## Options. In English [Part 1]

It’s getting harder and harder to make money in futures. Every year more of my friends say that their markets are either drying up, getting tighter, or are impossible to trade without participating in microsecond timeframes or paying up to get hedged. If you’re a market maker, demand for ever smaller time frames has either forced you to reconsider your niche in the world or your technology spend has ballooned to become your single largest cost-center. Speculators can’t make money either without a connection to Washington due to the current administration and the fed’s unending stream of manipulation.

Many traders are turning to options for solace. Options markets provide more opportunity than other instruments because the execution tools available haven’t yet turned into a Formula-One style competition where the team with the biggest tech budget wins. Depending on your risk management style, their fundamental differences from futures can make an attractive alternative. The real beauty of options is that opinions about direction or even the result of economic events do not necessarily affect the p&l of a properly hedged options position.

There are no shortage of options trading guides out there however I’ve found that they mostly fall into highly mathematical explorations of various valuation models or strategy peddling reminiscent of snake-oil brochures. The former are very useful for a sophisticated quant or a developer (This book was used to build the valuation models that you can trade using SD GateKeeper) but lacking in “plain old English” and everyday practicality.

This guide is meant to be a pragmatic exploration of options trading, how it differs from futures, forwards, stocks, bonds, and other asset classes. As my disclaimer already states, this is not meant to be construed as “how to make money in options” advice. While in Part 1 I will go over the various pricing models, it will be PURELY from the perspective of how they’re used to execute. Part 2 will discuss the practical applications of price models and how one might apply them to capture various market activities.

### The Basics

From the very beginning, an Options contract grants the buyer the right, but NOT the obligation to buy or sell a given **Underlying** asset at a given **Strike Price** up until its given date of expiry. An option that grants the buyer the right to buy the underlying asset is known as a **Call Option** and an option that grants the buyer the right to sell the underlying asset is known as a **Put Option**.

When an underlying asset is trading below a given strike price, puts are known to be **In-the-Money** and calls are **Out-of-the-Money**. Conversely, when an asset is trading above a given strike price, calls are considered In-the-Money and puts are Out-of-the-Money.

The mnemonic that I use to remember this relationship is that if an underlying asset is trading above the strike price, I want to *Call* it away from someone else’s account (and into mine), however if the underlying asset is trading below the strike price, I want it *Put* it in someone else’s account.

Each underlying asset has a long stream of option contracts; each at a given strike interval. This is known as an **Option Chain**. CME Ten Year Future Options, for example, have a one-half point strike interval, meaning that there are two sets of call and put options per-handle of the underlying. In the 10-Year Note example, the range of strikes for the September 2011 contract (OZNU1) is from 90000 (90) up to 149160 (149.5), giving a total of 119 strike prices and 238 tradeable instruments *for only one contract month*!

If you were to relate this to the various tables in a casino, trading the yield curve in the futures would be the equivalent of playing three to five hands of blackjack out of the same shoe. Trading options would be the equivalent of putting money on various numbers or combinations of numbers on a roulette wheel.

### The Basics – Valuation Explained

At the end of the day if you’re long an option that goes in-the-money, you’ll make money. If you’re short an option that goes out-of-the-money, you’ll also make money. If you buy an option that is $10 in the money when you **exercise** it, you’ll make $10 minus whatever you paid for the option.

Which leads me to my next point, how much is an option worth if it’s out-of-the-money? In-the-money? If an option is in-the-money, it has a **Intrinsic Value **of the underlying price minus strike price for calls, and strike price minus underlying price for puts. Options that are out-of-the-money do not have an intrinsic value because they cannot be exercised at a discount or premium (depending on whether you’re exercising to buy or sell) of the current underlying price. With that said, out-of-the-money options are still worth *something* because they *could* go in-the-money. That something is known as the option’s **Time Value**. In-the-money options have time value too because they could go further in-the-money. The value for an option that is In-the-money is roughly the time value added to intrinsic value.

Pricing models such as Black Sholes (and its derivatives equivalent), Monte Carlo, Binomial, and others ultimately attempt to answer the million dollar question (no really, this is actually a million dollar question) of “what is the time value of an option.” The assumptions of these models vary, and a thorough discussion of the various benefits and downsides to each of them would make a nice PhD dissertation. I hate fucking dissertations and academia in general, so we’re going to gloss over this portion and just say that some really smart people figured out some really fancy formulas that work real good and can be used to calculate how much an option is worth. All of them are basically figuring out how much you should pay for something based on its probability of going in-the-money based on a set of variables.

The math may be pretty complicated, but the formulas are based on some pretty obvious observations. The most obvious of these is the underlying asset. The closer it gets to being in-the-money, the more it is worth (it is conversely worth less the farther away from the money it is). The longer a period of time between now and when the option expires, the more opportunity the option has to go in-the-money. If interest rates are high, you should be paying a little more to buy an option (or be paid a bit more if you’re selling) because you’re essentially loaning the short money until you either exercise or it expires worthless. And finally the higher the volatility of the underlying instrument, the higher the probability of it going in-the-money.

Other than volatility, all of the inputs to a given pricing model are apparent in market-generated information and the sensitivities to changes in each input are the basis for price theory. Which brings us to the real meat of valuation, the greeks.

If the underlying ticks up or down one price increment, how much does a given option move up or down in relation to the change in underlying value? **Delta** is the change in price of an option given a one tick move in the underlying. From a practical standpoint, this is often seen as a hedge ratio or “underlying equivalent.”

Because delta is not linear up as an underlying price changes, hedge ratios change with either large options positions or during large price swings. The delta of delta, or **Gamma **of an option is the change in delta of an option given a one tick move in the underlying.

**Theta** is the sensitivity of an option to time. Since time as we know it only moves in one direction, it’s often referred to as theta decay or erosion. Theta is not linear. As an option approaches expiry, the rate of decrease in its value speeds up as each increment of time represents an increased percentage of “fewer opportunities to go in the money.”

**Rho** is the sensitivity of an option to changes in interest rates.

Volatility has its own unique properties such that many traders will actually quote the market in terms of **Implied Volatility **rather than dollars and cents because volatility can be used to compare one strike to another where price cannot. Part of this has to do with volatility being used as a band-aid to address the shortcomings of most price models farther away from **At-The-Money** or farther from expiry. Another reason is that Volatility is the only part of the price model that is subjective. In either case, **Vega** is the option’s price sensitivity to a one-unit change in volatility.

In Part 2, I will explain the practical ramifications of the basics on Trading, and the tools of the trade.

Vocab (in order of appearance in the article):

**Underlying **- The asset that an options contract is based on. Options can be used to purchase (or “call”) or sell (“put”) the underlying asset.

**Call** - An options contract that gives the bearer the right, but not the obligation, to purchase an underlying asset at a specified strike price before a specified expiration date.

**Put **- An options contract that gives the bearer the right, but not the obligation, to sell an underlying asset at a specified strike price before a specified expiration date.

**Strike Price** - (Excercise price) is the fixed price at which an options contract can purchase or sell an underlying asset regardless of the current market value.

**Date of Expiry** - The date at which an options contract expires worthless.

**Option Chain** - A string of options contract at a given interval through a given range of prices.

**Exercise **- The act of calling or putting an options contract to obtain or sell the underlying asset.

**Time Value **- The portion of an options contract’s value that is attributable to probability of going in-the-money. Sometimes referred to as premium.

**Intrinsic Value** - The portion of an options contract’s value that is attributable to “moneyness” or how far in-the-money it is.

**Delta** – The rate of change of option value with respect to changes in the underlying asset’s price.

**Gamma** – The rate of change of option delta with respect to changes in the underlying asset’s price.

**Theta** – The rate of change of option value with respect to changes in time before expiry. Also known as erosion or decay.

**Rho** – The rate of change of option value with respect to changes in interest rates.

**Implied Volatility** - The volatility of an options contract that is implied by the current market price of the option.

**Vega** – The rate of change of option value with respect to changes in volatility.

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