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Khác biệt giữa bản sửa đổi của “Quyền chọn (tài chính)”

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'''Quyền chọn''' ([[tiếng Anh]]: ''option'') là một dạng chứng khoán phái sinh (''derivative securities''). Có hai loại quyền chọn cơ bản: quyền chọn mua (''call option'') và quyền chọn bán (''put option'').
{{Thị trường tài chính}}
 
== Quyền chọn mua ==
Trong [[tài chính]], một '''quyền chọn''' là một hợp đồng trong đó cung cấp cho các chủ sở hữu quyền, nhưng không phải là nghĩa vụ, mua hoặc bán một tài sản hoặc công cụ nền tảng tại một [[giá thực hiện]] nhất định vào hoặc trước một [[kỳ hạn quyền chọn|ngày]] nhất định. Người bán phải gánh chịu một nghĩa vụ tương ứng để thỏa mãn giao dịch này, đó là bán hay mua, nếu người nắm giữ từ lâu quyết định "thực hiện" quyền chọn này trước kỳ hạn. Người mua trả một ''phí bảo hiểm'' cho người bán đối với quyền này. Một quyền chọn mà chuyển tải quyền mua một cái gì đó ở một mức giá cụ thể được gọi là một '''[[quyền chọn gọi mua| gọi mua]]''' , một quyền chọn mà chuyển tải quyền bán một cái gì đó ở một mức giá cụ thể được gọi là một '''[[quyền chọn đặt mua| đặt mua]]'''. Cả hai đều được giao dịch phổ biến, mặc dù trong tài chính cơ bản cho tính rõ ràng của quyền chọn gọi mua thường xuyên được thảo luận nhiều, vì nó di chuyển theo hướng tương tự như các tài sản cơ bản, chứ không phải ngược lại, như quyền chọn đặt mua.
chọn mua là một loại hợp đồng trong đó người nắm giữ quyền chọn có quyền (nhưng không bị bắt buộc) mua một loại tài sản nào đó (tài sản có thể là cổ phiếu, trái phiếu, hoặc là một món hàng hóa nào đó) với một giá đã được định trước (''strike price'') trong một thời gian đã định. Trong giao dịch này có hai phía: người mua quyền chọn mua, hay còn được gọi là người nắm giữ quyền chọn, và người bán quyền chọn mua. Người mua quyền chọn mua phải trả cho người bán quyền một khoản phí giao dịch (''option premium''). Người nắm giữ quyền chọn mua (''call option holder'') sẽ quyết định thực hiện quyền của mình khi thấy có lợi nhuận và người bán quyền chọn mua có nghĩa vụ phải bán tài sản đó cho người nắm giữ quyền chọn mua. Trong trường hợp cảm thấy không có lợi vì lý do nào đó (giá trên thị trường giảm...) người nắm giữ quyền chọn có thể không thực hiện quyền (hủy hợp đồng).
 
== Quyền chọn bán ==
Định giá quyền chọn là một chủ đề nghiên cứu liên tục trong tài chính kinh viện và tài chính thực hành. Để đơn giản của cuộc thảo luận, giá trị của một quyền chọn thường được phân tách ra thành hai phần: Phần đầu tiên là "giá trị nội tại," được định nghĩa là sự khác biệt giữa giá trị thị trường của [[underlying]] và giá thực hiện của quyền chọn đã cho. Phần thứ hai phụ thuộc vào một số yếu tố khác, thông qua một mối tương quan đa biến, phi tuyến, phản ánh [[giá trị dự kiến]] [[được chiết khấu]] của sự khác biệt đó trong kỳ hạn. Mặc dù định giá quyền chọn đã được nghiên cứu ít nhất là từ thế kỷ XIX, phương pháp tiếp cận hiện đại dựa trên [[mô hình Black-Scholes]] được xuất bản đầu tiên vào năm 1973.<ref> Eric Benhamou, Options pre-Black Scholes http://www.ericbenhamou.net/documents/Encyclo/Pre%20Black-Scholes.pdf</ref><ref>Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy 81 (3): 637–654</ref>
Quyền chọn bán là một loại hợp đồng trong đó người nắm giữ quyền chọn có quyền (nhưng không bị bắt buộc) bán một loại tài sản nào đó (tài sản có thể là cổ phiếu, trái phiếu, hoặc là một món hàng hóa nào đó) với một giá đã được định trước trong một thời gian đã định. Trong giao dịch này có hai phía: người mua quyền chọn bán, hay còn được gọi là người nắm giữ quyền chọn, và người bán quyền chọn bán. Người mua quyền chọn bán phải trả cho người bán quyền chọn bán một khoản phí giao dịch. Người nắm giữ quyền chọn bán (''put option holder'') sẽ quyết định thực hiện quyền của mình khi thấy có lợi nhuận và người bán quyền chọn bán có nghĩa vụ phải mua tài sản đó từ người nắm giữ quyền chọn bán. Trong trường hợp cảm thấy không có lợi vì lý do nào đó (giá trên thị trường tăng...) người nắm giữ quyền chọn có thể không thực hiện quyền (hủy hợp đồng).
 
== Các kiểu quyền chọn ==
Các hợp đồng quyền chọn đã được biết đến trong nhiều thế kỷ, tuy nhiên hoạt động trao đổi và quan tâm kinh viện tăng lên khi, bắt đầu từ năm 1973, các quyền chọn được phát hành với các điều kiện tiêu chuẩn và được trao đổi thông qua một trung tâm được bảo lãnh tại [[Chicago Board Options Exchange]]. Ngày nay, nhiều quyền chọn được tạo ra trong hình thức tiêu chuẩn hóa và được giao dịch qua clearinghouses trên các [[trao đổi quyền chọn]] có quản lý, trong khi các quyền chọn OTC khác được viết như các hợp đồng tùy chỉnh song phương, giữa một người mua và người bán duy nhất, một hoặc cả hai có thể là một đại lý hoặc người tạo thị trường. Các quyền chọn là một phần của một lớp các công cụ tài chính lớn hơn được gọi là các [[sản phẩm phái sinh]], hoặc đơn giản là các phái sinh.<ref>{{Citation
* Quyền chọn châu Âu (''European option'') - chỉ có thể được thực hiện vào đúng kì hạn (expiry date), tức là vào một ngày đã được định trước.
|last=Brealey
* Quyền chọn Mỹ (''American option'') - có thể được thực hiện vào bất kì ngày giao dịch nào trước hoặc cùng ngày hết hạn.
|first=Richard A.
* Quyền chọn Bermuda (''Bermudan option'') – có thể được thực hiện vào những ngày đã định rõ cùng hay trước ngày đáo hạn.
|author-link=Richard A. Brealey
* Quyền chọn châu Á (''Asian option'') – quyền chọn với khoản thanh toán bù trừ được xác định bằng trung bình giá tài sản gốc trong một khoảng thời gian định trước.
|last2=Myers
* Quyền chọn rào cản (''Barrier option'') – quyền chọn với đặc trưng chung là giá của tài sản gốc phải vượt qua một ngưỡng ("rào cản") nhất định trước khi quyền này có thể được thực hiện.
|first2=Stewart
* Quyền chọn kép (''Binary option'') – Một dạng quyền chọn tất cả hoặc không gì cả ("được ăn cả ngã về không"), trong đó việc thanh toán đầy đủ toàn bộ giá trị diễn ra nếu như tài sản gốc phù hợp với điều kiện đã xác định trước vào lúc đáo hạn, còn nếu không thì nó đáo hạn mà không có giá trị gì.
|author2-link=Stewart Myers
* Quyền chọn kỳ cục (''Exotic option'') – một phạm trù rộng các quyền chọn, có thể bao gồm các cấu trúc tài chính phức tạp<ref>{{Citation | last = Fabozzi | first = Frank J. | year = 2002 | title = The Handbook of Financial Instruments (Page. 471) | place = New Jersey | publisher = John Wiley and Sons Inc | edition = 1 | isbn = 0-471-22092-2}}</ref>.
|title=Principles of Corporate Finance
* Quyền chọn vani/quyền chọn chuẩn/quyền chọn thông thường (''Vanilla option'') – bất kỳ quyền chọn nào không phải là kỳ cục (exotic).
|publisher=McGraw-Hill
|year=2003
|edition=7th
|id=Chapter 20
}}</ref><ref>{{Citation
|last=Hull
|first=John C.
|title=Options, Futures and Other Derivatives (excerpt by Fan Zhang)
|publisher=Prentice-Hall
|year=2005
|location=Pg 6
|edition=6th
|url=http://fan.zhang.gl/ecref/options
|isbn=0-13-149908-4
}}</ref>
 
==Lợi nhuận==
==Contract specifications==
Với cả hai quyền chọn trên cơ bản (kiểu Mỹ hay châu Âu), lợi nhuận (pay-off) khi quyền chọn được thực hiện được tính bằng:
Every financial option is a contract between the two counterparties with the terms of the option specified in a [[term sheet]]. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications:<ref name=occ>{{citation | title=Characteristics and Risks of Standardized Options | publisher=Options Clearing Corporation | format=PDF | url=http://www.theocc.com/publications/risks/riskstoc.pdf | accessdate=2007-06-21}}</ref>
 
:max[(S-K), 0] ; cho quyền chọn mua
* whether the option holder has the right to buy (a [[call option]]) or the right to sell (a [[put option]])
:max[(K-S), 0] ; cho quyền chọn bán
* the quantity and class of the [[underlying]] asset(s) (e.g., 100 shares of XYZ Co. B stock)
* the [[strike price]], also known as the exercise price, which is the price at which the underlying transaction will occur upon [[exercise (options)|exercise]]
* the [[expiration (options)|expiration]] date, or expiry, which is the last date the option can be exercised
* the [[Settlement (finance)|settlement terms]], for instance whether the writer must deliver the actual asset on exercise, or may simply tender the equivalent cash amount
* the terms by which the option is quoted in the market to convert the quoted price into the actual premium&nbsp;– the total amount paid by the holder to the writer
 
với S là giá giao ngay (''spot price'') của tài sản gốc và K là giá điểm (''strike price'').
==Types==
The Options can be classified into following types:
 
==Ghi chú==
===Exchange-traded options===
{{tham khảo}}
*'''Exchange-traded options''' (also called "listed options") are a class of [[Derivative (finance)#OTC and exchange-traded|exchange-traded derivatives]]. Exchange traded options have standardized contracts, and are settled through a [[Clearing house (finance)|clearing house]] with fulfillment guaranteed by the Options Clearing Corporation (OCC). Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:<ref>{{Citation | title=Trade CME Products | url=http://www.cme.com/trading/ | publisher=Chicago Mercantile Exchange | accessdate=2007-06-21}}</ref><ref>{{Citation | title=ISE Traded Products | publisher=International Securities Exchange | url=http://www.iseoptions.com/products_traded.aspx | accessdate=2007-06-21 |archiveurl = http://web.archive.org/web/20070511003741/http://www.iseoptions.com/products_traded.aspx <!-- Bot retrieved archive --> |archivedate = 2007-05-11}}</ref>
{{sơ khai}}
**[[stock options]],
**[[bond option]]s and other [[interest rate derivative|interest rate options]]
**[[stock market index option]]s or, simply, index options and
**[[options on futures contracts]]
**[[callable bull/bear contract]]
 
[[Thể loại:Chứng khoán]]
===Over-the-counter===
*'''[[Over-the-counter (finance)|Over-the-counter]] options''' (OTC options, also called "dealer options") are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include:
#interest rate options
#currency cross rate options, and
#options on [[swap (finance)|swap]]s or [[swaption]]s.
 
===Other option types===
Another important class of options, particularly in the U.S., are [[employee stock option]]s, which are awarded by a company to their employees as a form of incentive compensation. Other types of options exist in many financial contracts, for example [[Option (law)|real estate option]]s are often used to assemble large parcels of land, and [[Prepayment of loan|prepayment]] options are usually included in [[mortgage loan]]s. However, many of the valuation and risk management principles apply across all financial options.
 
===Option styles===
{{Main|Option style}}
Naming conventions are used to help identify properties common to many different types of options. These include:
*'''European''' option&nbsp;– an option that may only be [[exercise (options)|exercised]] on [[expiration (options)|expiration]].
*'''American''' option&nbsp;– an option that may be exercised on any trading day on or before expiry.
*'''Bermudan''' option&nbsp;– an option that may be exercised only on specified dates on or before expiration.
*'''Asian''' option&nbsp;– an option whose payoff is determined by the average underlying price over some preset time period.
*'''Barrier''' option&nbsp;– any option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.
*'''Binary''' option&nbsp;– An all-or-nothing option that pays the full amount if the underlying security meets the defined condition on expiration otherwise it expires worthless.
*'''Exotic''' option&nbsp;– any of a broad category of options that may include complex financial structures.<ref>{{Citation
| last = Fabozzi
| first = Frank J.
| year = 2002
| title = The Handbook of Financial Instruments (Page. 471)
| place = New Jersey
| publisher = John Wiley and Sons Inc
| edition = 1st
| isbn = 0-471-22092-2
}}</ref>
*'''Vanilla''' option&nbsp;– any option that is not exotic.
 
==Valuation models==
{{Main|Valuation of options}}
The value of an option can be estimated using a variety of quantitative techniques based on the concept of [[risk neutral]] pricing and using [[stochastic calculus]]. The most basic model is the [[Black–Scholes]] model. More sophisticated models are used to model the [[volatility smile]]. These models are implemented using a variety of numerical techniques.<ref>{{Citation
| last =Reilly
| first =Frank K.
| author-link =
| last2 =Brown | first2 =Keith C.
| author2-link =
| title =Investment Analysis and Portfolio Management
| place=
| publisher =Thomson Southwestern
| year =2003
| location =
| volume =
| edition =7th
| url =
| doi =
| id = Chapter 23 }}
</ref>
In general, standard option valuation models depend on the following factors:
 
*The current market price of the underlying security,
*the [[strike price]] of the option, particularly in relation to the current market price of the underlying (in the money vs. out of the money),
*the cost of holding a position in the underlying security, including interest and dividends,
*the time to [[expiration (options)|expiration]] together with any restrictions on when exercise may occur, and
*an estimate of the future [[volatility (finance)|volatility]] of the underlying security's price over the life of the option.
 
More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.
 
The following are some of the principal valuation techniques used in practice to evaluate option contracts.
 
===Black–Scholes===
{{Main|Black–Scholes}}
Following early work by [[Louis Bachelier]] and later work by [[Edward O. Thorp]], [[Fischer Black]] and [[Myron Scholes]] made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock. By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price.<ref>Black, Fischer and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities," [http://www.journals.uchicago.edu/JPE/ Journal of Political Economy], 81 (3), 637–654 (1973).</ref> At the same time, the model generates [[Greeks (finance)|hedge parameters]] necessary for effective risk management of option holdings. While the ideas behind the Black–Scholes model were ground-breaking and eventually led to [[Myron Scholes|Scholes]] and [[Robert C. Merton|Merton]] receiving the [[Swedish Central Bank]]'s associated [[The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel|Prize for Achievement in Economics]] (a.k.a., the [[Nobel Prize]] in Economics),<ref>{{Citation
| last =Das | first =Satyajit
| author-link =
| last2 =
| first2 =
| author2-link =
| title =Traders, Guns & Money: Knowns and unknowns in the dazzling world of derivatives
| place=
| publisher =Prentice-Hall, Chapter 1 'Financial WMDs – derivatives demagoguery,' p.22
| year =2006
| location =London
| volume =
| edition =6th
| url =
| doi =
| isbn =978-0-273-70474-4}}
</ref>
the application of the model in actual options trading is clumsy because of the assumptions of continuous (or no) dividend payment, constant volatility, and a constant interest rate. Nevertheless, the Black–Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range.<ref>{{Citation
| last =Hull | first =John C.
| author-link =
| last2 =
| first2 =
| author2-link =
| title =Options, Futures and Other Derivatives
| place=
| publisher =Prentice-Hall
| year =2005
| location =
| volume =
| edition =6th
| url =
| doi =
| isbn =0-13-149908-4}}
</ref>
 
===Stochastic volatility models===
{{Main|Heston model}}
Since the market crash of 1987, it has been observed that market [[implied volatility]] for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic, varying both for time and for the price level of the underlying security. [[Stochastic volatility]] models have been developed including one developed by [[Heston model|S.L. Heston]].<ref name=gatheral /> One principal advantage of the Heston model is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.<ref name=gatheral>{{Citation | author=Jim Gatheral | title=The Volatility Surface, A Practitioner's Guide | year=2006 | publisher=Wiley Finance | url=http://www.amazon.com/Volatility-Surface-Practitioners-Guide-Finance/dp/0471792519 | isbn=978-0-471-79251-2}}</ref>
 
{{see also|SABR Volatility Model}}
 
==Model implementation==
{{See|Valuation of options}}
Once a valuation model has been chosen, there are a number of different techniques used to take the mathematical models to implement the models.
 
===Analytic techniques===
In some cases, one can take the [[mathematical model]] and using analytical methods develop [[Closed-form expression|closed form solutions]] such as [[Black–Scholes]] and the [[Black model]]. The resulting solutions are readily computable, as are their [[Greeks (finance)|"Greeks"]]. Although the [[Roll-Geske-Whaley]] model applies to an American call with one dividend, for other cases of [[American option]]s, closed form solutions are not available; approximations here include [[Barone-Adesi and Whaley]], [[Bjerksund and Stensland]] and others.
 
===Binomial tree pricing model===
{{Main|Binomial options pricing model}}
Closely following the derivation of Black and Scholes, [[John C. Cox|John Cox]], [[Stephen Ross (economist)|Stephen Ross]] and [[Mark Rubinstein]] developed the original version of the [[binomial options pricing model]].<ref>[[John C. Cox|Cox JC]], [[Stephen Ross (economist)|Ross SA]] and [[Mark Rubinstein|Rubinstein M]]. 1979. Options pricing: a simplified approach, [[Journal of Financial Economics]], 7:229–263.[http://www.in-the-money.com/artandpap/Option%20Pricing%20-%20A%20Simplified%20Approach.doc]
</ref>
<ref>{{Citation
| last =Cox | first =John C.
| author-link =John C. Cox
| last2 =Rubinstein | first2 =Mark
| author2-link =Mark Rubinstein
| title =Options Markets
| place=
| publisher =Prentice-Hall
| year =1985
| location =
| volume =
| edition =
| url =
| doi =
| id = Chapter 5 }}
</ref>
It models the dynamics of the option's theoretical value for [[Lattice model (finance)|discrete time]] intervals over the option's life. The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock (as in the Black–Scholes model) a simple formula can be used to find the option price at each node in the tree. This value can approximate the theoretical value produced by Black Scholes, to the desired degree of precision. However, the binomial model is considered more accurate than Black–Scholes because it is more flexible; e.g., discrete future dividend payments can be modeled correctly at the proper forward time steps, and [[American option]]s can be modeled as well as European ones. Binomial models are widely used by professional option traders. The [[Trinomial tree]] is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex.
 
===Monte Carlo models===
{{Main|Monte Carlo methods for option pricing}}
For many classes of options, traditional valuation techniques are [[Tractable problem|intractable]] because of the complexity of the instrument. In these cases, a Monte Carlo approach may often be useful. Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses [[Monte Carlo simulation|simulation]] to generate random price paths of the underlying asset, each of which results in a payoff for the option. The average of these payoffs can be discounted to yield an [[expectation value]] for the option.<ref>{{Citation
| last =Crack | first =Timothy Falcon
| author-link =
| last2 =
| first2 =
| author2-link =
| title =Basic Black–Scholes: Option Pricing and Trading
| place=pp. 91–102
| publisher =
| year =2004
| location =
| volume =
| edition =1st
| url =http://www.BasicBlackScholes.com/
| doi =
| isbn =0-9700552-2-6}}
</ref>
Note though, that despite its flexibility, using simulation for [[american option|American styled options]] is somewhat more complex than for lattice based models.
 
===Finite difference models===
{{Main|Finite difference methods for option pricing}}
The equations used to model the option are often expressed as [[partial differential equation]]s (see for example [[Black%E2%80%93Scholes#The_Black.E2.80.93Scholes_equation|Black–Scholes equation]]). Once expressed in this form, a [[Finite difference method|finite difference model]] can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including: [[explicit method|explicit finite difference]], [[implicit method|implicit finite difference]] and the [[Crank-Nicholson method]]. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method. Although the finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs&nbsp;– for example dividend yield, risk free rate, or volatility, or some combination of these&nbsp;– that are not [[tractable problem|tractable]] in closed form.
 
===Other models===
Other numerical implementations which have been used to value options include [[finite element method]]s. Additionally, various [[short rate model]]s have been developed for the valuation of [[interest rate derivatives]], [[bond option]]s and [[swaption]]s. These, similarly, allow for closed-form, lattice-based, and simulation-based modelling, with corresponding advantages and considerations.
 
==Risks==
As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the [[Stock option return|return]] from holding an option varies non-linearly with the value of the underlying and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict.
 
In general, the change in the value of an option can be derived from [[Ito's lemma]] as:
 
::<math>dC=\Delta dS + \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt \,</math>
 
where the [[Greeks (finance)|Greeks]] <math>\Delta</math>, <math>\Gamma</math>, <math>\kappa</math> and <math>\theta</math> are the standard hedge parameters calculated from an option valuation model, such as [[Black–Scholes]], and <math>dS</math>, <math>d\sigma</math> and <math>dt</math> are unit changes in the underlying's price, the underlying's volatility and time, respectively.
 
Thus, at any point in time, one can estimate the risk inherent in holding an option by calculating its hedge parameters and then estimating the expected change in the model inputs, <math>dS</math>, <math>d\sigma</math> and <math>dt</math>, provided the changes in these values are small. This technique can be used effectively to understand and manage the risks associated with standard options. For instance, by offsetting a holding in an option with the quantity <math>-\Delta</math> of shares in the underlying, a trader can form a [[delta neutral]] portfolio that is hedged from loss for small changes in the underlying's price. The corresponding price sensitivity formula for this portfolio <math>\Pi</math> is:
 
::<math>d\Pi=\Delta dS + \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt = \Gamma \frac{dS^2}{2} + \kappa d\sigma + \theta dt\,</math>
 
===Example===
A call option expiring in 99 days on 100 shares of XYZ stock is struck at $50, with XYZ currently trading at $48. With future realized volatility over the life of the option estimated at 25%, the theoretical value of the option is $1.89. The hedge parameters <math>\Delta</math>, <math>\Gamma</math>, <math>\kappa</math>, <math>\theta</math> are (0.439, 0.0631, 9.6, and −0.022), respectively. Assume that on the following day, XYZ stock rises to $48.5 and volatility falls to 23.5%. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:
::<math>dC = (0.439 \cdot 0.5) + \left(0.0631 \cdot \frac{0.5^2}{2} \right) + (9.6 \cdot -0.015) + (-0.022 \cdot 1) = 0.0614</math>
 
Under this scenario, the value of the option increases by $0.0614 to $1.9514, realizing a profit of $6.14. Note that for a delta neutral portfolio, whereby the trader had also sold 44 shares of XYZ stock as a hedge, the net loss under the same scenario would be ($15.86).
 
===Pin risk===
{{Main|Pin risk}}
A special situation called [[Pin risk (option)|pin risk]] can arise when the underlying closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer (seller) may not know with certainty whether or not the option will actually be exercised or be allowed to expire worthless. Therefore, the option writer may end up with a large, unwanted residual position in the underlying when the markets open on the next trading day after expiration, regardless of his or her best efforts to avoid such a residual.
 
===Counterparty risk===
A further, often ignored, risk in derivatives such as options is counterparty risk. In an option contract this risk is that the seller won't sell or buy the underlying asset as agreed. The risk can be minimized by using a financially strong intermediary able to make good on the trade, but in a major panic or crash the number of defaults can overwhelm even the strongest intermediaries.
 
==Trading==
The most common way to trade options is via standardized options contracts that are listed by various [[futures exchange|futures and options exchange]]s.
<ref>{{Citation
| last =Harris | first =Larry
| author-link =
| last2 =
| first2 =
| author2-link =
| title =Trading and Exchanges
| place=
| publisher =Oxford University Press
| year =2003
| location =
| volume =
| edition =
| url =
| doi =
| id = pp.26–27 }}
</ref> Listings and prices are tracked and can be looked up by [[Option symbol|ticker symbol]].
By publishing continuous, live markets for option prices, an exchange enables independent parties to engage in [[price discovery]] and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:
*fulfillment of the contract is backed by the credit of the exchange, which typically has the highest [[bond rating|rating]] (AAA),
*counterparties remain anonymous,
*enforcement of market regulation to ensure fairness and transparency, and
*maintenance of orderly markets, especially during fast trading conditions.
 
[[over-the-counter (finance)|Over-the-counter]] options contracts are not traded on exchanges, but instead between two independent parties. Ordinarily, at least one of the counterparties is a well-capitalized institution. By avoiding an exchange, users of OTC options can narrowly tailor the terms of the option contract to suit individual business requirements. In addition, OTC option transactions generally do not need to be advertised to the market and face little or no regulatory requirements. However, OTC counterparties must establish credit lines with each other, and conform to each other's clearing and settlement procedures.
 
With few exceptions,<ref>{{Citation | author=Elinor Mills | title=Google unveils unorthodox stock option auction | publisher=CNet | url=http://news.com.com/Google+unveils+unorthodox+stock+option+auction/2100-1030_3-6143227.html | date=2006-12-12 | accessdate=2007-06-19|archiveurl=http://archive.is/S5Nr|archivedate=2012-07-12}}</ref> there are no [[secondary markets]] for [[employee stock options]]. These must either be exercised by the original grantee or allowed to expire worthless.
 
==The basic trades of traded stock options (American style)==
These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used in hedging. An option contract in US markets usually represents 100 shares of the underlying security.<ref>[http://invest-faq.com/cbc/deriv-option-basics.html invest-faq] or [http://www.wfu.edu/~palmitar/Law&Valuation/chapter%204/4-4-1.htm Law & Valuation] for typical size of option contract</ref>
 
===Long call===
[[File:Long call option.svg|thumb|200px|Payoff from buying a call.]]
A trader who believes that a stock's price will '''increase''' might buy the right to purchase the stock (a [[call option]]) at a fixed price, rather than just purchase the stock itself. He would have no obligation to buy the stock, only the right to do so until the expiration date. If the stock price(spot Price,S) at expiration is above the exercise price(X) by more than the premium (price) paid, he will profit i.e. if S>X, the deal is profitable. If the stock price at expiration is lower than the exercise price, he will let the call contract expire worthless, and only lose the amount of the premium. A trader might buy the option instead of shares, because for the same amount of money, he can control ([[leverage (finance)|leverage]]) a much larger number of shares.
{{Clear}}
 
===Long put===
[[File:Long put option.svg|thumb|200px|Payoff from buying a put.]]
A trader who believes that a stock's price will '''decrease''' can buy the right to sell the stock at a fixed price (a [[put option]]). He will be under no obligation to sell the stock, but has the right to do so until the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, he will profit. If the stock price at expiration is above the exercise price, he will let the put contract expire worthless and only lose the premium paid.In the whole story, the premium also plays a major role as it enhances the break-even point. For example, if exercise price is 100 premium paid is 10 then a spot price of 100 to 90 is not profitable, he would earn profit if the spot price is below 90.
{{Clear}}
 
===Short call===
[[File:Short call option.svg|thumb|200px|Payoff from writing a call.]]
A trader who believes that a stock price will '''decrease''' can sell the stock short or instead sell, or "write," a call. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer's option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money, with the potential loss unlimited.
{{Clear}}
 
===Short put===
[[File:Short put option.svg|thumb|200px|Payoff from writing a put.]]
A trader who believes that a stock price will '''increase''' can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at the put buyer's option. If the stock price at expiration is above the exercise price, the short put position will make a profit in the amount of the premium. If the stock price at expiration is below the exercise price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the full value of the stock. A benchmark index for the performance of a cash-secured short put option position is the [[CBOE S&P 500 PutWrite Index]] (ticker PUT).
{{Clear}}
 
==Option strategies==
{{Main|Option strategies}}
[[File:Long butterfly option.svg|thumb|right|200px|Payoffs from buying a butterfly spread.]]
[[File:Short straddle option.svg|thumb|right|200px|Payoffs from selling a straddle.]]
[[File:Covered Call.jpg|thumb|right|200px|Payoffs from a covered call.]]
Combining any of the four basic kinds of option trades (possibly with different exercise prices and maturities) and the two basic kinds of stock trades (long and short) allows a variety of [[options strategies]]. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.
 
Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a [[Butterfly (options)|butterfly]] spread (long one X1 call, short two X2 calls, and long one X3 call) allows a trader to profit if the stock price on the expiration date is near the middle exercise price, X2, and does not expose the trader to a large loss.
 
An [[Iron condor]] is a strategy that is similar to a butterfly spread, but with different strikes for the short options&nbsp;– offering a larger likelihood of profit but with a lower net credit compared to the butterfly spread.
 
Selling a [[straddle]] (selling both a put and a call at the same exercise price) would give a trader a greater profit than a butterfly if the final stock price is near the exercise price, but might result in a large loss.
 
Similar to the straddle is the [[Strangle (options)|strangle]] which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the risk of loss in the trade.
 
One well-known strategy is the [[covered call]], in which a trader buys a stock (or holds a previously-purchased long stock position), and sells a call. If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit. If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as [[put-call parity]] and offers insights for financial theory. A benchmark index for the performance of a [[buy-write]] strategy is the [[CBOE S&P 500 BuyWrite Index]] (ticker symbol BXM).
 
==Historical uses of options==
Contracts similar to options are believed to have been used since ancient times. In the [[real estate]] market, call options have long been used to assemble large parcels of land from separate owners; e.g., a developer pays for the right to buy several adjacent plots, but is not obligated to buy these plots and might not unless he can buy all the plots in the entire parcel. Film or theatrical producers often buy the right&nbsp;— but not the obligation&nbsp;— to dramatize a specific book or script.
[[Line of credit|Lines of credit]] give the potential borrower the right&nbsp;— but not the obligation&nbsp;— to borrow within a specified time period.
 
Many choices, or embedded options, have traditionally been included in [[bond (finance)|bond]] contracts. For example many bonds are [[Convertible bond|convertible]] into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option. [[Mortgage loan|Mortgage]] borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.
 
In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of [[William and Mary]].<ref name="Global">{{Citation
| last =Smith
| first =B. Mark
| authorlink =
| coauthors =
| title =History of the Global Stock Market from Ancient Rome to Silicon Valley
| publisher =University of Chicago Press
| year =2003
| location =
| pages =20
| url =
| doi =
| isbn =0-226-76404-4}}</ref>
 
''Privileges'' were options sold over the counter in nineteenth century America, with both puts and calls on shares offered by specialized dealers. Their exercise price was fixed at a rounded-off market price on the day or week that the option was bought, and the expiry date was generally three months after purchase. They were not traded in secondary markets.
 
Supposedly the first option buyer in the world was the [[ancient Greece|ancient Greek]] mathematician and philosopher [[Thales]] of Miletus. On a certain occasion, it was predicted that the season's [[olive]] harvest would be larger than usual, and during the off-season he acquired the right to use a number of olive presses the following spring. When spring came and the olive harvest was larger than expected he exercised his options and then rented the presses out at much higher price than he paid for his 'option'.<ref>Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008</ref><ref>Aristotle. Politics.</ref>
 
==Xem thêm==
*[[American Stock Exchange]]
*[[Chicago Board Options Exchange]]
*[[Eurex]]
*[[Euronext.liffe]]
*[[International Securities Exchange]]
*[[NYSE Arca]]
*[[Philadelphia Stock Exchange]]
*[[LEAPS (finance)]]
*[[Real options analysis]]
*[[PnL Explained]]
 
==Chú thích==
{{Reflist|30em}}
 
==Đọc thêm==
*Fischer Black and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities," ''[http://www.journals.uchicago.edu/JPE/ Journal of Political Economy]'', 81 (3), 637–654 (1973).
*Feldman, Barry and Dhuv Roy. "Passive Options-Based Investment Strategies: The Case of the CBOE S&P 500 BuyWrite Index." [http://www.iijournals.com/JOI/default.asp ''The Journal of Investing''], (Summer 2005).
* [[Hagen Kleinert|Kleinert, Hagen]], ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets'', 4th edition, World Scientific (Singapore, 2004); Paperback ISBN 981-238-107-4 '' (also available online: [http://www.physik.fu-berlin.de/~kleinert/b5 PDF-files])''
*Hill, Joanne, Venkatesh Balasubramanian, Krag (Buzz) Gregory, and Ingrid Tierens. "Finding Alpha via Covered Index Writing." [http://www.cfapubs.org/loi/faj Financial Analysts Journal]. (Sept.-Oct. 2006). pp.&nbsp;29–46.
*Moran, Matthew. “Risk-adjusted Performance for Derivatives-based Indexes – Tools to Help Stabilize Returns.” ''[http://www.indexuniverse.com/JOI/ The Journal of Indexes]''. (Fourth Quarter, 2002) pp.&nbsp;34 – 40.
*Reilly, Frank and Keith C. Brown, Investment Analysis and Portfolio Management, 7th edition, Thompson Southwestern, 2003, pp.&nbsp;994–5.
*Schneeweis, Thomas, and Richard Spurgin. "The Benefits of Index Option-Based Strategies for Institutional Portfolios" ''[http://www.iijournals.com/JAI/ The Journal of Alternative Investments]'', (Spring 2001), pp.&nbsp;44 – 52.
*Whaley, Robert. "Risk and Return of the CBOE BuyWrite Monthly Index" ''[http://www.iijournals.com/JOD/ The Journal of Derivatives]'', (Winter 2002), pp.&nbsp;35 – 42.
* Bloss, Michael; Ernst, Dietmar; Häcker Joachim (2008): Derivatives&nbsp;– An authoritative guide to derivatives for financial intermediaries and investors Oldenbourg Verlag München ISBN 978-3-486-58632-9
* Espen Gaarder Haug & Nassim Nicholas Taleb (2008): [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075&rec=1&srcabs=5771 "Why We Have Never Used the Black–Scholes–Merton Option Pricing Formula"]
 
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