Aluminum Options Explained

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Bike Frames: Carbon, Steel And Aluminum, Explained

July 27, 2020 | By Lou Dzierzak

Ask a cyclist what kind of bike frame to buy and you can plan on a long conversation. What kind of bike? Are you considering a road, mountain, triathlon, cyclocross, or fat bike? And the biggie: Steel, aluminum, carbon, or titanium?

According to cycling historians, the first bike was constructed in 1817 completely of wood. Soon after came steel, then aluminum alloy, space-age carbon fiber, and now titanium.

All four construction methods have passionate and loyal followers who scoff at anything other than their preferred material. The formula to determine the “best frame material” has a number of variables. The relationships between cost, riding style, surface, distance, and feel all influence choice.

Steel: Strong, Durable, Heavy

More bikes have been constructed from steel than any other material. When Schwinn dominated the American cycling market in the mid-20th century, iconic models like the 10-speed Varsity and the cool Sting Ray had steel frames.

From a frame builder’s perspective, welding steel tubes results in a durable, strong, long-lasting bike. For riders, steel dampens rough road surfaces that can batter your hands, crush your legs, and make a century ride miserable. Steel frames can take all kind of abuse and are relatively easy to repair. Finally, steel is less expensive than the other frame options.

For all the positive attributes steel has to offer, it has a very large negative: I t’s heavy.

In a race, a steel frame represents a significant competitive disadvantage.

For some riders, steel is still the preferred frame material, but in a racing environment where ounces matter, aluminum and other materials captured racers’ attention.

A final negative: Steel can rust. Be wary if you live in a climate with lots of rain or where winter riding is pursued. Steel is fine in these situations as long as it’s cleaned and maintained, but it requires more care than other materials.

Aluminum: Light, Stiff, Perishable

Longtime cyclists recall the oversized oval aluminum tubes introduced on bikes from Klein and Cannondale. Frames constructed from aluminum alloys are lighter and less dense than steel without sacrificing stiffness. The trade-off?

For one, aluminum frames are less durable than steel. Spill an aluminum frame on a gravel-strewn road and repairs will challenge even the most skilled bike mechanic. Aluminum just can’t be welded or bent back to an original shape.

Aluminum can also be a harsher ride than steel. It tends to translate a lot of road vibration to the rider, which can lead to more fatigue after lots of miles on the bike.

For high-end road and racing bikes, aluminum frames are a strong option when weight influences performance. In many cases, bike brands will offer both aluminum and carbon frame options to fit a range of riders’ budgets.

Aluminum is extremely popular for full-suspension mountain bikes, where its ability to be formed into many shapes, and its weight to strength ratio, make it a solid choice for builders.

Titanium: Powerful, Impervious, Expensive

Bike builders never stop exploring and experimenting. For riders, the results are bike frames that push the standards of performance. Titanium offers some intriguing possibilities. Lighter than steel and more durable than aluminum, titanium represents the best of both worlds.

For riders above the snow belt who are comfortable pedaling year-round, titanium brushes off corrosive elements like road salt. You won’t find rust spots on a titanium frame. In fact, most titanium frames aren’t painted, letting the inherent beauty of the metal shine through.

Heavier riders will appreciate a titanium frame’s ability to dampen the bumps, rattles, and rough roads encountered on century tours, gravel races, and daily commutes. Like steel, a well-constructed titanium frame will last a lifetime. Aluminum and carbon just can’t live up to that guarantee.

On the downside, building a titanium frame requires skill and experience. Repairs, if needed, can be difficult. Finally, titanium frames cost significantly more than comparable steel models.

Carbon: Ultralight, Rigid, Fallible

In 1998, Marco Pantini captured the yellow jersey at the Tour de France riding an aluminum-frame Bianchi racing bike – for the last time. From that point forward, every winning bike has been constructed of carbon fiber. Noted for its light weight, stiffness, and strength, carbon fiber frame designs can be tailored to very specific applications. Tour de France time trial bikes and high-end triathlon models are good examples of frame designs enhancing race performance.

As early construction processes were evolving, carbon frames experienced issues with reliability. Inconsistencies lead to cracks and frame failures. As production methods improved, these issues have been resolved. Major bicycle brand flagship models are usually equipped with carbon fiber frames.

Like the other frame options, carbon has its weaknesses. Durability is one question. A crash that might scratch the paint on a steel frame could cause significant, hard-to-repair damage to a carbon frame. Since carbon fiber frames are generally more rigid than other materials, these stresses can lead to structural failures while in motion. A rare event, but not something a rider would encounter riding steel or titanium frames.

High end mountain bikes also take advantage of carbon, and here it is again a wonderful frame material. The biggest pitfall for mountain bikes is durability (big crashes can send that pricy frame flying into boulder fields) and price.

While still expensive overall, prices of carbon bikes have dropped over time and weekend warriors willing to defer saving for retirement can find a carbon frame priced within reach.

So, what’s your bike of choice: steel, aluminum, titanium, or carbon fiber? Let the debate begin.

Backpropagation concept explained in 5 levels of difficulty

What is backpropagation in neural networks in a pure mathematical sense?

Backpropagation is used by computers to learn from their mistakes and get better at doing a specific thing. So using this computers can keep guessing and get better and better at guessing like humans do at one particular task.

Then these computers can club a lot of small tasks that they are very good at to make a system that can do bigger things like drive a car.

High School Student:

Artificial intelligence can be obtained by giving a computer a lot of data along with the correct solution provided by humans(called labelled data) and training a model like a Linear Classifier, Neural Network etc which can generalize to data it hasn’t seen before. Backpropagation is the technique used by computers to find out the error between a guess and the correct solution, provided the correct solution over this data.

Backpropagation has historically been used to traverse trees in a fast way and in data structures. We have the computer guess a value and use calculus to calculate the error via partial derivatives. Then we fix this error to get a better guess and backpropagate again to find a more fine tuned error. This method of repeatedly guessing shows the recursiveness of backpropagation. The training of an artificial intelligence model takes a long time and a lot of computation and it needs everything it can get to speed it up.

Some people also think that backpropagation is a bad methodology and should be replaced by solutions that involve integrating the partial derivatives to directly get the final error in one go instead of in steps that take a lot of computational time, or some other algorithms. Replacing backpropagation with something else is still an area of research.

The complete algorithm for this is known as Gradient Descent. The part of Gradient Descent(or similar algorithms) where you infer the error(usually with calculus) and correct it is known as Backpropagation.


So backpropagation in Computer science is the algorithmic way in which we send the result of some computation back to the parent recursively.

In Machine learning, backpropagation sends feedback to the neural net.

So any training step includes calculating the gradient(differentiation in calculus) and then doing backpropagation(integrating the gradient to get back the way the weights should change).

Simple Case study to understand the calculus: Apples vs Oranges

So let’s say in a simple example we are training a simple line classifier that draws ` y = mx + c`. The goal of the classifier is to figure out the correct m and c values that does binary classification on apples and oranges given the radius of the fruit(x axis) and rgb value(y axis). So the classifier has to draw a straight line on the x-y plane to divide it into two parts, one for apples and one for oranges.

The gradient will be d/dx(mx+c) => m, which is the partial derivative of dy/dx, in this case the slope of the line.

Then we calculate the loss on some function we have to optimize, say RMS prop(root mean square of correct values vs predicted values) in which we apply the data to our predicted gradient values by substituting real points like (x1, y1), (x2, y2), … (xn, yn) to the equation.

loss =RMS prop(guess_m, guess_c)(data, correct_answers).

The reason for calling this loss is because it gives us the error between the guess and the correct answers. The loss is calculated by using calculus on the optimisation function of RMS prop.

This will give us a “delta” by which our current m and c values have to change.

Backpropagation step is when we calculate that “delta” and use it to update m and c values.

Now in more complex scenario say neural network

Every neuron/perceptron in the neural network consists of a weight which represents the data/bias it accumulates in training. This weight can be for example a 128 x 64 matrix of 0’s and 1’s. The 128 in this example will be the number of nodes in the previous layer as input and the 64 will be the number of output nodes in the next layer.

In the Adam optimization function we have equations having logarithmic value to normalize scale. This means doing integration and differentiation on “log”, or equations with “e” which can be represented as an infinite series in mathematics.

The Adam optimization function has an RMS prop value and a momentum function which it gets from AdaGrad. For the sake of backpropagation, I assume you are familiar with Gradient Descent which will be explained better in a lot of other places.

The backpropagation step will send back the “delta” of the values given in the Wikipedia link.

So weight(t+ 1) = weight(t) – delta.

In reality, the weights of every node in a layer of the neural net are calculated at the same time in parallel by a technique called vectorization which increases its performance via parallelisation on GPUs or TPUs or some microprocessor by using the matrix multiplication flag.

So a bit more on the

backpropagation(integrating the gradient to get back the way the weights should change)

Let’s say you train the model 100 times on the y=mx + c

So in iteration 1:

m1 = m0(random init) + delta(RMS loss equation), where the delta is obtained by partial differentiation of RMS loss equation for m

c1 = c0(random init) + delta(RMS loss equation), where the delta is obtained by partial differentiation of RMS loss equation for c

m2 = m1 + delta(RMS loss equation)

c2 = c1 + delta(RMS loss equation)

In iteration 1 to 100:

m100 = m0 + summation(delta_from 1 to 100(RMS prop equation))

which is the same as

m100 = m0 + integration(delta_from 1 to 100(RMS prop equation)), which works well for our simple apples vs oranges, except if the network is deep you would not be able to do it in one go but layer by layer.

So now that you understand this simple process which will also work on a single node of 128 x 64 weights, we have to discuss how to apply it to a network of such nodes in a neural network. For a quick refresher on partial derivatives and how the calculus part is computed check out Backpropagation in 5 minutes which you will now understand better.

If we are able to apply backpropagation to more complex neural networks like those described in Backpropagation through time, used in LSTM’s, RNN’s or GRU’s we can do text translation, generation of music etc.

So what we discussed until now was for training weights of one node which has output function f.

In a deep neural network(deep means many layers, the width of a layer is the number of nodes in it), you would have to forward propagate through every layer to get the predicted value, calculate the error and then backpropagate the error(update the weights by delta) across every layer.

So the delta will be calculated for every layer in reverse order as and the network will train as shown below. If a network has 5 layers, to calculate the backpropagated error for layer 1, we would have to forward propagate from layer 1 => layer 2 => … => layer 5 => output activation and then backpropagate from output activation => layer 5 => layer 4 … => layer 1 and then using this delta fix the weights of every node in layer 1.

or for Convolutional Nets you would have additional difficulties like backpropagating through a pooling layer

So in deep nets, after forward propagation, you would have to backpropagate the activation function(on the last layer) first like

= 0, if x Softmax which is multiple sigmoids stacked together

or Sigmoid => y = 1/(1+pow(e, -x))

and then you would pass the “delta” as the loss function to the second last layer which will calculate the delta of delta and so on. The functions described above seem easy to differentiate no?

And an even more complex scenario would be having to backpropagate a deep net which is being trained batch-wise or backpropagating through time(like in RNN’s or LSTM’s or GRU’s).

These Recurrent Neural Networks or RNN’s have something known as a “skip connection” which allows them to propagate changes easily in very deep networks. Also Gated Recurrent Units or GRU’s have a “memory gate” which keeps track of some “context” in the data and a “forget gate” to mark where the context is irrelevant. LSTM’s also have an extra “output gate” to the GRU gates and perform much better on larger datasets.

These LSTM’s can be used to build networks that can predict ethnicity, gender, translate between languages, generate music and mix art styles. Similarly, LSTM’s too have a unique way to backpropagate their errors you can estimate by partially differentiating their equations for the various gates. Look at this paper on Backpropagation through time for more details.

The fundamentals of backprop are that there will be a random Weight matrix W for every node, which backprop will update as W = W-delta, where delta is the derivative of the output function of that node which represents the error to be corrected in a step in the node.

For code references on getting a feel for implementing it yourself, check the medium articles at the bottom.

Postgraduate & PhD:

It is best to understand this concept in greater detail from research papers and videos by experts. I’ll provide some links for this.

Here is the paper for Adam.

Here is a video of Backpropagation by Yoshua Bengio who has supported backpropagation a lot over the decades.

Here is an article about why Geoffrey Hinton thinks we should abandon backpropagation and find a better method.

Tsvi Achler, M.D./PhD Computational Neuroscience & Neurology, University of Illinois at Urbana-Champaign (2006)

I don’t think Hinton goes far enough. Backprop is not the fundamental problem, it is network structures. Neural networks should not be limited to a feedforward configuration* . Backprop can only train feedforward networks and will remain one of the best solutions as long as networks are feedforward.

Also for a broader intuition of how you can get intelligence from randomness and repeated guesswork take a look at Monte Carlo methods and Markov chains.

If you do the course by Andrew Ng on Deep learning, he makes you implement backpropagation in code on various equations, my favorite loss function is

because it is used in a lot of machine learning algorithms as:

  • if y = 1 ==> L(y’,1) = -log(y’) ==> we want y’ to be the largest ==> y ‘ biggest value is 1
  • if y = 0 ==> L(y’,0) = -log(1-y’) ==> we want 1-y’ to be the largest ==> y’ to be smaller as possible because it can only has 1 value.

and then we do differentiation on L(y’, y) to get the gradients.

Part of being a Postgrad or Doctor means being able to read research papers to gain insight. NIPS and ICLR are famous events in this space to learn more and will help you with a lot of material you can go through.

I haven’t included code examples for backpropagation in numpy because you will usually end up using a library like PyTorch or Tensorflow which implements it for you. Also since backpropagation is closely tied to the type of network, there is usually a different implementation per node type but it remains constant in the fact that you use calculus to get the errors for the mathematical function you have, so you have to read all the papers to understand each backpropagation implementation . The point of learning backpropagation for most people is to understand the mathematics behind it for research or what their libraries are doing under the hood. I hope this article gives you intuition on this concept before you checkout some other advanced articles that start off at the difficulty of implementing it directly like

Essential Options Trading Guide

Options trading may seem overwhelming at first, but it’s easy to understand if you know a few key points. Investor portfolios are usually constructed with several asset classes. These may be stocks, bonds, ETFs, and even mutual funds. Options are another asset class, and when used correctly, they offer many advantages that trading stocks and ETFs alone cannot.

Key Takeaways

  • An option is a contract giving the buyer the right, but not the obligation, to buy (in the case of a call) or sell (in the case of a put) the underlying asset at a specific price on or before a certain date.
  • People use options for income, to speculate, and to hedge risk.
  • Options are known as derivatives because they derive their value from an underlying asset.
  • A stock option contract typically represents 100 shares of the underlying stock, but options may be written on any sort of underlying asset from bonds to currencies to commodities.


What Are Options?

Options are contracts that give the bearer the right, but not the obligation, to either buy or sell an amount of some underlying asset at a pre-determined price at or before the contract expires.   Options can be purchased like most other asset classes with brokerage investment accounts. 

Options are powerful because they can enhance an individual’s portfolio. They do this through added income, protection, and even leverage. Depending on the situation, there is usually an option scenario appropriate for an investor’s goal. A popular example would be using options as an effective hedge against a declining stock market to limit downside losses. Options can also be used to generate recurring income. Additionally, they are often used for speculative purposes such as wagering on the direction of a stock. 

There is no free lunch with stocks and bonds. Options are no different. Options trading involves certain risks that the investor must be aware of before making a trade. This is why, when trading options with a broker, you usually see a disclaimer similar to the following:

Options involve risks and are not suitable for everyone. Options trading can be speculative in nature and carry substantial risk of loss.

Options as Derivatives

Options belong to the larger group of securities known as derivatives. A derivative’s price is dependent on or derived from the price of something else. As an example, wine is a derivative of grapes ketchup is a derivative of tomatoes, and a stock option is a derivative of a stock. Options are derivatives of financial securities—their value depends on the price of some other asset. Examples of derivatives include calls, puts, futures, forwards, swaps, and mortgage-backed securities, among others.

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Call and Put Options

Options are a type of derivative security. An option is a derivative because its price is intrinsically linked to the price of something else. If you buy an options contract, it grants you the right, but not the obligation to buy or sell an underlying asset at a set price on or before a certain date.

A call option gives the holder the right to buy a stock and a put option gives the holder the right to sell a stock. Think of a call option as a down-payment for a future purpose. 

Call Option Example

A potential homeowner sees a new development going up. That person may want the right to purchase a home in the future, but will only want to exercise that right once certain developments around the area are built.

The potential home buyer would benefit from the option of buying or not. Imagine they can buy a call option from the developer to buy the home at say $400,000 at any point in the next three years. Well, they can—you know it as a non-refundable deposit. Naturally, the developer wouldn’t grant such an option for free. The potential home buyer needs to contribute a down-payment to lock in that right.

With respect to an option, this cost is known as the premium. It is the price of the option contract. In our home example, the deposit might be $20,000 that the buyer pays the developer. Let’s say two years have passed, and now the developments are built and zoning has been approved. The home buyer exercises the option and buys the home for $400,000 because that is the contract purchased.

The market value of that home may have doubled to $800,000. But because the down payment locked in a pre-determined price, the buyer pays $400,000. Now, in an alternate scenario, say the zoning approval doesn’t come through until year four. This is one year past the expiration of this option. Now the home buyer must pay the market price because the contract has expired. In either case, the developer keeps the original $20,000 collected.

Call Option Basics

Put Option Example

Now, think of a put option as an insurance policy. If you own your home, you are likely familiar with purchasing homeowner’s insurance. A homeowner buys a homeowner’s policy to protect their home from damage. They pay an amount called the premium, for some amount of time, let’s say a year. The policy has a face value and gives the insurance holder protection in the event the home is damaged.

What if, instead of a home, your asset was a stock or index investment? Similarly, if an investor wants insurance on his/her S&P 500 index portfolio, they can purchase put options. An investor may fear that a bear market is near and may be unwilling to lose more than 10% of their long position in the S&P 500 index. If the S&P 500 is currently trading at $2500, he/she can purchase a put option giving the right to sell the index at $2250, for example, at any point in the next two years.

If in six months the market crashes by 20% (500 points on the index), he or she has made 250 points by being able to sell the index at $2250 when it is trading at $2000—a combined loss of just 10%. In fact, even if the market drops to zero, the loss would only be 10% if this put option is held. Again, purchasing the option will carry a cost (the premium), and if the market doesn’t drop during that period, the maximum loss on the option is just the premium spent.

Put Option Basics

Buying, Selling Calls/Puts

There are four things you can do with options:

  1. Buy calls
  2. Sell calls
  3. Buy puts
  4. Sell puts

Buying stock gives you a long position. Buying a call option gives you a potential long position in the underlying stock. Short-selling a stock gives you a short position. Selling a naked or uncovered call gives you a potential short position in the underlying stock.

Buying a put option gives you a potential short position in the underlying stock. Selling a naked, or unmarried, put gives you a potential long position in the underlying stock. Keeping these four scenarios straight is crucial.

People who buy options are called holders and those who sell options are called writers of options. Here is the important distinction between holders and writers:

  1. Call holders and put holders (buyers) are not obligated to buy or sell. They have the choice to exercise their rights. This limits the risk of buyers of options to only the premium spent.
  2. Call writers and put writers (sellers), however, are obligated to buy or sell if the option expires in-the-money (more on that below). This means that a seller may be required to make good on a promise to buy or sell. It also implies that option sellers have exposure to more, and in some cases, unlimited, risks. This means writers can lose much more than the price of the options premium.   

Why Use Options


Speculation is a wager on future price direction. A speculator might think the price of a stock will go up, perhaps based on fundamental analysis or technical analysis. A speculator might buy the stock or buy a call option on the stock. Speculating with a call option—instead of buying the stock outright—is attractive to some traders since options provide leverage. An out-of-the-money call option may only cost a few dollars or even cents compared to the full price of a $100 stock.


Options were really invented for hedging purposes. Hedging with options is meant to reduce risk at a reasonable cost. Here, we can think of using options like an insurance policy. Just as you insure your house or car, options can be used to insure your investments against a downturn.

Imagine that you want to buy technology stocks. But you also want to limit losses. By using put options, you could limit your downside risk and enjoy all the upside in a cost-effective way. For short sellers, call options can be used to limit losses if wrong—especially during a short squeeze.

How Options Work

In terms of valuing option contracts, it is essentially all about determining the probabilities of future price events. The more likely something is to occur, the more expensive an option would be that profits from that event. For instance, a call value goes up as the stock (underlying) goes up. This is the key to understanding the relative value of options.

The less time there is until expiry, the less value an option will have. This is because the chances of a price move in the underlying stock diminish as we draw closer to expiry. This is why an option is a wasting asset. If you buy a one-month option that is out of the money, and the stock doesn’t move, the option becomes less valuable with each passing day. Since time is a component to the price of an option, a one-month option is going to be less valuable than a three-month option. This is because with more time available, the probability of a price move in your favor increases, and vice versa.

Accordingly, the same option strike that expires in a year will cost more than the same strike for one month. This wasting feature of options is a result of time decay. The same option will be worth less tomorrow than it is today if the price of the stock doesn’t move. 

Volatility also increases the price of an option. This is because uncertainty pushes the odds of an outcome higher. If the volatility of the underlying asset increases, larger price swings increase the possibilities of substantial moves both up and down. Greater price swings will increase the chances of an event occurring. Therefore, the greater the volatility, the greater the price of the option. Options trading and volatility are intrinsically linked to each other in this way. 

On most U.S. exchanges, a stock option contract is the option to buy or sell 100 shares; that’s why you must multiply the contract premium by 100 to get the total amount you’ll have to spend to buy the call.

What happened to our option investment
May 1 May 21 Expiry Date
Stock Price $67 $78 $62
Option Price $3.15 $8.25 worthless
Contract Value $315 $825 $0
Paper Gain/Loss $0 $510 -$315

The majority of the time, holders choose to take their profits by trading out (closing out) their position. This means that option holders sell their options in the market, and writers buy their positions back to close. Only about 10% of options are exercised, 60% are traded (closed) out, and 30% expire worthlessly.

Fluctuations in option prices can be explained by intrinsic value and extrinsic value, which is also known as time value. An option’s premium is the combination of its intrinsic value and time value. Intrinsic value is the in-the-money amount of an options contract, which, for a call option, is the amount above the strike price that the stock is trading. Time value represents the added value an investor has to pay for an option above the intrinsic value.   This is the extrinsic value or time value. So, the price of the option in our example can be thought of as the following:

Premium = Intrinsic Value + Time Value
$8.25 $8.00 $0.25

In real life, options almost always trade at some level above their intrinsic value, because the probability of an event occurring is never absolutely zero, even if it is highly unlikely.

Types of Options

American and European Options

American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type.   Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.

There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with “optionality” embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options.   Again, exotic options are typically for professional derivatives traders.

Options Expiration & Liquidity

Options can also be categorized by their duration. Short-term options are those that expire generally within a year. Long-term options with expirations greater than a year are classified as long-term equity anticipation securities or LEAPs. LEAPS are identical to regular options, they just have longer durations.

Options can also be distinguished by when their expiration date falls. Sets of options now expire weekly on each Friday, at the end of the month, or even on a daily basis. Index and ETF options also sometimes offer quarterly expiries. 

Reading Options Tables

More and more traders are finding option data through online sources. (For related reading, see “Best Online Stock Brokers for Options Trading 2020”) While each source has its own format for presenting the data, the key components generally include the following variables:

  • Volume (VLM) simply tells you how many contracts of a particular option were traded during the latest session.
  • The “bid” price is the latest price level at which a market participant wishes to buy a particular option.
  • The “ask” price is the latest price offered by a market participant to sell a particular option.
  • Implied Bid Volatility (IMPL BID VOL) can be thought of as the future uncertainty of price direction and speed. This value is calculated by an option-pricing model such as the Black-Scholes model and represents the level of expected future volatility based on the current price of the option.
  • Open Interest (OPTN OP) number indicates the total number of contracts of a particular option that have been opened. Open interest decreases as open trades are closed.
  • Delta can be thought of as a probability. For instance, a 30-delta option has roughly a 30% chance of expiring in-the-money.
  • Gamma (GMM) is the speed the option is moving in or out-of-the-money. Gamma can also be thought of as the movement of the delta.
  • Vega is a Greek value that indicates the amount by which the price of the option would be expected to change based on a one-point change in implied volatility.
  • Theta is the Greek value that indicates how much value an option will lose with the passage of one day’s time.
  • The “strike price” is the price at which the buyer of the option can buy or sell the underlying security if he/she chooses to exercise the option. 

Buying at the bid and selling at the ask is how market makers make their living.

Long Calls/Puts

The simplest options position is a long call (or put) by itself. This position profits if the price of the underlying rises (falls), and your downside is limited to loss of the option premium spent. If you simultaneously buy a call and put option with the same strike and expiration, you’ve created a straddle.

This position pays off if the underlying price rises or falls dramatically; however, if the price remains relatively stable, you lose premium on both the call and the put. You would enter this strategy if you expect a large move in the stock but are not sure which direction.   

Basically, you need the stock to have a move outside of a range. A similar strategy betting on an outsized move in the securities when you expect high volatility (uncertainty) is to buy a call and buy a put with different strikes and the same expiration—known as a strangle. A strangle requires larger price moves in either direction to profit but is also less expensive than a straddle. On the other hand, being short either a straddle or a strangle (selling both options) would profit from a market that doesn’t move much.   

Below is an explanation of straddles from my Options for Beginners course:

Straddles Academy

And here’s a description of strangles:

How to use Straddle Strategies

Spreads & Combinations

Spreads use two or more options positions of the same class. They combine having a market opinion (speculation) with limiting losses (hedging). Spreads often limit potential upside as well. Yet these strategies can still be desirable since they usually cost less when compared to a single options leg. Vertical spreads involve selling one option to buy another. Generally, the second option is the same type and same expiration, but a different strike.

A bull call spread, or bull call vertical spread, is created by buying a call and simultaneously selling another call with a higher strike price and the same expiration. The spread is profitable if the underlying asset increases in price, but the upside is limited due to the short call strike. The benefit, however, is that selling the higher strike call reduces the cost of buying the lower one.   Similarly, a bear put spread, or bear put vertical spread, involves buying a put and selling a second put with a lower strike and the same expiration. If you buy and sell options with different expirations, it is known as a calendar spread or time spread. 


Combinations are trades constructed with both a call and a put. There is a special type of combination known as a “synthetic.” The point of a synthetic is to create an options position that behaves like an underlying asset, but without actually controlling the asset. Why not just buy the stock? Maybe some legal or regulatory reason restricts you from owning it. But you may be allowed to create a synthetic position using options.   


A butterfly consists of options at three strikes, equally spaced apart, where all options are of the same type (either all calls or all puts) and have the same expiration. In a long butterfly, the middle strike option is sold and the outside strikes are bought in a ratio of 1:2:1 (buy one, sell two, buy one).

If this ratio does not hold, it is not a butterfly. The outside strikes are commonly referred to as the wings of the butterfly, and the inside strike as the body. The value of a butterfly can never fall below zero. Closely related to the butterfly is the condor – the difference is that the middle options are not at the same strike price. 

Options Risks

Because options prices can be modeled mathematically with a model such as the Black-Scholes, many of the risks associated with options can also be modeled and understood. This particular feature of options actually makes them arguably less risky than other asset classes, or at least allows the risks associated with options to be understood and evaluated. Individual risks have been assigned Greek letter names, and are sometimes referred to simply as “the Greeks.” 

Below is a very basic way to begin thinking about the concepts of Greeks:

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