified amount during a time frame that isn’t longer than a stipulated date. The seller of the call option undertakes the obligation to sell the asset if the financial option is put to use. An investor can buy a call option and expects that the yield will go up. While in the option period, the investor has an upward expectation that the underlying asset will climb in the market for more than what was paid for the option.

### A Little More About What is a Call Option

If an underlying asset rises in the market, the buyer or owner of a call option benefits from it. The asset has a higher price than the pre-determined price if the call option expires on the expiration date. The buyer of the option can apply the right afforded by the call option and purchase the asset at the agreed price and earns the difference from selling it at the current market price.

If the price ends up being less than the pre-established amount, it is known as a “strike price” or “strike,” in which the buyer will not use the right of the call option and loses the premium paid for acquiring it. In other words, the benefit has an endless possibility, but the loss is capped at the premium paid.

It’s the exact opposite for the seller of a call option. The most benefit will be the price for which the option gets sold. The seller will always have that when the asset doesn’t go upward in price. However, as the asset value rises, the profit gets diluted, until it comes to a point when it becomes a loss. After that point, the losses are endless.

The call option value will always be zero or higher on the due date. The amount of the call option is the maximum of zero or one variable. The variable then is the present value of the asset minus the strike price.

“Call = max (0, S – PE)”

**References for Call Option**

- http://www.businessdictionary.com/definition/call.html
- https://www.investopedia.com/terms/c/call.asp
- https://www.thefreedictionary.com/call
- https://en.wiktionary.org/wiki/call

**Academic Research on Call Options**

- • Anticipated information releases reflected in call option prices, Patell, J. M., & Wolfson, M. A. (1979).
*Journal of accounting and economics*,*1*(2), 117-140. This study examines the behavior of call option prices on dates as they approach and go beyond the disclosure date, thereby capturing the ex-ante information content of the yearly announcement of earnings. Previous asset price research has been ex-post in essence. The hypothesis is that investors prepare for the upcoming release of annual earning numbers to influence asset prices. Empirical evidence confirms this idea.

- • An empirical examination of the Black‐Scholes call option pricing model, MacBeth, J. D., & Merville, L. J. (1979).
*The Journal of Finance*,*34*(5), 1173-1186.This study is an explanatory examination and determination of how market prices of call options correlate with prices expressed as an outcome by the Black and Scholes option pricing model.

- • On jumps in common stock prices and their impact on call option pricing, Ball, C. A., & Torous, W. N. (1985).
*The Journal of Finance*,*40*(1), 155-173. There are systematic empirical biases shown in the Black-Scholes call option pricing model. The authors believe the Merton pricing model could potentially remove these biases. They provide statistical proof compatible with the presence of jumps in most of the daily returns of a sampling of common stocks listed on the New York Stock Exchange. However, the authors do not discover any significant operational differences between the Merton and Black-Scholes models.

- • The relationship between put and call option prices, Stoll, H. R. (1969).
*The Journal of Finance*,*24*(5), 801-824. Stoll defines options as negotiable contracts which at a premium gives the buyer the right to request the purchase or sale of a specific amount of shares within a pre-determined time frame at the contract price. The author defines a “put” as an option to sell and a “call” as an option to buy. The goal of this paper is to develop and evaluate some hypotheses about the connections between the call and put prices.

- • Valuation of American call options on dividend-paying stocks: Empirical tests, Whaley, R. E. (1982).
*Journal of Financial Economics*,*10*(1), 29-58. This paper evaluates the pricing efficiency of the valuation equation for call options on stocks in the U.S. with established premiums and compares it with two alternative approximation methods. The approximation gained by interchanging the stock price of the current value of the collateral profits into the Black-Scholes model is shown to encourage phony relationships between prediction error and several other areas, included but not limited to the stock’s dividend yield and standard stock return deviation.

- • Call option pricing when the exercise price is uncertain, and the valuation of index bonds, Fischer, S. (1978).
*The Journal of Finance*,*33*(1), 169-176. Fischer points out how the applicability of the option pricing formula to other asset pricing is one of the most attractive aspects of the recent work on option pricing, as epitomized by Smith along with Cox and Ross. The authors acknowledge how bonds are usually designated in insignificant terms, so the actual value of the payment agreed to bondholders is ambivalent, even if the firm is capable of making the payment.

- • The relationship between put and call option prices: Comment, Merton, R. C. (1973).
*Journal of Finance*,*28*(1), 183-184. Merton claims that if the value of an American put option is always the same value as its European counterpart, then the value of put option must be apt to zero because the time is infinite to maturity.

- • Call option valuation for discrete normal mixtures, Ritchey, R. J. (1990). Call option valuation for discrete normal mixtures.
*Journal of Financial Research*,*13*(4), 285-296. This study uses a mixed call option pricing model to test the repercussion of non-normal underlying returns frequencies. The mixture model offers a correct solution with casual appeal using full totals of Black-Scholes solutions.

- • An analytic valuation formula for unprotected American call options on stocks with known dividends, Roll, R. (1977). Sometimes it is worth it to put American-type call option to use prematurely before a cash issuance by the underlying asset.

- • Foreign currency option values, Garman, M. B., & Kohlhagen, S. W. (1983).
*Journal of international Money and Finance*,*2*(3), 231-237. The authors point out that foreign exchange options are a new market innovation and acknowledge how the regular Black-Scholes option pricing model doesn’t relate well to those options. The reason is that various interest rates are included which differ from the Black-Scholes assumptions. This paper presents different assumptions moving towards valuation formulas for foreign exchange call options.

- • Upper and lower bounds of put and call option value: Stochastic dominance approach, Levy, H. (1985).
*The Journal of Finance*,*40*(4), 1197-1217. The authors come up with upper and lower amounts for a call option price for all unconstrained and concave utility functions using investment rules with risk-free interest rate borrowing and lending.

- • The value of an option to exchange one asset for another, Margrabe, W. (1978).
*The journal of finance*,*33*(1), 177-186. This paper presents an equation for the value of an option to trade one risky security for another, which the theory of such an option is not discussed in any modern literature. The author’s argument comes from the Black-Scholes solution to the continuing call option pricing issue and Merton’s extension. The formula the author explains is for the European option but suitable for its American counterpart.