Most utilized option greeks are Delta, Theta, Vega and Rho. Option greeks signify sensitivity of an option’s price. Each greek is the sensitivity measurement for a variable that affects the option’s price directly in Black & Scholes formula.

Option greeks measure sensitivity to variables that are used in the option price calculations such as: underlying price, volatility, interest rate and time to maturity.

Delta (Δ)

Delta is the sensitivity of an option’s price to the change in the underlying asset’s price. If delta is 0.5 this means a price change of $1 in the underlying price will cause a price change of $0.5 in the options price. If the option is a call, then option price moves in the same direction and if the option is put then the delta will affect the option price in the opposite direction then the underlying price. We will cover some examples to elaborate this.

Gamma (γ)

Gamma is the only second order greek that we will cover in this post meaning it is a greek of a greek. It is the only commonly utilized second order greek as well. It shows the option’s delta change per $1 change in the underlying asset price.

Vega (v)

Another important greek is the vega, which shows sensitivity to the volatility. Option value increases parallel to the volatility of the underlying asset. It happens both for call and put options the same way since volatility increase causes the option prices to go up regardless of their type.

Theta (θ)

Theta describes the sensitivity or change in an option’s value based on the time remaining to expiration. The rate of change will vary depending on the time remaining and this is called option’s time decay. In this case as we sell the call option, we collect the theta value from the buyer up front. As time passes, time value of any option decreases. Meaning we realize the profit from the time value component of the option we sold. In other words, we sell the option when the theta is high, and it goes all the way down to zero on maturity. This is a fundamental concept of insurance as well, and that’s the reason why if you’d like to insure your car, your house, your life or anything, the higher the duration the more the insurance will cost. And if nothing bad happens during the insurance period, insurer realizes the premium you have paid. Covered call and selling any option is indeed allows you to do some sort of insurer role however in covered calls your position is rather hedged, hence the term covered, with the underlying product

Rho (ρ)

Rho is used to measure sensitivity to a rate change. Assume that a call option is currently priced at $10 and has a rho value of 0.5. If the interest rates increase by 1%, then the call option price will increase by $0.50 (to $10.50) or by the amount of its rho value. Most likely you don’t want the interest rates to increase too much after you sold your call option as you will have sold at a cheaper price then you would have but small interest rate fluctuations shouldn’t be that significant unless you have a very big position.

#### Option greek example

Apple Inc. (@AAPL) Call & Put options while APPL is trading at $150 (strike price: $150, ATM – at the money)

We see in the example that Call option has a delta of $0.64 and the put option has a delta of $0.43 meaning if the APPL stock price went up $1 call option would increase $0.64 and put option price would decrease $0.43.

We also see that call option has a gamma of 0.03 and put option has a gamma of 0.02. This means that if the APPL stock increase $1 in price, call’s delta will increase to ~0.67 and put option’s delta will increase to ~-0.41.

Rho for call option seems to be 0.110 and for put: -0.057. This means, 1% of interest rate increase is expected to cause $0.11 increase in the call option’s price and $0.057 decrease in the put price.

Thetas are showing the price decrease per 1 day. It seems call option is losing $0.119 everyday and put option is losing $0.06968 everyday. Theta’s value also changes as the other variables (such as time to maturity, volatility etc.) change.

Finally, vega of 0.19 each shows us that 1% increase in the underlying price volatility will cause an increase of %0.19 in both options’ price. A decrease of 1% decrease in volatility would decrease both options prices by $0.19. This may seem like a tiny change but options work differently and they can have very cheap prices. So, for instance, if an option costs $1.90, a change of $0.19 would mean 10% of price change. Similarly, if an option costs $0.02 (2 cents), a price increase to $0.20 would mean a price increase to 1000% or a 900% return. You can also lose money if the option price were to go the other way. There area a huge variety of option types and dynamics which is why it’s very important to observe different options and get some experience in a simulated or calculated setting before considering doing any serious trading with them. This will contribute to successful outcomes and this phase is usually neglected by most traders and investors.

There are also second order greeks such as: vanna, charm, vomma, veta and vera. They are not very commonly utilized except quantitative applications. Having good knowledge of first order greeks will give you a great base to understanding option behaviours and successfully trading them. It is always good to keep in mind that greeks are not constant values and they change as parameters that affect the option prices change.