We have had many readers write to us asking about volatility, hedges and other related aspects of trading, especially after the recent violent sell off. Below is a fresh up read on derivatives from our educational material (for the most basic option trading strategies visit the link here).

A **derivative** is a security where the price of the derivative contract depends on one or more underlying assets. The value is determined on the fluctuations of the underlying asset. Derivatives are used for commodities, currencies, stocks and other assets. There are natural users of derivatives; for example, corporations **hedging** their risk in oil price fluctuations, financial institutions designing a specific **hedging** exposure in order to match liabilities or a farmer wishing to *lock in* a specific price for his products. There are also *non-natural* users, that use derivatives in order to **speculate** in how the price will move of a certain underlying. There are several forms of derivatives such as; **futures, options, swaps **etc.

A **futures** contract (a derivative) is a legal agreement to *buy or sell an asset at a predetermined price at a specified time (time is decided now) in the future*. There are futures contracts on equities, indices, commodities, currencies etc. Delivery and payment of the contract is known as the **delivery date.**

Options and greeks

An **option** is a derivative representing *a contract sold by one counterpart (writer, also called short the contract) to another counterpart (holder, also called long the contract)*. The buyer has the **right**, but not the obligation to use the option (buy or sell the underlying, depending if the option is a call or put contract). The price where the option holder can buy or sell the asset is called the **exercise price**. Options are valid for a certain time period, the **exercise** **date**. On the exercise date, the option either finishes with a value or expires worthless.

A **call option** gives the buyer the **right to buy** an asset at the **strike price** at a given point in time. The seller of a call option enters a binding contract where he/she **must sell the asset at the strike price**. A call option increases as the underlying asset increases in value. A **put option** is basically the inverse of the call option; hence a buyer of a put option has the right to sell an asset at the strike price at a given point in time. Options are traded either as **standardized contracts **cleared by an exchange, as well as they trade as **OTC **products (over the counter, i.e. not cleared by an exchange). There are options on most financial assets. Options values depend on; current stock price, **intrinsic** value, **time to expiration**, **volatility**, **interest rate** and **dividends**. There are various models when it comes to valuing options, with the **Black and Scholes** being the most well-known. Options risks are referred to as the **greeks**.

Below is a payoff chart of the 4 **basic options positions**, often referred to *hockey sticks*. A trader long a call option (upper left), **limited downside **(premium you paid) and **unlimited upside**. The long put option (lower left). Note the long put option position has *almost* unlimited upside (an asset can’t go below zero).

Note the inverse is valid if you are short the options; upper right shows short call, lower right shows short put.

Delta

**Delta** of an option measures **option sensitivity to a change in the price of the underlying**. Delta is most likely the first risk parameter encountered by a trader of outright positions.

Below a chart showing delta of a call and a put option. Note the relationship of delta in relation to **moneyness** of an option. The further away from where the spot is trading the lower the delta (delta approaching zero). The more the option is **in the money** (**ITM**) the more the option will behave as the underlying itself (delta approaching 1).

Gamma

**Gamma** measures the rate of change of the **delta**, the *first derivative of the delta*. Gamma is lowest for deep in or out of the money options and is consequently highest at the money.

If you are long an option you are **long gamma**, if you are short options you are **short gamma**. One can say the delta of an option is its *speed* while gamma is its *acceleration*. Gamma for at the money options explodes as the option nears expiration.

Theta

**Theta** of an option is the **time decay** of the option. Traders often refer to **theta bleed** which is the value an option loses every day. *Buyers of options will have a negative theta while writers of options will have positive theta*. The effect of theta on options increases as the option nears the expiry day and trades close to the **strike price**.

Below is a chart showing theta.

*Theta accelerates as the option nears expiry.*

Volatility

**Volatility** is a central concept in trading options. Historical volatility is the *annualized standard deviation of past asset price movements*. It measures the daily price changes in the asset over the past year.

In contrast, **implied volatility** is *derived from an option’s price* and shows what the market implies about the stock’s volatility in the future. Professional options traders trade volatility as an asset itself. Retail clients on the other hand, usually use options to play directional plays and think in terms of premium, as opposed to volatility.

*Implied volatility of an option can rise or fall without the underlying asset moving.*

The image below is showing how a **typical options screen** looks on a real traders screen. The strike price, maturity etc is seen, also note the columns implied volatility and the theoretic price of the option. The implied volatility is the unknown input for an option from which the theoretical price is derived from. A volatility trader *trades the volatility* and doesn’t really care about the premium of the option.

*Source: ORC software*

Below is a typical volatility curve for a stock as shown on a professional traders screen. Note the **smile** that is often present in various assets showing how *volatility varies for strikes further away from at the money (ATM)*.

*Source: ORC software*

Below chart shows how profit and loss varies for a long call option holder as the implied volatility changes.

One example where novice traders many times get frustrated is that they buy options pre earnings of a specific company. Let’s assume a trader buys a call option and the stock moves higher post earnings but the option actually loses value (despite the stock actually trading higher). This is a classical example where implied volatility of the option decreases post earnings. Ceteris paribus, the uncertainty post earnings is gone, hence the fall in implied volatility.

*Before getting involved in serious options trading, volatility, as a concept should be studied*

The next image is showing the typical move in volatility for a stock going into earnings shortly. *Implied volatility tends to rise as we approach the day of earnings*. The curve shifts higher, and many times the **wings** (out of the money options) get an even higher rise in terms of percentage increase of implied volatility.

What many retail/novice traders experience is that they get the earnings day move right but they still manage losing money. This effect is best explained by the next image. Note the sharp decline lower in implied volatility. *The uncertainty is gone with regards how the earnings of the company will be, hence the move lower in volatility.*

**Skew** is a concept in options trading. Skew is the *phenomenon* where *options on the same underlying and maturity, but with different strike prices, trade with different implied volatilities*. Depending on being in the money, at the money or out of the money, options will trade with different implied volatilities. Skew (and the constant change in skew) is *primarily an effect of supply and demand*.

Generally speaking, fund managers tend to buy downside protection in stocks and indexes, hence making demand for puts big and therefore pushing implied volatility higher. The inverse is valid for upside calls, where fund managers many times write calls on their underlying, therefore supplying the market with calls and therefore pushing call volatility lower.

Below image shows a typical skew for a stock/index.

*Source: investopedia.com*

**Term structure** of volatility is *the curve showing different volatilities for different maturities*. The term structure is curved due to the fact that options with *shorter time maturities change faster than options with longer time maturities*. Depending on market conditions, events, earnings, supply/demand the entire curve shifts up and down, as well as the curvature itself. For example in a market crash term structure tends to go very steep due to the fact implied volatility of short term options become violent.

Below is a chart showing the term structure of SPX and SX5E. Note one is trading in backwardation (higher vols for shorter maturities, usually the looks in a market sell off) and the other in contango (shorter term options trade with lower volatility, usually the *normal* look).

*Source: cboe.com*

The **VIX** index, also called the fear index, is an *index of market expectations of near term volatility based on options on the S&P index*. The index gives traders and investors a broad picture of current volatility. When markets sells off the VIX index rises and vice versa. Trading in the VIX index and related products has increased in popularity over past years. Even if you don’t trade, it is a good *risk sentiment* indicator to keep track of. (Volatility is directly proportional to the square root of time, hence a little simplified, you can say a *16% volatility level indicates the market should move approximately 1% on a daily basis.*)

Options trading

**Dynamic delta hedging, option expiry trading and pin risk/opportunity **creates interesting dynamics for the underlying asset and affects traders and their positions. As an option nears expiration it will become increasingly more *probable of being in or out of the money*. An option can only be worth or worthless when expired.

Delta Hedging

Traders at hedge funds and banks trade options as volatility mostly, hence these traders hedge their options positions with buying or selling the underlying asset. This is called **delta hedging**. When an option trade is initiated with a delta neutral strategy (assume a call option), the trader will buy a call option and sell the equivalent amount of delta hedge. Depending on the delta of the option, the corresponding amount of shares, or other underlying asset, will be sold. Hence, the delta neutral trader will be long a call option and short the stock. This combination is also called to be long a **synthetic put**.

When the stock falls the option becomes less worth and the delta (probability of the option being in the money at expiry) falls. This creates the dynamic whereby the trader now has an option with much less delta than before and a position with short stocks.

Let’s assume the company profit warns and the stock price falls sharply. Then the call option will be very close to worthless and the trader is just short stock. The short stock position will produce gains, while the value of the call option is the loss. Depending on the magnitude of the move of the stock, the p/l will be affected.

*The delta neutral delta trader with long options positions wants big moves* because the loss of the option will be offset by the short stock position in our example. The trader is long **gamma**. In the most extreme example let’s assume the stock goes from 100 to 1, the call option obviously is worth zero, but the trader’s short stock position will contribute to large p/l gains.

In most cases the delta hedged trader adjusts the delta more often and with smaller moves than the above described. Say the trader is long the call and short the stock and we have a *normal* move lower (assume the stock falls from 100 to 90). The optionality of the option makes the call less worth and the delta is smaller.

In order to keep a **hedged** (balanced) position the trader needs to buy back some of the short stock in order to balance the portfolio and make it **delta neutral** again. Let’s assume the stock bounces higher and trades at 100 again. The trader has in this case bought *extra* shares at 95 that have gone up in value by 5. If the move happened in a short time period the call option will be practically worth the same, assuming no/minimal theta decay. *The trader will end up with a positive overall p/l.*

What happens if the stock continues even higher and trades at 110 the day after?

The trader will now have an even bigger gain from the shares bought at 95 (unless he sold out the hedge), as well as the call option now trading at a higher price as optionality of the option starts kicking in. The delta of the option increases and so does the need to sell extra shares to delta neutralize the position. The trader will have the *bonus* shares bought at 95 as a gain, the call option itself will be worth more and the position will need additional shares to be sold in order to balance the portfolio.

Let’s assume the trader sells the delta needed to hedge the portfolio and immediately after the shares go lower and trade at 90. The trader will once again end up with a call option that has decreased in value and who’s optionality has decreased, the delta is going to be much lower again, requiring the trader to buy more shares in order to make the position delta neutral again. This time the trader will have even more short shares, *remember the need to sell more shares at 110 when the option delta increased*, plus the *bonus*shares bought at 95 when the stock fell first time.

The above explained *procedure* is called **dynamic delta hedging** and is primarily used by traders that trade *volatility* as an asset. In the example above I explain the trader that is long an option. The same applies to the trader that is short an option and dynamically hedges the position, but it will be *the inverted dynamic to the long option trader.*

*The long premium trader wants large moves as he/she is long gamma.*

*The short premium trader wants the stock to be as non volatile as possible since he/she is short gamma.*

What happens at option expiry?

Let’s assume the above example but where the trading takes place on the last day of the option, the** expiry day**. The trader is long the 100 call, the stock trades at 105, the portfolio is hedged and it is the last day of trading.

The stock for some reason quickly falls to 95. The trader will be long a call option that will go from being in the money and behaving like the underlying stock (delta 1) to being worth zero and having a delta of practically zero. The trader is then just short the shares and can buy all the short shares at 95.

Let’s then assume the stock climbs higher and trades at 105 an hour later. The option will suddenly be in the money, worth the **intrinsic** value (and a bit more) and will once again have a delta of 1 and will behave like the stock. The trader will now be long again and can neutralize the position by selling shares again.

Assume the stock suddenly falls below the strike 100 and trades yet again at 95. The option will more or less *digitally* go *from delta one to delta zero *as the stock falls below the strike. All optionality is gone (delta zero) and the trader will be left with a short stock position again. In order to neutralize the risk, the trader needs to buy all short shares again.

The dynamic of the option expiry is rather clear! The trader long the strike will trade this expiry opportunity and if the stock moves above and below the strike many times the profit becomes very big. The trader short the strike will experience the inverse dynamic and will not want the stock to move through the strike. This is called **pin risk/opportunity**.

It is advisable to check the open interest on expiry dates as it can give additional information of the dynamics around specific strikes. Depending on the dynamics and who is long/short the strike on expiry, the underlying can experience *vacuum* moves.

*The expiration trading pin situations can be compared to a poker game*.

If one trader knows the big part of the open balance is in his/her portfolio, the trader will know that other traders will need to buy/sell the stock when it moves through the strike. It then becomes a *chicken* race. Do you hedge or not hedge as you know there is an opposite position that needs to be rebalanced?

Surely it sounds great to be *long the strike* on expiry day as it creates opportunity to buy and sell shares above/below the strike, but as we all know *there aren’t any free lunches*. The flip side to the coin being long the strike is the exponential cost of holding the option into expiration.

*Theta decay explodes as the option nears expiration and is the biggest at the money.*

The optionality decreases rapidly, hence the extreme theta bleed for at the money options. The inverse is of course valid for the trader having sold short the option into expiry. If nothing happens the short premium trader will produce big returns.

Possibly interesting trades around expiration is to own *teenie* options. These are basically lottery tickets that can produce very big returns should unexpected moves occur. Be aware of important earnings results, economic events or other interesting information around expiration days, these can move the markets a lot and make options go from practically worthless to becoming worth a fortune in a matter of minutes.

One wise rule is to *not be short teenie options*. Always close out short low premium options due to the possibility of unexpected events ruining your portfolio. Many traders have been totally wiped out by not paying attention to the portfolio containing short low premium options going into expiration.