### Compositedge E-learning- Option Greeks

Every tradable asset class has a certain degree of risk associated with it, even the likes of sovereign securities which most of us perceive to be completely risk-free. Since markets are highly unpredictable, you cannot eliminate trading risk completely, but if you want to be a successful trader, the key is to identify the risks early and manage them efficiently.

If you’re new to options or if you’ve been trading them without giving any thought to the underlying risk or wondering why your options strategy is losing money, then what you really need to do before you start trading them is to evaluate Option Greeks and how the price of the underlying instrument affects them.

Option Greeks are statistical values that give us an estimate of the risks associated with the volatility in the underlying financial asset, time to expiry, changes in interest rates, stock dividends etc. Based on the category of risk, Option Greeks are broadly categorised as

Delta- Sensitivity of the option to the price of the underlying

If you’d like to know how much the price of an option would change when the price of the underlying moves by ₹1, you’re in fact trying to calculate the Delta of the option. Put it simply, Delta measures the change in the theoretical value of an option for a ₹1 change in the price of the underlying. Long call/short put options have positive Delta which oscillates between 0 and 1 while long put/ short call options have negative Delta which will move between 0 and -1.

Assuming all other variables such as volatility, time to expiration and interest rates remain the same and if the Delta of an option is reading 0.5, it means that the price of the long call/ short put option for that particular strike will increase by ₹0.50 for every ₹1 rise in the price of the underlying,. Likewise, if the Delta of an option is -0.5, it indicates that the price of the long put/ short call option for that particular strike will drop by ₹- 0.50 for every ₹1 fall in the price of the underlying. Far IN THE MONEY options tend to have a Delta close to 1 while in the case of far OUT OF THE MONEY options, the Delta will be nearer to -1. AT THE MONEY options will generally have a Delta of around 0.5.

Key features of Delta-

- As options approach expiry, the Delta of IN THE MONEY options increases faster and approaches 1 while the Delta of OUT OF THE MONEY options will tend to fall quickly as they slip to 0.
- As volatility increases, the Delta of OUT OF THE MONEY options rise faster than the Delta of IN THE MONEY options.
- For a specific strike price, the Delta of the near-month options contract will rise or fall at a faster pace than the Delta of a far-month contract with the same strike.

Gamma- Rate of change of Delta

Gamma calculates the rate of change of Delta corresponding to a ₹1 change in the price of the underlying and is expressed in percentage. So, if the Delta is the speed at which the value of an option rises or falls, Gamma is the acceleration. Since Delta cannot exceed 1 or fall below -1, the value of Gamma drops and approaches 0 as the options go deeper IN THE MONEY or OUT OF THE MONEY and is at its max when the options is AT THE MONEY.

Key features of Gamma-

- As options approach expiry, the Gamma of AT THE MONEY options increase while the Gamma of IN THE MONEY and OUT OF THE MONEY options decline and approach 0.
- During periods of high volatility, the Gamma remains low across strike prices. However, when volatility decreases, the Gamma of AT THE MONEY options increases while the Gamma of IN THE MONEY and OUT OF THE MONEY options decline and approach 0.

Theta- Time decay

If you’ve noticed your option price declining in spite of no major change in the price of the underlying security, that’s because of Theta or Time Decay. Options lose value as the expiry of the contract approaches and Theta calculates the theoretical value of an option for a one-day decrease in the time to expiry with all other factors such as the price of the underlying and volatility remaining unchanged. Theta is non-linear with calls and puts at the same strike price and expiry having different Theta values.

In the case of equities, if the dividend yield is less than the interest rate, the cost of carry for the stock is considered to be positive. Therefore the Theta for the call will be higher than the put. On the contrary, if the cost of carry for the stock is negative i.e. if the dividend yield is higher than the interest rate, Theta for the put will be higher than the call.

Key features of Theta-

- Long options are negative Theta while short options are positive Theta.
- Theta of the underlying option instrument is always zero.
- Theta is at its max for AT THE MONEY options and gradually drops for IN THE MONEY and OUT OF THE MONEY options. Likewise, Theta is at the highest when volatility decreases and the options contract approaches expiry correspondingly.

Vega- Sensitivity of the option to volatility of the underlying

The price of an option is highly susceptible to volatility. When volatility rises, so does the option premium and vice-versa. That’s because when volatility rises, the possibility of the underlying instrument reaching extreme values increases while a fall in volatility contradicts this likelihood and negatively affects the price of the option.

Vega measures the sensitivity of the option to volatility in the underlying instrument and is calculated as the change in the theoretical value of an option to a 1 percent change in the volatility of the underlying. Vega only affects the Time Value of an option while it does not have any bearing on the Intrinsic Value. Larger the time to expiration, greater will be the impact of volatility on the option price.

Key features of Vega-

- Long calls and puts have positive Vega while short options have negative Vega.
- Vega is at its max for AT THE MONEY options and gradually declines for IN THE MONEY and OUT OF THE MONEY options.
- The Vega of an underlying option instrument is zero.

Rho- Sensitivity to changes in interest rates

Rho evaluates the change in the theoretical value of an option for a 1 percent change in the interest rate. In other words, Rho is the sensitivity of an option to changes in the risk-free interest rate. Generally, call options have positive Rho and puts have negative Rho. This is because as interest rates rise, the value of call options should increase while the value of puts should decrease. Rho is more sensitive for options with longer expiries like LEAPS than for short-term options.

Key features of Rho-

- Long calls and short puts have positive Rho’s while long puts and short calls have negative Rho.
- Rho is mostly looked at just before a monetary policy meeting especially if interest rates are expected to change.

Options Greeks are vital for managing portfolio risk. If you want to be a successful options trader, your primary objective should be to recognize the risks associated with options trading and interpret the Greeks in relation to the options strategy you intend to pursue.

The Compositedge-Protrader platform provides streaming real-time values of Option Greeks, implied volatility and time to expiry to gauge the probability of your options strategy expiring IN THE MONEY. The Compositedge trading platform also live streams second order Greeks like Vanna-Volga, lets you infer the implied volatility smile and paper trade your options strategies before implementing them in real-time markets with the one-touch order entry option.