Interesting video explaining the practical applicability of volatility on options pricing.

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Before we get to answering how IVs affect option price, let me first briefly talk about option price. As you might be aware of, option price (aka option premium) comprises of two components: Intrinsic Value and Extrinsic Value (aka Time Value).

Intrinsic value is the extent to which an option is In-the-Money (ITM). For At-the-Money (ATM) and Out-of-the-Money (OTM) options, intrinsic value is zero. The only variables that impact the intrinsic value of an option are the underlying price and the strike price. Meanwhile, extrinsic value is that portion of the option price that is affected by the time remaining to expiration and volatility. The higher these factors are, the higher will be the extrinsic value, and vice versa. Extrinsic value is calculated as the option price less the intrinsic value.

Keep in mind that ITM options comprise of both intrinsic and extrinsic value, whereas ATM and OTM options comprise of extrinsic value only.

**BASICS OF IMPLIED VOLATILITY:**

As the name suggests, IV is the volatility that is *implied* by option traders based on various factors, such as news, sentiment, demand and supply for an option, future company announcements etc. It is expressed as a percentage and measures the extent to which the underlying is likely to move over a specified period. For instance, if the underlying price is 100 and annualized IV is 20%, it means the 1-standard deviation range of the underlying over the next one year is ±20 points.

IVs tend to rise when there is fear and when the price of a security is declining. Meanwhile, IVs tend to decline when there is optimism and when the price of a security is rising.

**FACTORS THAT INFLUENCE THE PRICE OF AN OPTION:**

There are several models that are used to price options, but the one that is most widely used for the pricing of options (European style) is the Black Scholes model. In this model, the price of a stock option can be computed by inputting the following six variables:

- Current price of the underlying
- Strike price of the option
- Time remaining to expiration of the option contract
- Implied volatility
- Risk-free interest rate
- Dividend

By inputting these six variables in the Black Scholes model, the theoretical price of a call and put option can be computed along with each of the option Greeks. However, when trading options on an exchange, five of these variables are known. The only variable that is unknown is the implied volatility. As the market price of an exchange-traded option is known, you can back solve for IV using the Black Scholes model.

The table below shows the relationship between each of the aforementioned six variables and the price of a stock option (because stock options traded on Indian exchanges are European, I have focused just on European options here):

Call price | Put price | |

Current price of the underlying | + | - |

Strike price | - | + |

Time to expiration | + | + |

Implied Volatility | + | + |

Risk-free interest rate | + | - |

Dividend | - | + |

**HOW IVs AFFECT OPTION PRICE:**

As you can see from the above table, there exists a positive correlation between IV and the price of an option. That is, as IVs increase, the price of a call and a put option also increases. Similarly, as IVs decrease, so does the price of a call and put option. Let us understand this using an example:

Parameters | Inputs |

Underlying Price | 100 |

Strike Price | 98 |

Risk-Free Rate (Annualized) | 10% |

IV (Annualized) | 20% |

Dividend Yield | 0% |

Expiry (in days) | 30 |

When the above values are inputted into the Black Scholes model, the following prices are arrived:

Option | Theoretical Price | Intrinsic Value | Extrinsic Value |

Call | 3.93 | 2.00 | 1.93 |

Put | 1.13 | 0.00 | 1.13 |

Let us now keep each of the above five variables constant and see what happens to the Call and Put price when the IV increases to 25%.

Option | Theoretical Price | Intrinsic Value | Extrinsic Value |

Call | 4.44 | 2.00 | 2.44 |

Put | 1.64 | 0.00 | 1.64 |

Notice that as the IV increases, so does the option price. See that only the extrinsic value of the option is affected and not the intrinsic value. Again, let us now keep each of the above five variables constant and see what happens to the Call and Put price when the IV decreases to 15%.

Option | Theoretical Price | Intrinsic Value | Extrinsic Value |

Call | 3.45 | 2.00 | 1.45 |

Put | 0.65 | 0.00 | 0.65 |

See that as the IV decreases, so does the option price.

On the FYERS School of Stocks, we have spoken quite extensively about IVs and about the Option Greek that measures the impact on option price for a given change in IV.

To read the chapter on IV, click * here*32.

To read the chapter on Vega, click * here*36.