I could have entitled this article simply “Option Strategies”. But it’s not the case. This article will not be a presentation of option strategies, as it might have been normal, after the presentation of the greeks. Rather, we will outline the process of thinking and designing option strategies , with accent on a few elements that will be the building blocks of tomorrow’s generation of EAs.

There are two major classes of option strategies, derived from the basic ones:
- first, the ones that aim on winning on movements of the underlying asset , which have as risk underlying movements in the wrong way, and the decay;
- second, the ones that aim on preserving premium and use also the decay, which have as risk underlying movements in the wrong way as well as their strength;

There are more tuned strategies that derive from gamma trading:
- first, the ones that aim on winning from ranging markets;
- second, the ones that aim on trending markets;

And finally, pure implied volatility strategies that aim on relatively high/low implied volatilities. But this is another game ; it is a double edged sword, affecting all strategies in both ways.

It seems that underlying movements in the wrong way are a quite common risk of option strategies derived from the basic strategies, as well as in simple underlying trading. This happens because these strategies, which are many, are directional themselves.

However, what has to be clear in mind, first is how much are we prepared to lose?
If a trader would view the entire time to expiry, he would see the premium as maximum loss/maximum gain.

However, if trades are going to be kept only for the lifetime of a signal, we must have a clear image on what may happen with the option price. Some factors are harder to account for, others are more easy to see.

Study case: we have a bullish volatility signal on the underlying

We could buy a straddle.

A long straddle strategy consists in the purchase of a Call and a Put on the same underlying, having the same strike and expiry.

To have a balanced delta effect , we will pick an ATM strike, where deltas are similar as absolute value;
To give the strategy more time to have effect, we could pick a far expiry, where thetas are minimum ; this will expose us to vega .
It will be extremely indicated an implied volatility analysis ; this is a good go if implied volatility for chosen options is relatively low, as profits will be more probable, in the case of an increase ; it will not be indicated to do it in the case of a relatively high volatility ; because there would be the danger of an implied volatility going down, pulling down option prices with power, because for far expiries vega may be more powerful than delta.

The most interesting case is what happens if our signal is for instance on H4 ; if we are supposed to have powerful underlying movements over the next bars, with a maximum of 2-3 trading days, then probably we shouldn’t be too afraid of implied volatility. And if implied volatility will move too slow and decay will not have too much effect either, then we will be insulated from these effects, there will remain only delta effect. But remember, we didn’t have a directional expectation , as we intentionally picked similar deltas in absolute value. But remember the charts of delta versus the underlying (it’s easier to understand than gamma). Click here for a link to my previous article, in a new browser window, and look on the charts.
So, if the underlying is going quickly up, the delta of the Call will grow in size, making it more valuable, while the delta of the Put will fall in absolute value, insulating the Put price more and more. This will create an accelerating profit on the Call side, at the same time with decelerating losses on the Put side. If implied volatility doesn’t ruin the game, our profits will start forming up from the acceleration difference between Call and Put, that will have to finance spreads and decay. Got the catch? (N.B. There are also Option Spread strategies. When I write about this kind of strategy, I will write “Spread”, and when I write about the bid-ask difference, it will be “spread”).

Study case: we have a bearish volatility signal on the underlying
Side note: bearish volatility may not be necesarilly bearish; if a powerful counter-trend forms on the chart, our BBoverStdDev indicator will plot it as bearish volatility, because it reads “the return of the price to the average of the last values”. If prices return for good, the indicator will continue plotting bearish volatility for real, but if prices continue trending, the indicator will turn again to higher volatility plots. A bearish volatility signal would be then the intersection of the standard deviation with the lower Bollinger Band. Click here for the article in a different browser page.

Supposing that the signal is correct,
We could short a straddle.

A short straddle strategy consists in the sale of a Call and a Put on the same underlying, having the same strike and expiry.
The delta considerations should be the same, as for theta, we are now interested in decay. We will pick first expiry month. This will make the vega effect to be smallest in comparison to delta, throwing vega out of the picture. If the signal is correct, and what follows is a ranging market with a lower and lower volatility, we will have a hedge between the Call and the Put, as deltas will – first have not too much effect because the underlying itself doesn’t move too much, second, due to up/down movement , transfer profits/losses from the Call to the Put and viceversa – have no effect overall, being hedged. As time passes until signal clears out, the decay produces its effect , financing spreads and minor losses by delta unhedged deviations, thus generating profit.

Just a short parenthesis about hedging. You can see in this strategy that we emphasized accelerating profits versus decelerating losses. When you do the “hedging” as it is widely accepted by forex communities, by going long and short at the same time, that’s not really a hedge. It is a pause. It pauses any results until hedging is removed, by closing or adding trades that un-flatten the resultant position. Whilst the real hedging, the one that amounts to arbitrage, will insure that there will be accelerating profits versus decelerating losses (as in the first case), or keeping losses steady (as in the second case) of course, in such conditions that the trades have enough time to profit until outside parameters will produce their effects, meaningly implied volatility and decay.

These are just two examples. We will return to these examples as soon that both Strategy Tester and options will be available. Remember however that option traders don’t have proper tools on their hand. For this reasons, they invented strategies that put the accent on reducing payed premiums while capping maximum payout. Why ? Because there isn’t going to be any unlimited market action for unlimited profits, so there is no reason in paying full premiums.

Options are themselves hedged instruments. Especially the buyer has this feeling, that he uses a hedged instrument : unlimited upside potential, limited downside potential. However, a lot of option strategies will cap the upside potential and reduce costs of the downside potential. These strategies make up classes like Spreads (Bull Call Spread, Bear Call Spread, Bull Put Spread, Bear Put Spread) and Collars (Collar, Costless Collar, Fence). Strategies that aim on decay are Calendar Spreads and Iron Condors mostly.

You can read about these strategies on several option sites, including :
TheOptionsGuide.com , OptionsEducation.org , Optionetics.com , OptionTradingTips.com, OptionTradingPedia.com etc.

However, the point is not to know the strategies themselves. They are around for some time and can be found on Internet. Strategies should be played function of what you can analyse better: Straddles or Condors, if it’s underlying volatility, basic strategies or Spreads, if it’s underlying direction, or long term expiry options, if it’s implied volatility.

Sure, there is also possibility of option arbitrage. An arbitrage in the underlying market would mean to simultaneously buy and sell the underlying at different prices. Both buying and selling the underlying can be emulated with options, by the use of synthetic positions. For instance, Synthetic Long is composed by Shorting a Call and Longing a Put with the same strike and expiry.. The reverse, Synthetic Short is composed by Longing a Call and Shorting a Put with the same strike and expiry.. You can obtain the equivalent of an arbitrage thru a Conversion, which is long underlying and Synthetic Short or by a Reversion , done by Short Underlying and Synthetic Long. Another arbitrage is a Box , which is made by a both synthetics at the same time. But remember you work with options. When it comes to arbing this way, it’s about expiry, while what happens until expiry, a stretch/skew in profit, is dependant on the market and the greeks. As author Sheldon Natenberg says in his book, “Option Volatility & Pricing: Advanced Trading Strategies and Techniques” , there are no riskless strategies : there are strategies with greater or lesser risk.I recommend you read this extraordinary book when you will have options available, cause it has a lot of information there, accentuating this theme, the strategy option design side, rather than a presentation of option strategies.

However, I am pretty doubtful that option arbitrages will be possible rightaway under MT5. Option trading should be regarded in the same context as the multiasset trading. If you can arb between fx and fx futures, then surely one of them can be replaced with a synthetic, which may create extra opportunities due to lower option markets liquidity and higher latency.

Now, due to MT5’s extended capacities, option trading can gain new meanings, such as pair trading with options or gap trading with options. Possibilities are limitless, but they depend on the capabilities of the Strategy Tester as well as option spreads, that have an influence, more or less, depending on chosen strategies. We are hoping to record some option data until MT5 is completed with Strategy Tester and options, so strategies could be analysed more in-depth even without the help from MT5.

The evolution of option valuation models in time

Like any other assets transacted on a market, options go thru a valuation process. Traders of other assets make up their mind using technical analysis, they analyse previous prices in order to forecast evolution for the future, but when option markets were created, traders didn’t had a clue on how option price forms up. That was the moment when the first option valuation model, the Black-Scholes model, largely used even nowadays, despite its limits, emerged. Once that traders had a model, even far from perfection, options could have been priced and have a market. After the appearance of every new option, the model role is to tell when options are overbought or oversold. However, the most important factors in option trading are option greeks, sensitivities of option price to several parameters that allow building up completely different strategies than the ones based on overbought/oversold situations or the simple ones based on underlying estimations. But again, these sensitivities are results of the option model as well. So let’s review the option models….

The Black-Scholes model
Also called “the grand daddy” of the option models, it was the first and it has the largest use. It was made by Fischer Black and Myron Scholes in 1973 and it got them the Nobel prize for Economics in 1997. Its limits are:
a. it can be used only for european options (the ones that don’t allow early exercise)
b. implied volatility (volatility plugged into the model that gives option value equal to option price) is considered constant;
c. no dividend payouts for the lifetime of the option.

The binomial model
It is based on the same assumptions as the Black-Scholes model, but adjusted to allow american option pricing ; also , it has a better integrity over time. It breakes down the interval to expiry into a series of steps, building a tree of underlying prices. Each step, the underlying is considered to go either up or down. However, it is not pricing the fact that most of the time markets don’t move. This was its limit to be overcome by the next model, the trinomial model , that accounts for the fact that markets can stay. The model also takes into consideration the volatility smile which is not present in the previous ones. Since the trinomial model went pretty good, someone came with the idea to use more nodes , and so the adaptive mesh model was born.

The VSK model is a newer , different breed of option models. It means Volatility, Skewness and Kurtosis. Previous models accounted for a normal distribution of stock returns. But stock returns don’t follow a normal distribution. The distribution may be different, so the model has to adjust for skewness , which is the disbalance of the mean (the mean is not in the middle of the event array) , and kurtosis , which is the fattening of the tail of the distribution’s bell curve. The model is a Black-Scholes model adjusted for volatility, skewness and kurtosis.

The finite difference model is able to calculate the volatility surface created by skewness and kurtosis.

An option model outputs the option value, and option sensitivities, the greeks.

In this article I’m using and commenting charts from OptionTradingTips.com (statistics sites are source for distribution pictures). Also a very good option education source are the Options University courses by Ron Ianieri.

Delta

Delta is the first derivative of option value, indicating how much the value of the option will move at a modification in underlying price. This is why delta is called percent change. Delta is also called percent chance, its value indicating what is the chance for that option to expire in the money. Delta is at the same time hedge ratio , indicating how much of the underlying contract must be bought/sold in order to equal the movement in option price. Deltas are additive. The delta of an option portfolio made up by several options on the same underlying asset, is the sum of individual options delta times position sizes. This kind of delta is called position delta. If we are to include the underlying in a portfolio, we can say the underlying has a delta of 1.

Option Delta

Look carefully at these charts. Charts two and three might seem to contradict the first, but in the first chart the horizontal axis is the on money status of the options, whether in two and free the horizontal axis is the underlying price. Delta ranges from 0 to 1 for Call options, and from 0 to -1 for Put options. Please note that there is also a percentual notation for option, where options might have deltas of 100 or -100. The more out of the money options are, the closer to 0 delta is , i.e. options are almost insensitive to underlying shifts; the more in the money options are, the more extreme values it takes, i.e. options value almost copies underlying movement. Also, the sum of the call delta and the absolute value of it’s correspondent put must yield 1 (or 100, if percentually).

Call Deltas and expiries

Put Deltas and expiries

As we look at farther expiries, we find decreasing deltas for ITM Calls, and increasing deltas for OTM Calls. For Put options, the situation is reversed : we find increasing deltas for ITM Puts, and decreasing deltas for OTM Puts (we may consider the same situation, but applied to the absolute delta value). Delta has a tendency to remain quite constant for ATM options. For farther expiries, the delta range (maximum and minimum delta per all strikes) is shrinking. As days go by, the ITM calls delta will be increasing (as chance to remain ITM goes higher) and the OTM calls delta will be decreasing (as their chance to become ITM decreases). Same behaviour applies to the absolute value of Put options delta. This effect is known as trumpification , which is a delta effect caused by time and volatility, that increases the deltas of OTM options, decreases the delta of ITM options, pushing them all towards 0.5 (absolute).

Gamma

Gamma is the second derivative of option value, showing how much the delta moves at a movement in unerlying price (delta of the delta) .

The above graph shows gamma vs underlying price for 3 different strike prices. You can see that gamma increases as the option moves from being in-the-money reaching its peak when the option is at-the-money. Then as the option moves out-of-the-money the gamma then decreases. gamma is of two types : long and short. Long gamma (positive number) is obtained by buying an option, short gamma (negative number) is obtained by selling an option; gamma is the same for both calls and puts. Gamma is highest in the front month, at the ATM strikes.

Gamma is additive, the same as delta is, and the sum of all gammas times position sizes for options on a certain underlying make the position gamma. Holding the underlying has no effect on position gamma, because underlying has 0 gamma, since its delta is constant.

Long gamma: if underlying goes up, delta increases ; if underlying goes down, delta decreases;
Short gamma: if underlying goes up, delta decreases ; if underlying goes down, delta increases.

Gamma Trading

Allows to flip the underlying back and forth, while hedged. In a Long Gamma Trading strategy, you can pick an underlying, be long on it, and also buy Puts to cover. From the expiry point of view, all movements in underlying are cancelled by the protective Put. Say you bought underlying at S price and your long Put has gamma power to create delta . If the underlying moves to S+1 , your long Put created already gamma deltas. These new deltas have to be hedged by selling underlying to cover it, thus becoming flat. Underlying moves back to S, and now you have -gamma deltas to hedge , which will be done by buying underlying. These trades will create profit, but you have to constantly fight the decay – because you payed money on the premium of the Put, which is constantly decaying as an effect of time.
The reverse strategy, that bets on larger decay than the underlying flips, is Short Gamma Trading. We will be long again on the underlying, but instead of buying puts, we will sell Calls. If the underlying moves to S+1 , the short call created already -gamma deltas, that have to be hedged by buying underlying. Underlying moves back to S, and now you have gamma deltas to hedge , which will be done by selling underlying. This strategy will create losses as underlying flips, but the goal of it is to collect premium from the sold calls, as the decay is slowly decreasing calls value. This strategy is applicable when we have momentum happening on the underlying, that is, when underlying volatility is increasing. Remember that in my previous article from the November edition, Volatility analysis : bridging the cap from volatility forecasting to price forecasting I stated that the price direction is much harder to forecast than the volatility. It is my belief that volatility analysis is to be used mostly for option trading rather than plain underlying trading. We will go back to these strategies as soon as both Strategy Tester and options will become available.

Vega – the volatility greek

And when we talk about volatility’s influence on the option price, we talk about implied volatility rather than historical volatility (underlying volatility) . This implied volatility is the volatility plugged into the option model that yields the current price as option value. From this moment, “volatility” will be read as “implied volatility”. Vega is not a greek letter, so the greek letter used for vega is actually Nu (uppercase N, lowercase v). The volatility “smile” refers to different strikes but in the same month. It is called smile because the ATM options have the lowest volatility, and OTM and ITM have higher volatilities. Following is a table of the volatility surface. Each series of strikes per each month make up a “volatility smile”. Same strike volatilities, per a months, make up a “volatility tilt”. Some option softwares contain volatility surface graphing (like this example).

Smile and tilt are ways to analyse whether there volatility misprincings. Vertical spread is a strategy to use for a mispriced smile. A time spread strategy is used to take advantage from the misprice of a volatility tilt.Deciding whether volatility is too high or too low has to take into account the historical evolution of implied volatilities , and hopefully MetaQuotes will introduce in the CopyRates() an array for historical access to implied volatility. Volatility influences option prices directly. When volatility increases, all options go up , and when volatility decreases, all options go down. Volatility has a reversed effect on gamma. When volatility increases, gammas go down, and when volatility decreases, gammas go up.

Vega indicates how much the option price is going to move at a 1 percentual point move in volatility.

Vegas are additive too, however it is necessary that option prices to be adjusted to the same volatility before an analysis to be done. This will be done by picking up the volatility of an option and adjusting the other ones prices to that volatility, using their own vegas.

The behaviour of a vega across strikes is similar to gamma. However, the behaviour of vega in time is reversed compared to gamma. As expiries go farther and farther , gamma decreases, while vega increases.
Having a portfolio of options on the same underlying, the vega impact has to be estimated after all of them are brought to the same volatility (like a common denominator), i.e. by adding, on each one of them, n ticks multiplicated by each vega to make up the required average volatility.

Vega is important, because for farther expiries, it can be more powerful than delta.

Theta – the time greek

Theta measures an option’s rate of decay over time. The decay applies to option’s extrinsic value.
Now the value of the option is composed by the intrinsic value and extrinsic value. The intrinsic value is not subject of decay, because it measures what is rock solid at any given moment in time : the difference between underlying price and strike price, for Call options, or the reverse, for Put options. The extrinsic value accounts for chance given by time left to expiry: it is the difference between option price and intrinsic value. Since this chance is given by time, extrinsic value is called also time value.

The passing of the time has effect not only on option value, but also on delta. Because delta means “percent chance”, it will decrease the delta of the OTM options, and will increase the delta of the ITM options. ATM options delta will remain unaffected. Because of this influence of time over delta, it has an influence also on gamma, depending on where delta was.

Theta , viewed across strikes and expiries, has quite the same pattern as gamma. Theta is always highest front month, ATM. However, front month very far ITM and OTM strikes might have smaller theta values than for the rest, because they lose their sensibility.

Rho – the interest rate greek

Rho is the change in option value that results from movements in interest rates.
The value is represented as the change in theoretical price of the option for a 1 percentage point movement in the underlying interest rate. For example, say you’re pricing a Call option with a theoretical value of 2.50 that is showing a Rho value of .25. If interest rates increase from 5% to 6%, then the price of the call option, theoretically at least will increase from 2.50 to 2.75.

Take a look at the above graphs, which plot the Rho of a Call and a Put option at 3 different points in time, across a range of strike prices, with a spot price of 100.

There are also second tier greeks. These greeks quantify impact of volatility and time over delta , gamma and theta. These greeks are helpful for traders that trade options in a non-automated way, because they map the impacts of time and volatility on the first tier greeks. On the other hand, an automated options EA has to be programmed into permanently reading portfolio situation and first tier greeks in order to restructure portfolio according to them.

An application of the Black-Scholes model for european options including value and greeks determination can be found in our article Virtual methods in MQL5 – an application on options .

I am not an options specialist , and I’ve never been. This article is part of a series that I intend to write about options, however. Quite most MetaTrader folks never been into options. Never available on MT4, or not automated on option platforms, or without the possibility to hedge with underlying, we were kinda kept out of the options realm. And how good are options – asymetric trading assets, providing exactly the flavour needed for trading, going beyond simple directional trading!

Definition of an option:

An option is contract who gives the buyer the right to buy or sell a security (underlying contract) at a specified price (strike), by paying to the seller of the option a premium. Or, basically, the buyer buys the option to buy/sell or do nothing, and the seller sells his option, abiding to the request of the buyer. Options are of many types, but in terms of exercise there are two basic classes : american option, that gives its buyer the right to exercise the option all the time to expiry, and european option, which can be exercised only at contract expiry.

We will not dwelve into the intricacies of the exercising mechanism. Under MetaTrader there will be no exercise, and also most likely no american options. There will be offered european options, that will be traded by the traders at their market value (the current option premium). The value at expiry will be the one given by the option mechanism, while the market value is dictated by the option models which are the basis for option quotes posted by market participants. The two values will be equal at expiry.

By mechanism, options divide into call options (that give the right to buy) and put options (that give the right to sell). These are called vanilla options, because they were the first type of options created. Nowadays there are a plenty of exotic options , which are nothing more than bets with a market value. Our article series will focus on vanilla options.

To get acquainted with how options work, you have to become familiar with payoff diagrams. Payoff diagrams show the profit at expiry. Since there are two basic option types, which can be bought or sold, we have four basic payoff diagrams, also known as the four basic option strategies.

From this place on I’m using charts from OptionTradingTips.com and  TheOptionsGuide.com . These are some of the best free option sites that can be found on Internet. I will return frequently to their articles that contain key information on option trading.

This is a long call diagram, a call from the perspective of the buyer. The buyer acquired a call with a strike of $40, paying $200. (Actually he bought 100 calls , with an individual call premium of $2). As you see, he remains with his $200 loss for underlying at expiry below $40, because there is no reason to receive a stock that values less. This is what he payed the premium for. From $40 to up, there is a slight profit. Gets the stock delivered at $40, while the market value is higher. Even so, it is not enough to breakeven. Breakeven point is, as graphics show, between 40 and 50.

(Breakeven – Strike) x Call Options = Premium

(Breakeven – 40) x 100 = 200

That yields a breakeven happening at $42, where the underlying gain of $2 for 100 calls recovers the  $200 payed.

From the perspective of the writer (seller) , the diagram is mirrored around the stock price axis. For share price lower than 40 at expiry, he can keep all the $200 received from buyer. For higher prices, the buyer exercises his option to buy, and the seller has to deliver a more expensive stock (from the current market price) to the buyer for the strike price, lower ($40). That causes losses. The breakpoint is the same, since chart is mirrored.

This is a long put diagram, a put from the perspective of the buyer. The buyer acquired a put with a strike of $40, paying $200. This example is forged to have same data as the call one. In real markets, this will never happen. As you see, he remains with his $200 loss for underlying at expiry above $40, because there is no reason to sell a stock that values more. This is what he payed the premium for. From $40 to down, there is a slight profit. Deliveres the stock at $40, while the market value is lower. Even so, it is not enough to breakeven. Breakeven point is, as graphics show, between 30 and 40.

(Strike – Breakeven) x Put Options = Premium

(40 – Breakeven) x 100 = 200

That yields a breakeven happening at 38, where the underlying loss of 2 for 100 puts recovers the  $200 payed.

From the perspective of the writer (seller) , the diagram is mirrored around the stock price axis. For share price higher than 40 at expiry, he can keep all the $200 received from buyer. For lower prices, the buyer exercises his option to sell, and the seller has to buy a less valuable stock (the current market price) from the buyer for the strike price, higher (40). That causes losses. The breakeven is the same, since chart is mirrored.

Don’t forget the real breakevens are not in the same position. Fees and spreads will push it away – not only per option type, also per option operation – the buyer will not have same breakeven as the seller , as in regular trading.

According to where the underlying price is in respect to the strike, options are divided in :

- out of the money options (strike > underlying, for Calls, strike < underlying, for Puts)

- at the money options (strike ~ underlying)

- in the money options (strike < underlying, for Calls, strike > underlying, for Puts)

In the following articles, abbreviations such as OTM, ATM, ITM will be used for the “money” state of the options.

Option markets are risk markets. Buyers are risk haters, sellers are risk lovers.

From the breakpoint, the seller is exposed to unlimited losses, while the buyer will receive unlimited profits.

The buyer sacrifices funds on spot while hoping for delayed profits ; the seller receives funds on spot while being exposed to delayed losses. However, the buyer will not feel a dramatic equity loss, and the seller won’t feel an inflow of cash ; rather , both participants, but especially the seller, will see a growth in consummed margin . Costs are fees and spread for both participants.

Note that these are basic option strategies. The realities of option markets are far beyond these. Option pricing and greeks are the ones that matter. However, one cannot simply discard the fact that with the upcoming of MetaTrader 5, even the basic strategies become interesting. After all, now indicators can trigger option trades instead of regular underlying trades.