Mastering Volatility

Knowing when to hedge/speculate/neutral

# Risks Pricing

Option master always know their prices.

# Speculating

Long gamma

# Hedging

Making the best out of BLACKSWAN EVENTS

Risks Neutral

making time your ally.

# Understanding Volatility

### Some facets of volatility

There are many ways to look at volatility.

The intuitive meaning of the word is that

**volatility measures the level of fluctuations for a particular price**.The way we measure it, the unit we use, the time scale at which we are looking all have an impact and should be specified in order to transform a single volatility number into a solid understanding of how much level of fluctuation there is in that particular stock.

By taking a more academic approach based on statistics, one can argue that

**the value of the stock in one year is uncertain and assign a probability distribution to it**. It could be desirable to**use the width or standard deviation of this distribution to link to the volatility of the stock**. This point of view is exactly what has become**the market standard**.It is clear that the statistical approach is focused on the one-year horizon, whereas a trader, who wants to delta-hedge on a daily basis, is not so interested in knowing the uncertainty accumulated over the year. What he is really interested in is understanding how the uncertainty plays a role on a much smaller scale, such that piled up over the year it leads to the same distribution as the statistician has presented.

In mathematical terms, knowing the distribution at one time (or multiple times) is not enough to complete the dynamic picture. One needs to know how the distribution changes over time. Clearly, on a very short time scale, the uncertainty is very small and the distribution function should be sharply peaked about the current level of the stock. As the time horizon increases, the density should widen.

One can show that

**at any time t, the solution of the Black-Scholes SDE**, describing a model for the movement of the stock,**is a random variable S(t) that behaves according to a lognormal distribution**. So**at any time t, we have a density that depends on the original parameters in the equation**, being the drift µ and the volatility parameter σ.Note that

**the volatility is not the standard deviation of this distribution, but it does control the wideness of the distribution**. Clearly, if we used another model for the stock price, it would lead to another family of density functions, and to other formulas for the moments.**In a way, when people use the word volatility, they also agree on the underlying mathematical model**!A higher volatility means more uncertainty about the size of an asset’s fluctuations and, as such, it can be considered a measurement of uncertainty.

**Volatility is dynamic and changes a great deal over time**. It experiences high and low regimes, but it also has a long-term mean to which it reverts. Also, as a stock market witnesses a large decline, volatility tends to shoot up: we therefore generally see a negative correlation between such assets and their volatilities.Trader& Quant's Den

# Options Greek Dynamics

Options trading has become increasingly popular in recent years as it offers investors an opportunity to profit from market movements without actually owning the underlying asset. However, trading options can be complex and requires an understanding of various option pricing factors, including the Greeks. In this article, we will explore the five main Greeks used in options trading and introduce higher-order Greeks that can be used to fine-tune trading strategies.

**What are the Greeks?**The Greeks are measures of the sensitivity of an option's price to changes in various factors, such as the underlying asset price, time, volatility, and interest rates. They are used to help traders assess risk and develop trading strategies. There are five primary Greeks: Delta, Gamma, Theta, Vega, and Rho.

**Delta**Delta measures the sensitivity of an option's price to changes in the underlying asset price. It ranges from 0 to 1 for calls and -1 to 0 for puts, with an at-the-money option having a delta of approximately 0.5. A delta of 0.5 means that the option price will increase by $0.50 for every $1 increase in the underlying asset price, and vice versa for a decrease in price. The delta also reflects the probability that the option will expire in-the-money.

**Gamma**Gamma measures the sensitivity of an option's delta to changes in the underlying asset price. It is highest for at-the-money options and decreases as the option moves further in- or out-of-the-money. A high gamma means that the delta of the option can change rapidly, which can be either good or bad depending on market conditions.

**Theta**Theta measures the sensitivity of an option's price to changes in time. It is negative for both calls and puts, indicating that the option's price decreases as the time to expiration decreases. Theta increases as the option gets closer to expiration, reflecting the time decay of the option's value. This is particularly important for traders who sell options, as they are effectively selling time.

**Vega**Vega measures the sensitivity of an option's price to changes in implied volatility. It is positive for both calls and puts, indicating that the option's price increases as implied volatility increases. This is because higher volatility increases the probability of the option expiring in-the-money. Vega is also highest for at-the-money options and decreases as the option moves further in- or out-of-the-money.

**Rho**Rho measures the sensitivity of an option's price to changes in interest rates. It is positive for calls and negative for puts, indicating that the option's price increases as interest rates increase for calls and decreases for puts. Rho is typically less important for traders than the other Greeks, as interest rate changes are usually small and infrequent.

**Higher-order Greeks**Higher-order Greeks are more complex measures that are used to fine-tune trading strategies. They include Charm, Vanna, Vomma, Ultima, and Speed.

**Charm**Charm measures the sensitivity of an option's delta to changes in time. It is a second-order Greek, meaning it measures the rate of change of delta with respect to time. Charm is particularly important for traders who hold options near expiration, as it reflects the accelerated rate of time decay in the final days of an option's life.

**Vanna**Vanna measures the sensitivity of an option's delta to changes in implied volatility. It is a second-order Greek, meaning it measures the rate of change of delta with respect to implied volatility. Vanna is particularly important for traders who hold options with longer expiration dates, as it reflects the impact of changes in volatility over time.

**Vomma**Vomma measures the sensitivity of an option's vega to changes in implied volatility. It is a second-order Greek, meaning it measures the rate of change of vega with respect to changes in implied volatility. Vomma is important for traders who are trying to predict future changes in implied volatility, as it can help them adjust their positions accordingly.

**Ultima**Ultima measures the sensitivity of an option's vega to changes in the underlying asset price. It is a third-order Greek, meaning it measures the rate of change of vega with respect to changes in the underlying asset price. Ultima is important for traders who are trying to anticipate extreme market events, as it reflects the impact of changes in volatility and time decay during such events.

**Speed**Speed measures the sensitivity of an option's gamma to changes in the underlying asset price. It is a third-order Greek, meaning it measures the rate of change of gamma with respect to changes in the underlying asset price. Speed is important for traders who are trying to anticipate sudden market movements, as it reflects the rapid changes in delta that can occur during such movements.

The Greeks are essential tools for options traders, as they provide insight into the various factors that can affect an option's price. Delta, Gamma, Theta, Vega, and Rho are the primary Greeks that traders should be familiar with, while higher-order Greeks such as Charm, Vanna, Vomma, Ultima, and Speed can be used to fine-tune trading strategies. By understanding the Greeks and their applications, traders can make informed decisions and manage risk effectively.

# Technical Indicators

Here are 10 commonly used technical indicators and technical analysis skills when trading stocks,for more info you can unlock them via purchase our trading course/memberships:

**1. Moving averages:**##### This is one of the most basic technical indicators. It helps traders to identify trends in the price of a stock by smoothing out the fluctuations in the price over a given period of time.

**2. Relative strength index (RSI):**This is another popular technical indicator that is used to determine whether a stock is overbought or oversold. It compares the magnitude of recent gains to recent losses in an attempt to determine overbought and oversold conditions.

**3. Bollinger Bands:**This technical indicator consists of a set of three lines that are plotted on top of the price of a stock. It is used to determine the volatility of a stock and to identify potential price breakouts.

**4. Moving average convergence divergence (MACD):**This is a popular technical indicator that is used to identify changes in momentum. It consists of two moving averages that oscillate around a zero line.

**5. Fibonacci retracements:**This technical analysis skill involves using Fibonacci ratios to identify potential levels of support and resistance in a stock's price.

**6. Candlestick charts:**This type of charting is used to identify price patterns in a stock's price. It is based on the premise that the price action of a stock can be predicted by studying the shapes of candlesticks.

**7. Stochastic oscillator:**This is a momentum indicator that compares the closing price of a stock to its price range over a given period of time.

**8. Average directional index (ADX):**This technical indicator is used to determine the strength of a trend in a stock's price.

**9. Relative volatility index (RVI):**This technical indicator is used to measure the direction and magnitude of a stock's volatility.

**10. Ichimoku cloud:**This is a technical indicator that is used to identify potential levels of support and resistance in a stock's price. It is based on five different lines that are plotted on top of the price of a stock.

# Useful links

1. Yahoo finance

2. Barron's

3. Bloomberg

4. Economist

5. Macro Tourists

6.Seeking Alpha

7. Quantopian

8.Zerohedge...

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