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The word choice is specified in a variety of ways in contracts. A call, for example, is a type of option that grants the bearer the right to buy or obtain a certain asset at a predetermined time (Chen, Xiaowei, Yuhan, and Dan 3). A put contract, on the other hand, allows the bearer to sell a specified commodity at a specified date (Lewis 2). As a result, an option is simply a deal that gives the investor the right, rather than the obligation, to sell an asset at a specified price and time. (Chen, Xiaowei, Yuhan, Dan 5) Options are divided into two categories: American style options and European style options. An ‘American type option’ refers to an option exercisable freely, i.e., anytime during its life (Chiarella, Carl, and Boda 72). The American type, therefore, allows the contract holders to be at liberty of exercising the option at any time before its expiration date with no specifications or limitations on the said time. This option differs significantly from the European option in the sense that the latter can only be exercised at a pre-defined moment in time, which is usually at the end of its life, also known as maturity point. (Chiarella, Carl, and Boda 72)
The American option has increased flexibility when compared to the European option. The increased flexibility enables the American Option increase value over the European in some situations thus leading to the generation of a premium. Ultimately, the American option can be equated as the sum of the European Option plus premiums, where they must be higher or equal to zero. (Cheang, Gerald, Carl, and Andrew 243) Mathematically, American Option= European Option+ Premiums; where the premium >=0.
The primary advantage of the American option is the flexibility that accrues to both the sellers and the buyers. The buyers are therefore at liberty of buying assets at any time before the expiration of the option while the sellers can consequently sell during the unlimited timelines(Lewis 4). The buyers and sellers can maximize returns from trading as the option does not limit them to specified trading days only. For instance, in an American Option, the sellers can be able to select the most appropriate times when they can sell their assets. By continuously studying the trends in the market, the sellers can be able to identify the point at which they can maximize their earnings and sell at that particular time. Such options are not available for the European type since the only time a sale can occur is when the maturity period is due. The buyers in an American Option also benefit since they get to select the most opportune time that they can buy an asset cheaply and most favorably.
Also, since most American style options are contracts sold on exchanges, the services of brokers can be efficiently rendered. The sellers and buyers, therefore, have the option of selecting knowledgeable intermediaries who help them make decisions pertaining to the best time and rates for the buying and selling of assets. The buyers and sellers enjoy this flexibility as it ensures that they can earn without much effort. Such benefits are not available to the European option.
That notwithstanding, the European options is advantageous in the sense that there is certainty about the timeline one has until the option is exercised. As discussed, the European option can only be exercised during maturity and no other period prior. The set date is, therefore, the only day when the exercise of the options can be completed. This limited activity removes the uncertainty about the possible earlier execution of the contract, enabling buyers and sellers focus on other things before the set date.
Also, the valuation of the European options is much simpler than that of the American options. Typically, the American Option has to determine the value of the flexibility, otherwise known as the premium, a valuation complex which is relatively complicated. The European option has no such difficulties thereby enabling it to value its assets more simply.
The European option is also very cheap when compared to the others. The lower price is a massive advantage to the sellers since it ensures that they spend far less in the acquisition of the said assets. European options are valued by the use of a specified price of the said asset at a particular date and time.
Finally, a significant advantage of the European option is the considerably lower risk due to the inability of the option to be exercised at any time. The sellers are always sure about the time frames of the execution of the options and do not have to worry about option buyers applying the options at a date before the set maturity date.
The premium for an option refers to the income received by a seller or a writer of a contract to another person. (Rusnakova 150). The premium may also apply to an option’s current price for a deal set to expire. Typically, the premium for a particular option is calculated through the consideration of the two essential components, namely the intrinsic value of the contract as well as the current market price of an asset. The effect of the American option on the pricing premium is that there is the necessity to consider time as a discrete variable. Typically, the time value of money results to an increase in the principal amount of a contract. Since the time aspect is greatly considered, the valuation of the American option is much higher than that of the European Option. Also, for an American call option with dividends, it is always wise to exercise the option before the maturity date since the owner of the call is after that entitled to dividends which would have otherwise not been obtained. Therefore, before the announcement of bonuses, a specific premium has to be preset based on the distribution of expected profits. Once announced, the premiums have to be readjusted to account for the revised information.
The valuation of a Europeans option premium is straightforward in the sense that the Black Scholes formula or black model formula is applied. These formulas consist of simple equations that have a closed form solution. The American option cannot use this formula in its valuation due to the lack of consensus concerning the worth of options at a given time. Figure 1 below represents the European Option formula.
Figure 1. (Trader University np)
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Cheang, Gerald HL, Carl Chiarella, and Andrew Ziogas. "The representation of American options prices under stochastic volatility and jump-diffusion dynamics." Quantitative Finance 13.2 (2013): 241-253.
Chen, Xiaowei, Yuhan Liu, and Dan A. Ralescu. "Uncertain stock model with periodic dividends." Fuzzy Optimization and Decision Making (2013): 1-13.
Chiarella, Carl, and Boda Kang. "The evaluation of American compound option prices under stochastic volatility and stochastic interest rates." Journal of Computational Finance (2013) :71-92
Lewis, Mervyn Keith. "Off-balance sheet activities and financial innovation in banking." PSL Quarterly Review 41.167 (2013).
Rusnakova, Martina. "Commodity price risk management using option strategies." Agricultural Economics-Zemědělská ekonomika 61.4 (2015): 149-157.
Trader University. 2017, https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2012&as_yhi=2017&q=The+premium+for+an+option+refers+to+the+income+received+by+a+seller+&btnG=.
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