Practical use[ edit ] For a vanilla option, delta will be a number between 0. The difference between the delta of a call and the delta of a put at the same strike is equal to one.

See the formulas below. These numbers are commonly presented as a percentage of the total number of shares represented by the option contract s. This is convenient because the option will instantaneously behave like the number of shares indicated by the delta.

For example, if a portfolio of American call options on XYZ each have a delta of 0. The sign and percentage are often dropped — the sign is implicit in the option type negative for put, positive for call and the percentage is understood.

Delta is always positive for long calls and negative for long puts unless they are zero. The total delta of a complex portfolio of positions on the same underlying asset can be calculated by simply taking the sum of the deltas for each individual position — delta of a portfolio is linear in the constituents.

Since the delta of underlying parametrii opțiunii delta is always 1. This portfolio will then retain its total value regardless of which direction the price of XYZ moves. Albeit for only small movements of the underlying, a short amount of time and not-withstanding changes in other market conditions such as volatility and the rate of return for a risk-free investment.

As a proxy for probability[ edit ] Main article: Moneyness The absolute value of Delta is close to, but not identical with, the percent moneyness of an option, i. For example, if an out-of-the-money call option has a delta of 0.

At-the-money calls and puts have a delta of approximately 0. The actual probability of an option finishing in the money is its dual deltawhich is the first derivative of option price with respect to strike. This is due to put—call parity : a long call plus a short put a call minus a put replicates a forward, which has delta equal to 1.

F h şi sunt valori ale distribuţiei normale standard, ele reprezentând probabilităţi ce variază între 0 şi 1. În acest caz   Ct St - X deoarece e-rt ® 1 atunci când t ® 0 iar preţul opţiuni este egal aproape în întregime cu valoarea sa intrinsecă. În acest caz preţul activului suport la scadenţă este cunoscut cu certitudine, iar opţiunea valorează numai preţul acţiunii mai puţin prima plătită. Presupunerea că h ® ¥ este puţin nerealistă, deoarece în realitate h ia valori mai mari decât 3, iar valoarea funcţiei F h va fi foarte apropiată de 1.

If the value of delta for an option is known, one can calculate the value of the delta of the option of the same strike price, underlying and maturity but opposite right by subtracting 1 from a known call delta or adding 1 to a known put parametrii opțiunii delta.