Derivatives Essentials by Aron Gottesman

Author:Aron Gottesman
Language: eng
Format: epub
ISBN: 9781119163565
Publisher: Wiley
Published: 2016-06-20T00:00:00+00:00

9.3.2 Why Delta of an option position varies across the underlying asset price

The Delta of an option position varies across the underlying asset price as the long position to an option is not obligated to transact. Therefore:

When the option is deep-OTM, it doesn't matter very much that the underlying asset price has changed, as there is low likelihood the transaction will occur. Hence, there is little value sensitivity and Delta is negligible.

When the option is deep-ITM, changes in the underlying asset price impact the counterparties, as there is high likelihood that the transaction will occur. The option positions are fully sensitive and Delta is 1 for the purchasing counterparty and −1 for the selling counterparty.

When the option is near-the-money, changes in the underlying asset price are somewhat impactful, as there is some likelihood that the transaction will occur. The option positions are therefore somewhat sensitive, and Delta will be between 0 and 1 for the purchasing counterparty and between 0 and −1 for the selling counterparty.

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