GettingStarted
Strategies &Advanced Concepts
Options EducationProgram
Seminars& Events
Tools& Resources
News& Research
Options forAdvisors
&&Strategies & Advanced Concepts&&&Advanced Concepts&&&Put/Call Parity
Advanced Concepts
Put/Call Parity
Put/call parity is a captivating, noticeable reality arising from the options markets. By gaining an understanding of put/call parity, one can begin to better understand some mechanics that professional traders may use to value options, how supply and demand impacts option prices and how all option values (at all the available strikes and expirations) on the same underlying security are related. Prior to learning the relationships between call and put values, we’ll review a couple of items.
Let us begin by defining arbitrage and how arbitrage opportunities serve the markets. Arbitrage is, generally speaking, the opportunity to profit arising from price variances on one security in different markets. For example, if an investor can buy XYZ in one market and simultaneously sell XYZ on another market for a higher price, the trade would result in a profit with little risk.
The selling pressure in the higher priced market will drive XYZ’s price down. Conversely, the buying of XYZ in the lower price market will drive XYZ’s price higher. The buying and selling pressure in the two markets will move the price difference between the markets towards equilibrium, quickly eliminating any opportunity for arbitrage. The “no-arbitrage principle” indicates that any rational price for a financial instrument must exclude arbitrage opportunities. That is, we can determine the value of a financial instrument if we assume arbitrage to be unavailable. Using this principle, we can value options under the assumption that no arbitrage opportunities exist.
When trying to understand arbitrage as it relates to stock and options markets, we often assume no restrictions on borrowing money, no restrictions on borrowing shares of stock, and no transactions costs. In the real world, such restrictions do exist and, of course, transaction costs are present which may reduce or eliminate any perceived arbitrage opportunity for most individual investors. For investors with access to large amounts of capital, low fee structures and few restrictions on borrowing, arbitrage may be possible at times, although these opportunities are fairly rare.
Defining Derivatives
Opt they derive their value from other factors. In the case of stock options, the value is derived from the underlying stock, interest rates, dividends, anticipated volatility and time to expiration. There are certain factors that must hold true for options under the no arbitrage principle.
For example, a $50 call option on XYZ expiring June of the current year must be priced at the same or lower price than the September XYZ $50 call option for the current year. If the September call is less expensive, investors would buy the September call, sell the June call and guarantee a profit. Note that XYZ is a non-dividend paying stock, the options are American exercise style and interest rates are expected to be constant over the life of both options.
Here is an example of why a longer term option premium must be equal to or greater than the premium of the short term option.
Transaction 1: Buy September call for $3.00
Transaction 2: Sell June call for $3.50
Transaction 3: Assigned on June call, receive $50/share, short 100 XYZ
Transaction 4: Exercise September call, pay $50/share, flatten existing short position
Result: $0.50 per share profit
*note XYZ is a non-dividend paying stock*
In our interest free, commission free, hypothetical world, the timing of the assignment does not matter, however the exercise would only occur after an assignment. Note too that if XYZ falls below the $50 strike price, it does not impact the trade as a result of the $0.50 credit received when the positions were opened. If both options expire worthless, the net result is still a profit of $0.50.
This example shows why a $50 XYZ call option expiring this June, must trade at the same or lower premium than a $50 call option expiring the following September. If the June premium was higher (like in the example), investors would sell the June call, causing the price to decline and buy the September, causing the price of that option to rise. These trades would continue until the price of the June option was equal to or below the price of the September option.
A similar relationship can be seen between two different strike prices but the same expiration. For example, if an XYZ June $50 call was trading at $4.00 and the June $45 call was trading at $3.00, a rational investor would sell the $50 call, buy the $45 call, generating a $1 per share credit and pocket a profit.
Synthetic Relationships
With stock and options, there are six possible positions from three securities when dividends and interest rates are equal to zero – stock, calls and puts:
Long Stock
Short Stock
Short Call
Original Position
Equivalent
Long Stock
Short Stock
Short Call
Long Stock
Short Call
Short Stock
Short Stock
Long Stock
Short Call
Synthetic relationships with options occur by replicating a one part position, for example long stock, by taking a two part position in two other instruments. Similar to how synthetic oil is not extracted from the fossil fuels beneath the ground. Rather synthetic oil is manufactured with chemicals and is man-made. Similarly, synthetic positions in stocks and options are generated from positions in other instruments.
To replicate the gain/loss characteristics of a long stock position, one would purchase a call and write a put simultaneously. The call and put would have the same strike price and the same expiration. By taking these two combined positions (long call and short put), we can replicate a third one (long stock). If we were to look at the gain/loss characteristics of a long stock position, the gain/loss characteristics of a combined short put/long call position would be identical. Remember the put premiums typically increase when the stock prices decline which negatively im and of course the call premiums typically increase as the stock price increases, positively impacting the call holder. Therefore, as the stock rises, the synthetic position als as the stock price falls, the synthetic position also falls.
Let’s take a closer look at a synthetic long stock position. ABC is trading at $49 per share. The $50 put is trading at $2.00 and the $50 call is trading at $1.00 – the call and the put have the same expiration - for purposes of this example the actual expiration does not matter. An investor can purchase the call and write the put. In doing so, the investor generated a $1.00 credit per share.
If assigned on the short put, the put writer pays the strike price of $50 (a total of $5,000 for one put) and receives 100 shares of ABC. If the investor elects to exercise the call, they would pay $50 per share and (similar to the assigned put) receives 100 shares. But remember the investor took in a credit of $1 when they entered the synthetic position, thus the “effective” purchase price of the stock is $50 (paid when assignment or exercise occurs) less $1 credit from initial trade equals $49/share – the price of ABC in the market.
ABC = $49/share
ABC $50 put = $2.00
ABC $50 call = $1.00
The relationship of put/call parity can now be seen. In the previous example, if the relationship did not hold, rational investors would buy and sell the stock, calls and puts, driving the prices of the calls, puts and stock up or down until the relationship came back in line.
Change the ABC price to $49.50 and leave the call and put premiums the same. The synthetic long stock position can be established for $49/share - $0.50 less than the market price of ABC. Rational investors would buy calls and sell puts instead of purchasing stock (and maybe even short the stock to offset the position completely and lock in a $.50 profit – technically called a “reversal”). Eventually the buying of the calls would drive the price up and the selling of the puts would cause the put premiums to decline (and any selling of the stock would cause the stock price to decline also). This would occur until the put/call parity relationship falls back in line, thus diminishing the opportunity for arbitrage.
Bid/ask spreads and other transaction costs impact the ability of investors to implement the above trades. Other factors too will change the relationship – notably dividends and interest rates. Options are priced using the “no arbitrage principle”. The previous examples show how the markets participants would react to a potential arbitrage opportunity and what the impact may be on prices.
All this leads us to the final put/call parity equation-assuming interest rates and dividends equal zero: +stock = +call – put where “+” is long and “-“ or stated as written: stock price equals long call premium
any credit received or debit paid is added to or subtracted from the strike price of the options. The strike price of the call and put are the same. This assumes the strike prices and the expirations are the same on the call and put with interest rates and dividends equal to zero.
Impact of Dividends & Interest Rates
The next logical question is how ordinary dividends and interest rates impact the put call relationship and option prices. Interest is a cost to an investor who borrows funds to purchase stock and a benefit to investors who receive and invests funds from shorting stock (typically only large institutions receive interest on short credit balances). Higher interest rates thus tend to increase call option premiums and decrease put option premiums.
For a professional trader looking to remain “delta neutral” and not be impacted by market movements the offset to a short call is long stock. Long stock requires capital. The cost of these funds suggests the call seller must ask for higher premiums when selling calls to offset the cost of interest on money borrowed to purchase the stock. Conversely, the offset to a short put is short stock. As a short stock position earns interest (for some large investors at least), the put seller can ask for a lower premium as the interest earned decreases the cost of funds.
For example, an investor is looking to sell a one-year call option on a $75 stock at the $75 strike price. If the one-year interest rate is 5%, the cost of borrowing $7,500 for one year is: $7,500 x 5% = $375. Therefore, the call option on this non-dividend paying stock would have to be sold (at a minimum) for $3.75 just to cover the cost of carrying the position for one year.
Dividends reduce the cost of borrowing – if an investor borrows $7,500 (or some percentage thereof) to purchase 100 shares of a $75 stock and receives a $1/share dividend, he pays less interest on the money borrowed (assuming the $100 from the dividend is applied to the loan). This reduces the cost of carry – as the cost of carrying the stock position into the future is reduced from the dividend received by holding the stock. Opposite of interest rates, higher dividends tend to reduce call option prices and increase put option prices.
Professional traders understand the relationships among calls, puts, interest rates and dividends, among other factors. For individual investors, understanding the early exercise feature of American style options is essential. When writing options, intuition as to when assignment may occur and when holding options understanding when to exercise at an opportunistic time is very important. For dividend paying stocks, exercise and assignment activity occurs more frequently just before (call exercises) and after (put exercises) an ex-dividend date.
Our position simulator and pricing calculators can help evaluate these relationships:
For additional insight into options pricing, our &may help.
Put/Call Parity Formula - Non-Dividend Paying Security
c = S + p – Xe–r(T– t)
p = c - S + Xe–r(T– t)
c = call value
S = current stock price
p = put price
X = exercise price of option
e = Euler’s constant – approximately 2.71828 (exponential function on a financial calculator)
r = continuously compounded risk free interest rate
T-t = term to expiration measured in years
&&&&T = Expiration date
&&&&t = Current value date
Put-call parity: The relationship that exists between call and put prices of the same underlying, strike price and expiration month.
Conversion: An investment strategy in which a long put and short call with the same strike and expiration is combined with a long stock position. This is also referred to as conversion arbitrage.
Reverse Conversion: An investment strategy in which a long call and short put with the same strike and expiration is combined with a short stock position. This is also referred to as reversal arbitrage.
Arbitrage: Purchase or sale of instruments in one market versus the purchase or sale of similar instruments in another market in an effort to profit from price differences. Options arbitrage uses stock, cash and options to replicate other options. Synthetic options imitate the risk reward profile of &real& options using a combination of call and put options and the underlying stock.
Synthetic positions
- Interest rates and dividends equal zero
- Strike prices and expirations the same for call and puts
Synthetic Long Stock = Long Call and Short Put (same expiration & strike)
*Synthetic Long Call = Long Put and Long Stock
Synthetic Long Put = Long Call and Short Stock
Synthetic Short Stock = Long Put and Short Call (same expiration & strike)
Synthetic Short Call = Short Put and Short Stock
*Synthetic Short Put = Short Call and Long Stock
*Most covered call writers (and protective put buyers) don't realize they are trading synthetic positions!
Talk to Options Professionals
Questions about anything options-related?
Call or chat with an options
professional now.
Call 1-888-OPTIONS
Chat with Options Professionals
Questions about anything options-related?
Chat with an options professional now.
Email Options Professionals
Questions about anything options-related?
Email an options professional now.
REGISTER FOR THE OPTIONSEDUCATION PROGRAM
Free, unbiased options education
Learn in-person and online
Advance at your own pace
Chicago, IL
Official OIC Sponsors
This web site discusses exchange-traded options issued by The Options Clearing Corporation. No statement in this web site is to be construed as a recommendation to purchase or sell a security, or to provide investment advice. Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of . Copies of this document may be obtained from your broker, from any exchange on which options are traded or by contacting The Options Clearing Corporation, One North Wacker Dr., Suite 500 Chicago, IL 60-678-4667).
The Options Industry Council - All rights reserved. Please view our
This web site discusses exchange-traded options issued by The Options Clearing Corporation. No statement in this web site is to be construed as a recommendation to purchase or sell a security, or to provide investment advice.Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of
(PDF). Copies of this document may be obtained from your broker or from any exchange on which options are traded or by contacting The Options Clearing Corporation, One North Wacker Dr., Suite 500 Chicago, IL 6-678-4667).
Don't have an account?
Find answers to the most common questions fielded by our help desk.
From A-Z, find definitions for hundreds of options terms.
Having trouble finding what you're looking for? View our site map for a detailed listing of all our content and tools.
A selection of helpful web sites for Quotes & News, Options Exchanges, Education and Tools, and other organizations.
Want to incorporate options content into your organizations web site? Learn more about our partnership program
Still not finding what you're looking for? We urge you to call our options professionals at 1-888-678-4667.
NEED MORE ASSISTANCE?put call parity
[put k?:l 'paer?ti:]
[p?t k?l 'paer?ti]
[财]看跌—看涨期权平价
大家都在背：
1.看跌—看涨期权平价
2.期权平价原则
1. 认沽认购等价关系
日&-& 认沽认购等价关系 relationship of put-call parity 认沽权证 put warrant 认股期权 share option 认股权证 warrant 认购subscription 认购不足.
- 基于10个网页
1. 买入-出售价差
投资分析机构财经词典(O-R) ... Put Bond 可卖回债券 Put-Call Parity 买入-出售价差 Put-Call Ratio 买入-出售比率.
- 基于61个网页
2. 期权平价关系
根据看跌一看涨期权平价关系(Put-call parity )同样可以推导出相同标的物、期限和行权价格的看跌期权的价格。B-S模型只解决了不 …
- 基于50个网页
0){var rand = parseInt(Math.random() * (000)+100000);top.location.href='/'+encodeURIComponent(document.getElementById('s').value.trim().replace( / /g, '_'))+'?renovate='+}else{top.location.href='/'+encodeURIComponent(document.getElementById('s').value.trim().replace( / /g, '_'));};}" action="/">
查过的词自动加入生词本
Tip：此功能设置只能在登录状态下生效
put call parity
需要改进的内容：
单词大小写
其他（请在下面补充描述）
错误描述：
您还可在这里补充说明下 O(∩_∩)O~
方便的话，请您留下一种联系方式，便于问题的解决：什么是Put-call_parity?
什么是Put-call_parity?
10-02-23 & 发布
买卖权平价关系（Put-call parity） 　　买卖权平价关系是指具有相同的行使价与到期日的，其与买权价格间所必然存在的基本关系。如果两者不相同，则存在的空间。买卖权平价关系可应用于，即不能提前、只能在到期日履行。在合约期内的任何时间都可以履行。
请登录后再发表评论!Put-Call Parity代表什么？_百度知道
Put-Call Parity代表什么？
同学你好，很高兴为您解答！　　Put-Call Parity买入-出售价差对同一种证券、到期日相同的出售期权价格与买入期权价格之间的关系。　　对于各个投资领域内的专业人员，包括基金经理、证券分析师、财务总监、投资顾问、投资银行家、交易员等等，CFA非常重要；它直接证明了你的职业素养和能力，被投资业看成一个“黄金标准”,这一资格被认为是投资业界中具有专业技能和职业操守的承诺。考生考过CFA对自己将会有很大帮助。　　希望的回答能帮助您解决问题，更多财会问题欢迎提交给。高顿祝您生活愉快！
已回答17901
响应时间&19小时
其他类似问题
为您推荐：
其他1条回答
看跌—看涨期权平价
等待您来回答
下载知道APP
随时随地咨询
出门在外也不愁