Lesson 5 – Advanced Concepts

When studying something in-depth, you will come across topics that are super easy and extremely hard. We cannot vouch that you will find only simple topics. When speaking about Options, it is one of the hardest topics for someone who has just started learning it. But for the ones who have some kind of idea, it wouldn’t be as hard as for the naïve learners. However, if you find it hard to understand, it is wise to read this course over and over again.

It is not unknown that advanced concepts are pretty tough. This is precisely why we decided to help you with key concepts. So once you learn the key concepts, you can easily understand options investing and trading.

Let’s begin by learning the lesson of the Black Scholes Pricing Model and Greeks. Not only that, but we’ll also retouch the Time Decay and Volatility concept while discussing the Bell Curve concerning the pricing of options. Advanced topics have a lot to cover. But we have decided to help you with the initial stage so you’d be able to prepare yourself when you engage yourself in the market. Let’s start learning Greek!

Learning Greek

You might have concluded that Greeks are all about learning the culture or language. In some other context or literature context, this would be true. But not when we are discussing options, it’s not the case. In regards to options, Greek is all about translating the pricing of options. The basis of current-day mathematics links to Ancient Greece, so it is understandable how the pricing of options can be handled with Greeks.  

So, the risk exposure related to the option position can be calculated using the Greek measurements. Trading instruments, including options, have a wide range of risk exposure that might differ dramatically with time or movements of the market. The reason is options were created to manage risk, so it’s a risk management tool. Meanwhile, mathematicians introduced measurements to help to analyze the risk that impacts the pricing of options.

The term “Greeks” has come into the picture because mathematical analyses deal with Greek letters. Some of the examples are such as Theta, Vega, Rho, Gamma, and Delta. These primary measurements are utilized in pricing models of options, including the Black Scholes Formula. We will discuss this in detail later.

So, here are the benefits of utilizing Greeks:

• To find the exact amount of portfolio risk management or hedging required.
• To find the risk exposure of the portfolio or position and the place where the risk is.
• To find the value changes of the options as with the changes in the movements of the underlying stock price.
• To find the losing time value of a position, you can get an indication.

As you are at the beginner’s level, it is not vigilant for us to pour mathematics into your head. Thus, we’ll stick to helping you with Greeks. And, you wouldn’t love the mathematics session of this as it is not at all fun like this. Without further explanation, let’s check the Greek symbols and what they mean.

• Theta: using Theta, one can find the changes in the price of the options when it gets near to the expiration period.
• Delta: using Delta, one can find the level of sensitivity of the options in regards to the underlying share price changes.
• Gamma: using Gamma, one can find the Delta change in regards to the share price changes.
• Rho: using Rho, one can find the option price changes in regards to interest rate changes.
• Vega: using Vega, one can find the option price changes in regards to underlying volatility changes.

These formulas are used in order to get the measurement of a risk-reward for a portfolio or trading position.

Some strategies are based on discrepancies in the above Greek values, whereas other strategies will require monitoring of the Greeks to assist in your decision-making process.

As you already know, the measurements we just discussed are utilized in the Black Scholes Pricing model. “The Pricing of Options and Corporate Liabilities” is a paper released by Myron Scholes and Fisher Black in 1973. They also secured the Noble Prize for doing their part for the finance sector. The main reason for using the formula is to settle for a fair price. There are many variables taken into consideration when settling for an option’s fair price. They are such as:

• Time until expiration
• Interest rates
• Current price
• Option strike price
• Volatility
• Dividends

So the trader can compare the current price with the rhetorical fair value. Once done, the trader can study whether the option is undervalued or overvalued.

That said, learning Greeks and Black Scholes Pricing Model should continue when you start experiencing the markets. As of now, you will be able to manage trading with the advanced concepts that we are learning in this course.

Digging Deeper into the concept of Time Decay

We covered some sections of the Time Decay, Option Volatility, and Delta in the earlier lessons. Now, let’s dig a little deeper into the concepts.

Time Decay concept deals with the expiration of the options. It discusses how an option’s value reduces when it gets near to the expiration. When there’s less time for expiration, there’s only less time for anything to happen in regards to the price of the underlying stock. The Time Decay will enhance at a higher rate during the expiration’s final weeks.

As for the Greeks, the Time Decay is called Theta. This is why the definition of Theta was ‘using Theta, one can find the changes in the price of the options when it gets near to the expiration period.’

As you go deeper into the concept, you will realize that Theta describes the option price’s value reduction for every passing day while other factors are held equal. Also, the Theta will not have a positive figure because the option price’s impact would be negative.

This applies to an option buyer or a taker. If you have bought Put or Call option with an interest of underlying directional move, then it’s going to be a negative Theta experience. This means the option’s value will reduce because of Time Decay.

For example, a $3.50 worthy option has a -0.20 Theta. Tomorrow, while the underlying price at the same rate, along with other factors equal, the value of the option would be $3.30. So, it would be reduced Theta loss -0.20 from $3.50.

For options traders, Time Decay isn’t a positive factor. This is why it is essential to consider the time before entering into options positions. As Time Decay reduces at a higher rate during the expiration’s final weeks, options traders should be ready with their exit strategies before Time Decay creates a huge value change.

In contrast, Time Decay is the objective of Option Writers to enter into options. Commonly, 3-5 weeks from the expiration is when options writers enter into positions. Therefore, option writers consider Theta as a positive figure. When the Theta is higher, the Time Decay would be higher, so it benefits the option writers.

The Bell Curve is used to view the Time Value pricing of an option in a diagram. The reason is Bell Curve helps to display distribution for a measurement series. By examining the Bell Curve, you can find that the major Time Value will be in the middle part of the curve, lesser Time Value will be in the below and above part of the curve.

If the ATM strike is displayed in the curve’s middle part, you should understand that the major Time Value will happen near it. But the lower Time Value will be displayed at the further ITM and OTM strike levels. Initially, the ATM options will decay slower and increase when it reaches the expiration. Due to this, the Time Value for ATM options is higher.

Meanwhile, ITM and OTM options will decay linearly while erosion would lower near expiration.

A negative factor is that even though the rhetoric representation of options’ activity around normal distribution is possible, in reality, there can be changes when trading. So the bell curve could be produced with unequally distributed data or high Kurtosis.

In-Depth Learning of Volatility

Now, it’s the part to learn Volatility in-depth.

The Greeks are used in representing Volatility mathematically. Kappa or Vega is used as the measurement to find the option price change concerning volatility.

From the previous lesson, you would have understood that higher volatility will increase the option’s premium price. This makes options expensive for the buyer or taker while making it great for option writers.  

Sometimes, the fallen value of your option will be because of Vega, even if the share’s underlying price has moved in the expected direction. This is not going to be easy but can be easily described using Vega.

For example, you purchased a Call option with an expectation of an increase in share price, but there is a high-level Vega for the option. This defines that the volatility is high. If the value of the share price increases, the value of the Call option should also be increased as for your expectation. However, if the Vega reduces during this time, the volatility of the underlying stock will also reduce. Then, the call option will eventually reduce in value.

The reduction in Vega can nullify and excel in the stock’s underlying price increment. Concerning the concept of the Black Scholes Pricing Model, the volatility we are referring to is actually implied volatility.

Materials

Lesson 5 – Advanced Concepts

When studying something in-depth, you will come across topics that are super easy and extremely hard. We cannot vouch that you will find only simple topics. When speaking about Options, it is one of the hardest topics for someone who has just started learning it. But for the ones who have some kind of idea, it wouldn’t be as hard as for the naïve learners. However, if you find it hard to understand, it is wise to read this course over and over again.

It is not unknown that advanced concepts are pretty tough. This is precisely why we decided to help you with key concepts. So once you learn the key concepts, you can easily understand options investing and trading.

Let’s begin by learning the lesson of the Black Scholes Pricing Model and Greeks. Not only that, but we’ll also retouch the Time Decay and Volatility concept while discussing the Bell Curve concerning the pricing of options. Advanced topics have a lot to cover. But we have decided to help you with the initial stage so you’d be able to prepare yourself when you engage yourself in the market. Let’s start learning Greek!

Learning Greek

You might have concluded that Greeks are all about learning the culture or language. In some other context or literature context, this would be true. But not when we are discussing options, it’s not the case. In regards to options, Greek is all about translating the pricing of options. The basis of current-day mathematics links to Ancient Greece, so it is understandable how the pricing of options can be handled with Greeks.  

So, the risk exposure related to the option position can be calculated using the Greek measurements. Trading instruments, including options, have a wide range of risk exposure that might differ dramatically with time or movements of the market. The reason is options were created to manage risk, so it’s a risk management tool. Meanwhile, mathematicians introduced measurements to help to analyze the risk that impacts the pricing of options.

The term “Greeks” has come into the picture because mathematical analyses deal with Greek letters. Some of the examples are such as Theta, Vega, Rho, Gamma, and Delta. These primary measurements are utilized in pricing models of options, including the Black Scholes Formula. We will discuss this in detail later.

So, here are the benefits of utilizing Greeks:

• To find the exact amount of portfolio risk management or hedging required.
• To find the risk exposure of the portfolio or position and the place where the risk is.
• To find the value changes of the options as with the changes in the movements of the underlying stock price.
• To find the losing time value of a position, you can get an indication.

As you are at the beginner’s level, it is not vigilant for us to pour mathematics into your head. Thus, we’ll stick to helping you with Greeks. And, you wouldn’t love the mathematics session of this as it is not at all fun like this. Without further explanation, let’s check the Greek symbols and what they mean.

• Theta: using Theta, one can find the changes in the price of the options when it gets near to the expiration period.
• Delta: using Delta, one can find the level of sensitivity of the options in regards to the underlying share price changes.
• Gamma: using Gamma, one can find the Delta change in regards to the share price changes.
• Rho: using Rho, one can find the option price changes in regards to interest rate changes.
• Vega: using Vega, one can find the option price changes in regards to underlying volatility changes.

These formulas are used in order to get the measurement of a risk-reward for a portfolio or trading position.

Some strategies are based on discrepancies in the above Greek values, whereas other strategies will require monitoring of the Greeks to assist in your decision-making process.

As you already know, the measurements we just discussed are utilized in the Black Scholes Pricing model. “The Pricing of Options and Corporate Liabilities” is a paper released by Myron Scholes and Fisher Black in 1973. They also secured the Noble Prize for doing their part for the finance sector. The main reason for using the formula is to settle for a fair price. There are many variables taken into consideration when settling for an option’s fair price. They are such as:

• Time until expiration
• Interest rates
• Current price
• Option strike price
• Volatility
• Dividends

So the trader can compare the current price with the rhetorical fair value. Once done, the trader can study whether the option is undervalued or overvalued.

That said, learning Greeks and Black Scholes Pricing Model should continue when you start experiencing the markets. As of now, you will be able to manage trading with the advanced concepts that we are learning in this course.

Digging Deeper into the concept of Time Decay

We covered some sections of the Time Decay, Option Volatility, and Delta in the earlier lessons. Now, let’s dig a little deeper into the concepts.

Time Decay concept deals with the expiration of the options. It discusses how an option’s value reduces when it gets near to the expiration. When there’s less time for expiration, there’s only less time for anything to happen in regards to the price of the underlying stock. The Time Decay will enhance at a higher rate during the expiration’s final weeks.

As for the Greeks, the Time Decay is called Theta. This is why the definition of Theta was ‘using Theta, one can find the changes in the price of the options when it gets near to the expiration period.’

As you go deeper into the concept, you will realize that Theta describes the option price’s value reduction for every passing day while other factors are held equal. Also, the Theta will not have a positive figure because the option price’s impact would be negative.

This applies to an option buyer or a taker. If you have bought Put or Call option with an interest of underlying directional move, then it’s going to be a negative Theta experience. This means the option’s value will reduce because of Time Decay.

For example, a $3.50 worthy option has a -0.20 Theta. Tomorrow, while the underlying price at the same rate, along with other factors equal, the value of the option would be $3.30. So, it would be reduced Theta loss -0.20 from $3.50.

For options traders, Time Decay isn’t a positive factor. This is why it is essential to consider the time before entering into options positions. As Time Decay reduces at a higher rate during the expiration’s final weeks, options traders should be ready with their exit strategies before Time Decay creates a huge value change.

In contrast, Time Decay is the objective of Option Writers to enter into options. Commonly, 3-5 weeks from the expiration is when options writers enter into positions. Therefore, option writers consider Theta as a positive figure. When the Theta is higher, the Time Decay would be higher, so it benefits the option writers.

The Bell Curve is used to view the Time Value pricing of an option in a diagram. The reason is Bell Curve helps to display distribution for a measurement series. By examining the Bell Curve, you can find that the major Time Value will be in the middle part of the curve, lesser Time Value will be in the below and above part of the curve.

If the ATM strike is displayed in the curve’s middle part, you should understand that the major Time Value will happen near it. But the lower Time Value will be displayed at the further ITM and OTM strike levels. Initially, the ATM options will decay slower and increase when it reaches the expiration. Due to this, the Time Value for ATM options is higher.

Meanwhile, ITM and OTM options will decay linearly while erosion would lower near expiration.

A negative factor is that even though the rhetoric representation of options’ activity around normal distribution is possible, in reality, there can be changes when trading. So the bell curve could be produced with unequally distributed data or high Kurtosis.

In-Depth Learning of Volatility

Now, it’s the part to learn Volatility in-depth.

The Greeks are used in representing Volatility mathematically. Kappa or Vega is used as the measurement to find the option price change concerning volatility.

From the previous lesson, you would have understood that higher volatility will increase the option’s premium price. This makes options expensive for the buyer or taker while making it great for option writers.  

Sometimes, the fallen value of your option will be because of Vega, even if the share’s underlying price has moved in the expected direction. This is not going to be easy but can be easily described using Vega.

For example, you purchased a Call option with an expectation of an increase in share price, but there is a high-level Vega for the option. This defines that the volatility is high. If the value of the share price increases, the value of the Call option should also be increased as for your expectation. However, if the Vega reduces during this time, the volatility of the underlying stock will also reduce. Then, the call option will eventually reduce in value.

The reduction in Vega can nullify and excel in the stock’s underlying price increment. Concerning the concept of the Black Scholes Pricing Model, the volatility we are referring to is actually implied volatility.