# Option Greeks

The Greeks measure different dimension to the risk in an option position and the aim of the trader is to manage the Greeks so that all risks are acceptable. Or we can say Greeks are sensitivities to particular market variable. Sensitivity is nothing but risk in some form or the other.

The different Greeks are: Delta, Gamma, Theta, Vega, and Rho.

**DELTA**: It is defined as the rate of change of the option price with respect to the price of the underlying asset. It is the slope of the curve that relates the option price to the underlying asset.

The delta varies between 0 and 1 for a call option, and -1 to 0 for a put option.

For e.g., If you purchase 1 lot of Bank Nifty Futures (Lot Size = 40) and 1 lot of Bank Nifty “At the Money” Call Option. The delta for the option is 0.6. Now if Bank Nifty moves by 10 points then the Option price will move by 6 Points. In Simple terms, in 1 lot of futures you will make a profit of Rs. 400 and for 1 lot of Call Option Rs. 240.

Thus if you want a perfect hedge for your futures long position, you need to do the delta neutral balancing to calculate the exact number of lots of short call options required.

Delta is always on the move as No one can stop the markets from its natural movement.

**GAMMA: **It is defined as the rate of change of portfolio’s delta with respect to the price of underlying asset – in other words, the second order partial derivative of the portfolio with respect to the asset price.

It indicates the amount the delta would change given a 1 point move in the underlying security.

If the gamma is small, delta changes slowly, and adjustments to keep a portfolio delta neutral need to be made only relatively infrequently. However if Gamma is highly negative or highly positive, delta is very sensitive to the price of the underlying asset. It is then quite risky to leave a delta neutral portfolio unchanged for any length of time. Let’s understand this thing in the example below:

Figure below illustrates this point. When the stock price move from S to S’, delta hedging assumes that the option price moves from C to C’, when in fact it moves from C to C”. The difference between C’ and C” leads to a hedging error. The size of the error depends on the curvature of the relationship between the option price and the stock price (which is known as Gamma).

Thus Gamma Neutrality protects against large changes in the price of the underlying asset between hedge rebalancing.

**THETA: **It is defined as the rate of change of the value of the portfolio with respect to the passage of time with all else remaining the same. It is sometimes referred to as the time decay of the portfolio. It helps the trader identify the right strike to trade under a given circumstance.

It also helps the trader identify the right strike to trade under a given circumstance.

You may have heard of traders say that they lost money in put options, even though the markets moved up. The reason is simply the time value decay and wrong selection of strikes at the wrong time.

For e.g., Right at the start of the month, Nifty is at 10300 and you expect this month’s expiry to be around 10500 and you purchase a call option at the start of the month at a price of 70. Now one day before the expiry and Nifty is at 10361 and the option price is 2.5. The loss of (70-2.5 = 67.5) points in the option value is just the time value decay and wrong selection of strike. What would have been a better option is to select an “At the Money” strike Call option at the money starting.

POSITION INITIATION |
EXPECTED TIME TO REACH TARGET PRICE |
STRIKES TO CHOOSE TO TAKE POSITIONS IN OPTIONS |

Start of the Series | 5 days from initiation | OTM |

Start of the Series | 15 days from initiation | ITM or ATM |

Start of the Series | 25 days from initiation | ITM |

Start of the Series | At expiry | ATM |

Second Half of the series | One Day (event Specific) | OTM |

Second Half of the series | 5 days from initiation | Target Strike (OTM) |

Second Half of the series | 10 days from initiation | ATM, slightly OTM |

Second Half of the series | 15 days from initiation | ITM or ATM |

OTM – Out of the Money

ATM – At the Money

ITM – in the Money

Thus theta has an continuous effect as No one can stop time.

**VEGA: **Up to now we have implicitly assumed that the volatility of the asset underlying a derivative is constant. In practice, Volatilities change over time. This means that the value of a derivative is liable to change because of movements in volatility as well as because of changes in the asset price and the passage of time.

The Vega of a portfolio of derivative is the rate of change of the value of the option portfolio with respect to the volatility of the underlying asset. Or we can say the Market is driven by the emotions of investors/traders which is nothing but the volatility.

If Vega is highly positive or highly negative, the portfolio’s value is very sensitive to small changes in volatility. If it is close to zero, volatility changes have relatively little impact on the value of the portfolio.

For e.g., an option with a Vega of 0.15 indicates the option’s value is expected to change by 15 cents if the implied volatility changes by 1%

Vega neutrality protects against implied volatility. When volatilities change, the implied volatilities of short – dated options tend to change by more than the implied volatilities of long – dated options.

**RHO: ** It is defined as the rate of change of the value of the portfolio with respect to the interest rate.

Call options have positive Rho while Put options have negative Rho. Thus, Call options generally rise in price as interest rates increase and put options generally decrease in price as interest rates increase.

Rho is larger for options that are in-the-money and decreases steadily as the option changes to become out-of-the-money.

Also, rho increases as time to expiration increases.

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