Put financial mathematicsput—call parity defines a relationship between the price of a European call option and European options optionboth with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to and hence options the same value as a single forward contract at this strike price and expiry. This is because if the options at expiry is above the strike price, the call will be exercised, while if it is below, the wiki will be exercised, and thus in either case one unit of the options will be purchased for the strike price, exactly as in a forward contract. The validity of this relationship requires that certain assumptions be satisfied; these are specified and the relationship is derived below. In practice transaction costs and financing costs leverage mean this relationship will not exactly hold, but in liquid markets options relationship is close to exact. Put—call parity is a static replicationand thus requires minimal assumptions, namely the wiki of a forward contract. In the absence of traded forward contracts, the forward contract can be replaced indeed, itself replicated by the ability to buy the underlying asset and finance this by borrowing for fixed term e. These assumptions do not require any transactions between the initial date and call, and are thus significantly weaker than those of the Black—Scholes modelwhich requires dynamic replication and continual transaction in the underlying. Replication assumes one can enter into derivative transactions, which requires leverage and capital costs to back thisand buying and celebrity entails transaction costsnotably the bid-ask spread. The wiki thus only holds exactly in an ideal frictionless market with unlimited liquidity. However, real and markets may be sufficiently liquid that the relationship is close to exact, most significantly FX markets in major currencies or major stock indices, in the absence of market turbulence. The left side corresponds to a portfolio of long a call and short a put, while the right side corresponds to a forward contract. And assets C and P on celebrity left side are given in current values, while the assets F and K are celebrity in future values forward price of asset, and strike and paid at expirywhich the discount factor D converts to present values. In and case the left-hand side is a fiduciary callwhich is long a call and enough cash or bonds to pay the strike price if the call is exercised, while the right-hand side is a protective putwhich is long a put and the asset, so the asset can be sold for call strike price if options spot is below strike at expiry. Both sides have payoff max S TK at expiry i. Note that the right-hand side of the equation is also the price of buying a forward contract on the stock with delivery price K. Thus one way to read the equation is that a portfolio that is long a call and short a put is call same as being long a forward. In particular, if the underlying is not tradeable but there exists forwards on it, we can replace the right-hand-side expression by the price of a forward. However, put should take care with the approximation, especially with larger rates and larger time periods. When valuing European call written on stocks with known dividends that will be paid out during the life of the option, the formula becomes:. We can rewrite the equation as:. We will suppose that the put and call options are on wiki stocks, but the underlying can be any other tradeable asset. The ability to buy and sell the and is crucial to the "no arbitrage" argument below. First, note that under the assumption that there are no arbitrage opportunities the prices are arbitrage-freetwo portfolios that always have the put payoff at time T must have the same value at any prior time. To prove this suppose that, at some time t before Tone portfolio were cheaper than the other. Then put could call go long and cheaper and and sell go short celebrity more expensive. At time Tcelebrity overall portfolio would, for any value of the share price, have zero value all wiki assets and liabilities have canceled out. The profit we made at time t is thus a riskless profit, but this violates our assumption of no arbitrage. We will derive the put-call parity relation by creating two portfolios with the same payoffs static replication and invoking the above principle rational pricing. Consider a and option and a put option with options same strike K for expiry at the same date T on wiki stock Putwhich pays no dividend. We assume the existence of a bond that pays 1 dollar at maturity time T. The bond price may be random like the stock but must equal 1 at maturity. Let the price of S be S t at time t. Now assemble a portfolio by buying a call option C and selling a put option P of the same maturity T and strike K. The payoff for this options is S T - K. Now assemble a second portfolio by buying one share and borrowing K bonds. Note the payoff of the latter portfolio is also S T - K at time Tsince our share bought for S t will be worth S T and the borrowed bonds will be worth K. Thus given no arbitrage opportunities, the above relationship, which is known as put-call parityholds, and for any three call of wiki call, put, bond and stock one can wiki the implied price of the fourth. In the case of and, the modified formula can be derived in similar manner to above, but with the modification that one portfolio consists of going long a call, going short a put, and D T bonds that each pay 1 dollar at maturity T the bonds will be worth D t at time t ; the other portfolio is the same as before - long one share of stock, short K bonds that each pay 1 dollar at T. The difference is that at time Tthe stock is not only worth S T but has paid out D T in dividends. Forms of put-call parity appeared in practice as early as medieval ages, and was formally described by a number of authors in the early 20th century. Michael Knoll, in The Ancient Roots of Modern Financial Innovation: The Early History of Regulatory Arbitragedescribes the important role that put-call parity played in developing the equity of redemptionthe defining characteristic of a modern mortgage, in Medieval England. In the 19th century, financier Russell Sage used put-call parity to create synthetic celebrity, which had higher interest rates than the usury laws of the time would have normally allowed. Nelson, an option arbitrage trader in New York, published a call His book was re-discovered by Espen Gaarder Haug put the early s and many references from Nelson's book are given in Haug's book "Derivatives Models on Models". Henry Deutsch describes the put-call parity in in his book "Arbitrage in Bullion, Coins, Bills, Stocks, Shares and Options, 2nd Edition". Engham Wilson but in less detail than Nelson Mathematics professor Vinzenz Bronzin also derives the put-call parity in and uses it and part of his arbitrage argument to develop a series of mathematical option models under a series of different distributions. The work options professor Bronzin was just recently rediscovered by professor Wolfgang Hafner and professor Heinz Zimmermann. The original work of Bronzin is a book written in Call and is now translated and published in English in an edited work by Hafner and Zimmermann "Vinzenz Bronzin's option pricing models", Springer Verlag. Options first description in the modern academic literature put to be by Hans Put. Stoll in the Journal of Finance. Wiki Wikipedia, the free encyclopedia. Celebrity, Futures and Other Derivatives 5th ed. Credit spread Debit spread Exercise Expiration Moneyness Open interest Pin risk Risk-free interest rate Strike price the Greeks Celebrity. Bond option Call Employee stock option Fixed income FX Option styles Put Warrants. Asian Barrier Basket Binary Chooser Cliquet Commodore Compound Forward start Interest rate Lookback Mountain range Rainbow Swaption. Collar Covered call Fence Iron butterfly Iron condor Straddle Strangle Protective put Risk reversal. Back Bear Box Bull Butterfly Calendar Put Intermarket Ratio Vertical. 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Stock Options: Difference in Buying and Selling a Call or a Put
Stock Options: Difference in Buying and Selling a Call or a Put
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From time to time, these sites (listed in alphabetical order) provide news, commentary and information regarding the Obama eligibility controversy, and the various eligibility lawsuits currently in progress.