Note: Updates to follow (8/22)

An** Option ** is a vehicle for traders to bet on price movements without having direct exposure to the underlying security; these allow traders to buy or sell a certain **stock** at a certain **price** at a certain **time** in the future. All of **these** you can choose to fit your desired exposure.

### Terms for reference as you read through the text:

**Long**= pay for exposure; i.e. pay premium.**Short**= get paid for giving someone else exposure; i.e. collect premium.**Premium**= cost or price of an option.**Underlying price**= price of the stock that the option is written on i.e. attached to.**Strike price**= price you choose; value of the option at expiry is strike price relative to underlying price.**Intrinsic value**= Absolute value of (Strike price – Underlying price); can never be negative**Option value**= intrinsic value + time value; can never be negative**Time value**= a function of time to expiry; time value is zero at expiry**Time to expiry**= time period you choose; life of the option, can be from a week to many years. It’s August, so a December option has 4 months to expiry.

### Greeks: Delta & Gamma

The Greeks are metrics or variables used by option traders to assess their risks when trading and analyzing options trades. They are: Delta, Gamma, Theta, Vega, and Rho.

**Delta** is the probability of your option being in the money. Ranges from 0.00 to 1.00. Traders drop the decimal and just say 0 to 100. An equity security has a delta value of 100. Always. Options have a delta value between 0 and 100.

50 delta options are at the money (ATM), meaning strike price = underlying price. 50 Delta options are the most sensitive to changes in the underlying; i.e. they have the highest gamma, which brings us to our next Greek.

“**Gamma** is a measure of how fast an option changes it’s directional characteristics.” (Natenberg, 105); i.e. it is the sensitivity of delta to changes in the underlying price. Gamma is largest in at the money options. Both calls and puts have positive gamma. Buying a put or call gives you positive gamma exposure. Selling a call or put gives you negative gamma exposure.

### Delta or Directional Hedge:

If you want directional exposure, i.e. you have a feeling that a stock will move in a certain direction, you can either trade the underlying or buy/sell options outright. If you’re not sure of direction, or want to profit in some other way than the directional move of stocks, you can use what’s called a delta hedge.

Delta, recall, is a probability; it’s computed from a complicated formula (called Black-Scholes**). As your delta rises, probability of actual purchase or sale of the underlying upon expiry becomes more likely, thus to delta hedge, you need to buy or sell the underlying to stay directionally neutral.

Note: greeks are additive, which makes the math easy.

Example: If you buy a 50 Delta option, you’re long 50 deltas. You’ll sell 50 deltas in another market (underlying) to become directionally neutral. You can accomplish this by selling short 50 shares of the underlying’s stock. Long 50 deltas in the option, short 50 deltas in the underlying = net zero delta exposure.

### Long Gamma = Short Theta

You pay for owning options in theta. When you’re long options, you’re long gamma. If you’re long gamma, you’re short theta.

**Theta** is time decay. You have to pay for exposure to options. More time to expiry means more time value. As time passes, this time value decays. When short an option, you get paid in theta, the value of the option will decrease as long as volatility, price of the underlying, and interest rates stay constant.

Being long gamma means you’re short theta.

### Sell High, Buy Low:

Selling into strength and buying on weakness is what we strive to do as traders.

When you’re long gamma, and you readjust your delta hedge, the strategy forces you to sell high and buy low. Seems like easy money? Remember our old pal theta. When long gamma, you’re short theta, meaning your options lose value over time. As long as your delta hedging provides enough small profits to outpace time decay (theta), you can make money.

### Buy weakness, sell strength:

If a trader is long gamma, he will correct his hedge against the market momentum. In other words, the trader will sell short the underlying when the underlying rises in order to maintain his delta (directional) hedge.

This goes against a momentum trader’s dogma. If you subscribe to school of “Trend is your friend”, consider a short gamma strategy.

### Trend is your friend:

If a trader is short gamma, he will correct his hedge with market momentum. I.e., the trader will buy the underlying when it is rising, and sell when the underlying is falling. One can be short gamma by selling options outright, or though spreads.

If you take in money (premium) when initiating a strategy, you’re short gamma.

**Black-Scholes takes in strike price, underlying price, time to expiry, volatility, and an interest rate and shoots them through a normal distribution to spit out your greeks, which are easy(er) to quickly understand.