When trading options for profit, a rule of thumb is to sell options when the Implied Volatility is high, and buy options when the IV is lower.

But do you know what market volatility represents in general and how differences in volatility can affect options prices?

In this article, we'll try to provide an in-depth explanation of what is market volatility, because a solid understanding of volatility is important to trading options for consistent income. We also share the differences between Historical Volatility (HV) and Implied Volatility (IV).

Contents

## What Is Volatility?

Volatility is the fluctuations and dispersion of data points, and we can use it to indicate the fluctuation of stock prices in the market. Mathematically speaking, volatility is the deviation of the data dispersion.

Thinkorswim shares various market volatility data in the Options Statistics. The most important of them all are Historical Volatility (HV) and Implied Volatility (IV).

## What Are the Differences Between HV and IV?

HV is the past volatility of the underlying, while IV is forward-looking for the theoretically expected future moves.

## How to Calculate Historical Volatility?

In case you have left your high school years long behind you, we’ll take it step by step through the process of calculating volatility.

Let us use a recent data set of closing prices of BABA to calculate the volatility. Such backward-looking determination of volatility is commonly known as Historical Volatility (HV).

- We calculate the mean of 10 recent BABA closing prices by dividing the sum by the number of data points. So in the 10 trading days, BABA prices moved around a mean value of $157.35.
- Then we calculate the deviation of each data point from the mean.
- We square each difference to find the variance.
- The sum of the variances is 1089.5288, so the mean variance is around 108.95288.
- Then we calculate the square root of the mean variance to get the standard deviation.

Trading Days | Close | Deviation | Variance |
---|---|---|---|

10/4 | 139.63 | -17.72 | 313.9984 |

10/5 | 143.14 | -14.21 | 201.9241 |

10/6 | 144.10 | -13.25 | 175.5625 |

10/7 | 156.00 | -1.35 | 1.8225 |

10/8 | 161.52 | 4.17 | 17.3889 |

10/11 | 163.95 | 6.60 | 43.5600 |

10/12 | 163.00 | 5.65 | 31.9225 |

10/13 | 167.40 | 10.05 | 101.0025 |

10/14 | 166.78 | 9.43 | 88.9249 |

10/15 | 168.00 | 10.65 | 113.4225 |

Mean close | 157.35 | Mean variance | 108.95288 |

The square root of the mean variance is $10.44., which is the standard deviation.

The famous Gaussian normal distribution describes the random outcomes of a data set in our real world where 50% of all outcomes fall on the left side of the mean and the other 50% on the right side of the mean.

1 standard deviation (σ) on either side of the mean mark the range in which 68% of all fluctuations of the given process would fall. While +/-2σ mark the probability of 95%.

So in the last 10 trading days, BABA’s closing prices fell with a 68% probability between $146.91 and $167.79.

If we convert the standard deviation into a percentage, the Historical Volatility (HV) of the last 10 days is 6.63%.

If BABA’s closing prices fluctuated more with a bigger standard deviation, its HV would be high.

If the closing prices fluctuated less with a smaller standard deviation, the HV would be low.

## How Does IV Affect Options Prices?

Option prices are a function of IV, which is the expected move of the underlying. IV is also calculated from the options pricing model.

Options provide us with rights to sell or buy an asset at a certain price. Such right is inherently associated with a certain cash inflow or outflow and has to be discounted by interest and dividends.

The famous Black Scholes option pricing model was rewarded with a Nobel Prize and provides us with a set of elaborate formulas that allows us to calculate Call and Put option prices. It uses a log-normal distribution model because the price can't go lower than 0, and has a long tail as prices approach infinity.

Call and Put option prices are calculated as follows:

- σ = IV
- δ = dividends
- S = stock price
- K = strike price
- r = risk-free interest rate
- T = time to expiration (year)
- N = normal distribution
- N(d
_{1}) = the expected value of cash/stock inflow if option expires ITM - N(d
_{2}) = the probability the option expires ITM

Let us calculate the value of AAPL $150 ATM Call option that expires in 39 days. We can use the Option Chain from Thinkorswim to validate our calculations.

- σ = 22.38%
- S = $151.28
- K = $150
- r = 0.04%
- T = 39/365 = 0.106849
- d
_{1}= 0.153314 - d
_{2}= 0.080158 - N(d
_{1}) = 0.56 - N(d
_{2}) = 0.53 - C(39) = $5.05

As you may notice, the calculated option price of $5.05 is between the bid price of $4.90 and the ask price of $5.15 shown in Thinkorswim.

So IV and option prices, which comes first?

The Market Maker collects all order flows from brokers, such as TD Ameritrade, Firstrade, Interactive Brokers, then derive ATM option prices based on the increase and decrease of supply and demand for Put and Call options as well as the underlying itself.

Once, you have the ATM options price, you can calculate the IV based on the option pricing model. We have to do some trial and error to approximate the IV value to match the AAPL Call price.

IV | Call Prices |
---|---|

10% | 2.67 |

30% | 6.56 |

50% | 10.47 |

70% | 14.37 |

90% | 18.27 |

We see the IV between 10%-30% give results closest to $5.05.

We interpolate the IV between 10% and 30% to find the correct IV as 22.30%, which is the market expectation of future price moves.

Now you have a better understanding of how volatility and options prices relate to each other. You can use the Options Scanner to find high probability Iron Condors to sell during high IV, and buy to close at low IV.

Nick剛才發現選擇權分析器真的可以快速找到高IV的股票清單

這樣我就可以找到更多的Iron Condor交易機會了

謝謝

Tony沒錯

只要了解波動率對期權價值的關係就可以交易勒式和鐵兀鷹

Dennis謝謝分享IV和HV的差別，讓我交易選擇權更有信心了

TonyHV和IV雖然都是分析波動的數據

一個是過去的標準差

一個是預估的未來標準差