Introduction

Delta hedging is a fundamental concept in risk management for options. It involves continuously adjusting a portfolio’s position to maintain a neutral or desired level of market exposure. In this chapter, we will explore the dynamic aspects of delta hedging and distinguish between dynamic hedging and hedge-and-forget strategies. Understanding these dynamics is crucial for effectively managing option positions.

Dynamic Delta Hedging

Delta, often referred to as the hedge ratio, represents the sensitivity of an option’s price to changes in the underlying asset’s price. It measures how much an option’s price is expected to change for a unit change in the underlying asset’s price. Delta can be positive or negative depending on whether the option is a call or put.

To dynamically hedge an option position, traders continuously adjust the position’s delta to keep it neutral or aligned with their risk tolerance. This involves buying or selling the underlying asset in response to price movements. Here’s how dynamic delta hedging works:

• Example: Consider a trader who is long (owns) 10 call options with a delta of 0.6 each. This means the position has a net positive delta of 6 (10 contracts $\times$ 0.6 delta each), indicating that it benefits from a rise in the underlying asset’s price. To maintain a delta-neutral position, the trader would need to sell 6 units of the underlying asset for every point increase in its price.

Hedge-and-Forget Strategies

In contrast, a hedge-and-forget strategy involves establishing a hedge at the outset of an options position and then leaving it unchanged until expiration. This strategy doesn’t involve continuous adjustments based on delta changes.

• Example: A trader buys 10 put options with a delta of -0.4 each to protect their portfolio from a potential market downturn. The trader doesn’t make any further adjustments to the hedge throughout the option’s lifespan.

Dynamic Hedging Vs Hedge-and-Forget Strategies

• Risk Management: Dynamic hedging actively manages risk by adjusting positions in response to market changes. Hedge-and-forget strategies are simpler but may leave the portfolio exposed to unanticipated risks.

• Cost and Complexity: Dynamic hedging can be more costly due to transaction fees and requires continuous monitoring. Hedge-and-forget strategies are cost-effective and straightforward.

• Effectiveness: Dynamic hedging is highly effective in maintaining a desired level of market exposure. Hedge-and-forget strategies provide a basic level of protection but may not respond adequately to evolving market conditions.