__Delta Hedging:__

In mathematical finance, the **Greeks** are the quantities representing the sensitivities of derivatives, such as options, to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are often denoted by Greek letters. The Greeks are also called risk sensitivities, risk measures or hedge parameters. The Greeks in the Black-Scholes model are easy to calculate, a desirable property of financial models, and are very useful for derivatives traders; especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging delta, gamma and vega are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black-Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant.

The most common of the Greeks are the first order derivatives: Delta, Vega, Theta and Rho as well as Gamma, a second-order derivative of the value function. Delta will always be a number between 0.0 and 1.0 for a call and 0.0 and -1.0 for a put.

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**Delta Hedging-**is the process of setting or keeping the delta of a portfolio as close to zero as possible. In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re-hedged too frequently.

i.e. establishing the required hedge - may be accomplished by buying or selling an amount of the underlier that corresponds to the delta of the portfolio. By adjusting the amount bought or sold on new positions, the portfolio delta can be made to sum to zero, and the portfolio is then delta neutral.

Options market makers, or others, may form a delta neutral portfolio using related options instead of the underlying. The portfolio's delta (assuming the same underlier) is the sum of all the individual options' deltas. This method can also be used when the underlier is difficult to trade, for instance when an underlying stock is hard to borrow and therefore cannot be sold short. 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. Since the delta of underlying asset is always 1.0, the trader could delta-hedge their entire position in the underlying by buying or shorting the number of shares indicated by the total delta. Given a call and put option for the same underlying, strike price and time to maturity, the sum of the absolute values of the delta of each option will be 1.00