Introduction

Delta hedging is a crucial concept in options trading and risk management. It involves managing the exposure of an option by trading the underlying asset in the opposite direction. This chapter will provide a comprehensive understanding of delta hedging, including its significance, calculation, and dynamic aspects.

Delta Hedging for an Option

Delta, often referred to as the option’s sensitivity to changes in the underlying asset’s price, is a fundamental concept in option pricing. Delta measures how much an option’s price is expected to change for a one-unit change in the price of the underlying asset. Delta is a key component of option sensitivity measures, also known as the “Greeks”. Delta hedging is the process of using delta to offset and manage the risk associated with holding an option position.

Delta Calculation

The delta of an option can be calculated using the following formula:

$$\text{Delta }(\Delta) = \frac{\text{Change in Option Price}}{\text{Change in Underlying Asset Price}} $$

Delta values typically range from -1 to 1 for individual options. A delta of -1 indicates that the option’s price will move in the opposite direction of the underlying asset, mimicking a short position. A delta of 1 suggests that the option’s price will move in lockstep with the underlying asset, resembling a long position.

Example: Let’s consider a call option with a delta of 0.7. If the underlying asset’s price increases by USD 1, the call option’s price is expected to increase by USD 0.70. This positive delta indicates a bullish stance, as the option benefits from the upward movement of the underlying asset.

Dynamic Aspects of Delta Hedging

Delta is not a constant value; it changes as the price of the underlying asset fluctuates. This dynamic aspect is known as delta sensitivity. To effectively hedge an option position, traders must continuously adjust their hedge positions to maintain a delta-neutral or desired delta exposure.

For example, if you hold a call option with a delta of 0.7 and the underlying asset’s price increases, the delta of the call option may increase to 0.8. To maintain a delta-neutral position, you would sell an amount of the underlying asset equivalent to the increased delta.

Delta hedging allows traders to manage risk and volatility by ensuring that changes in the option’s value are offset by changes in the underlying asset’s value.