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Option (Stock) – Definition

Option Definition

Options are the financial derivative that the option writer sells to the option buyer. The contract gives buyer the right to either buy (call option) or sell (put option) the associated asset at an agreed price (called the strike price) at a certain date or within specific time frame. You can exercise American option any time even before their expiry, but European options cannot be exercises before their expiration. Exercising implies using the right to sell or buy the security underlying the option.

A Little More on What is an Option

Options are versatile by nature. Traders invest in options to hedge or speculate their existing holding. They also try to earn income by option writing. Typically, the option on stock contains 100 shares. Hence If the cost of the option is $0.35,one option purchase will cost you $35.

Call Option

Call options give the option buyer a right to purchase an underlying security at agreed price (strike price), hence the buyer wishes the stock to go up. On the flip side, the option writer is required to provide the underlying security to an option buyer, at the strike price, in case if the stock’s market price becomes higher than the strike price.

An option writer selling a call option presumes that the price of the underlying stock either decline or stay the same as compared to the strike price of the option during the option life, as that’s the way they can maximize their profit. The maximum profit for the writer is the premium obtained by selling the option.

If the buyer’s anticipation is right and stock price exceeds the strike price,the buyer would get the stock for a strike price and sell it at current market price to gain profit. However, if the stock price is less than the strike price, on its expiry, the option buyer will lose the premium paid for call option.

The call buyer’s risk is confined to the premium paid on option, irrespective of the stock movement. At expiry, the profit will be calculated as:

Profit = Current market price of Underlying – (Strike Price + Premium paid)

Then multiply the profit by number of contracts and multiply the resultant by 100 (considering that each contract has 100 shares). It will show the total profit/loss in dollars.

The call writer’s risk is higher. Their profit is the premium obtained, but they can encounter unlimited risk as stock price can keep rising.To avoid this risk, option writers tend to use covered calls.

Put Option

Put options provide the option buyer a right to sell at the strike price, hence put buyer wishes stock to drop. The vice versa is true for put option writer. For instance, a put option buyer is tends to have underlying stock with a hope that its market price will drop down relative to specified strike price either before or on  specified date. On the contrary, an option writer writing a put option hopes that underlying stock’s price will remain the same or rise over the life of the option.

If the price of the stock exceeds the specified strike price at the time of expiry, the writer of the put option will achieve maximum profit.

Vice versa, a put option bearer takes advantage of the stock price falling below its trike price. In this case, the put option writer must acquire shares of the stock at strike price. The profit, if applicable, can be calculated as:

Strike Price – (Current market price + Premium paid).

Multiply it by 100 (if each contract has 100 shares) and the number of contracts acquired.

The option writer bears the risk of purchasing stock at the strike price if the stock price falls. Some writers get put options at the strike price if they wish to purchase stock anyway. If the price falls to that level, they purchase stock as the option buyer would exercise their option. They acquire the stock at their desired price,with extra advantage of getting the premium.

References for Option

Academic Research on Options

Theory of rational option pricing, Merton, R. C. (1973).  Theory of Valuation, 229-288.

Option pricing: A simplified approach, Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Journal of financial Economics, 7(3), 229-263.

Option pricing when underlying stock returns are discontinuous, Merton, R. C. (1976). Journal of financial economics, 3(1-2), 125-144.

Foreign currency option values, Garman, M. B., & Kohlhagen, S. W. (1983). Journal of international Money and Finance, 2(3), 231-237.

Empirical performance of alternative option pricing models, Bakshi, G., Cao, C., & Chen, Z. (1997). The Journal of finance, 52(5), 2003-2049.

The GARCH option pricing model, Duan, J. C. (1995). Mathematical finance, 5(1), 13-32.

The variance gamma process and option pricing, Madan, D. B., Carr, P. P., & Chang, E. C. (1998). Review of Finance, 2(1), 79-105.

A jump-diffusion model for option pricing, Kou, S. G. (2002). Management science, 48(8), 1086-1101.

Prices of state-contingent claims implicit in option prices, Breeden, D. T., & Litzenberger, R. H. (1978). Journal of business, 621-651.

Recovering probability distributions from option prices, Jackwerth, J. C., & Rubinstein, M. (1996). The Journal of Finance, 51(5), 1611-1631.

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