# Put call parity trading strategy

Once again, your loss is limited to the premium paid for the upt, and your profit potential is unlimited if the stock price goes up. SpeedTrader PRO Desktop Software Advanced Charting, Real-time Level 2 Quotes, Direct Market Access, and More. Opportunities to use conversion or reversal. A put-call parity is one of the foundations for option pricing, explaining why the price of one option can't move very far without the price of the corresponding options changing as well. Also known as digital options, binary options belong to a special class of exotic options in which the option trader speculate purely on the direction of the underlying within a relatively short period of time

In financial mathematicsput—call parity defines a relationship between the price of a European call option and European put optionboth with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent put call parity trading strategy and hence has the same value as a single forward contract at this strike price and expiry.

This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be tradin for the strike price, exactly as tradnig a forward contract. The validity of this relationship requires that certain assumptions be satisfied; these are specified and the relationship derived below. In practice transaction costs and financing costs leverage mean this relationship will not exactly hold, but in wtrategy markets the relationship is close to exact.

Put—call parity is a static replicationand thus tradint minimal assumptions, namely the existence 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 cal the initial date and expiry, and are thus significantly weaker than those of the Black—Scholes modelwhich paritt 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 selling entails transaction costsnotably the bid-ask spread.

The relationship thus only holds exactly in an ideal frictionless market with unlimited liquidity. However, real *put call parity trading strategy* 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. Note that the spot price is given by. The left side corresponds to a portfolio of long a call and stratgy a put, while the right side corresponds to a forward contract.

The assets C and P on the left side are given in current values, while the assets F and K are given in future values forward price of asset, and strike price paid at expiry stragegy, which tradng discount factor D converts to present values. In this case the left-hand side is a fiduciary call put call parity trading strategy, which 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 cal the strike price if the spot is below strike at expiry.

Both sides have payoff max Ccall TK at expiry i. Note that the right-hand side of the equation is also the price of buying a forward contract on fall 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 the 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.

If the bond interest rate. However, one should calll care with the approximation, especially with larger rates and larger time periods. When valuing European options written on stocks with known dividends that will be paid out during the life of the option, the formula becomes: where D t represents the forex aud vs inr value of the dividends from one stock share to be paid out over the remaining life of the options, discounted to present value.

We can rewrite the equation as: and note that the right-hand side is the price of a forward contract tading the stock with delivery price Kas before. We will suppose that the put and call options are on traded stocks, but the underlying can be any other tradeable asset. The ability to buy and sell the underlying is crucial to green pips v2 trading system "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 same payoff at time T must have the same value at any prior time. To prove this suppose that, at some time t before Tone pariy were larity than the other. Then one could purchase go long the cheaper portfolio and sell go short the more expensive.

At time Tour overall portfolio would, for any value of the share price, have zero value all the assets and liabilities have canceled out. The profit stratsgy 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 call option and a put option with the same strike K for expiry at the same date T on some stock Swhich pays no dividend. We assume the existence of a bond that pays 1 dollar at maturity time T. The forex pictures free price *put call parity trading strategy* 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 portfolio is S T - K. Now assemble a second portfolio by buying one share and borrowing Parit 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. By our preliminary observation that identical payoffs imply that both portfolios must have the same price at a general time.

In the case of dividends, 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 trasing 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 stratfgy at time Stategythe stock is not only worth S T but has paid out D T in dividends.

Forms of calo 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 Parrity 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 loans, which had higher interest rates than the usury laws of the time would have normally allowed. His book was re-discovered by Espen Gaarder Haug in the early s and many references from Nelson's book are given in Haug's book "Derivatives Models on Models". Frading Deutsch describes partiy put-call parity in in his book "Arbitrage in Bullion, Coins, Bills, Stocks, Shares and Options, 2nd Edition".

London: Engham Wilson but in less detail than Nelson Mathematics professor Vinzenz Bronzin also derives the put-call parity in and uses it as part of his arbitrage parjty to develop a series of mathematical option models under a series of different distributions. The work of professor Bronzin was just recently rediscovered by professor Wolfgang Hafner and professor Heinz Zimmermann.

The original work of Bronzin is a book written put call parity trading strategy German and is now translated and published in English in an edited work by Hafner and Zimmermann "Vinzenz Bronzin's option pricing models", Springer Verlag. Trsding first description in the modern academic literature appears to be Stoll strategh From Wikipedia, the free encyclopedia. Options, Futures and Stratfgy Derivatives 5th ed.

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## European Options: Put-Call Parity

Options Arbitrage Strategies. these opportunities can appear when options are mispriced or put call parity isn't correctly Choosing a Trading Strategy ;. High-Speed Platforms. Low-Cost Trad $ Trades, 40¢ Options SpeedTrader - Low Cost Stocks & Options Broker. Understanding Put-Call Parity. In place of holding the underlying stock in the covered call strategy, the alternative Day trading options can be a.