Hedging a call option is the process of mitigating the risk associated with options trading. The concept requires a firm understanding of the risks embedded within an option, which can be evaluated using a Black Scholes pricing model. This mathematical model expresses the theoretical risks engrained in a call option, which are called the Greeks of an option.

## Option Basics

A call option is the right, but not the obligation, to purchase an underlying stock at a specific price on or before a specific date. The price at which the option purchaser can buy the underlying stock is called the strike price, while the date when the option expires is called the expiration date.

## Delta Risk

The most volatile risk associated with a call option is the delta risk. The delta of an option is the theoretical exposure of a call option to the outright direction of the underlying stock. The delta of a call option on a stock is reflected in percentage terms that can be used to calculate the theoretical number of shares. For example, one call option that controls 100 shares of XYZ stock with a delta of 50 percent is exposed to 50 shares of stock. As the price of the underlying stock climbs, the delta of a call option increases; as the price of the underlying stock declines, the delta of the call decreases.

## Hedging the Delta

Hedging the delta of a call option requires either a short sale of the underlying stock or the sale of an option that will offset the delta risk. To hedge using a short sale of stock, an investor would actively mitigate the delta by shorting stock equal to the delta at a specific price. For example, if 1 call option of XYZ stock has a delta of 50 percent, an investor would hedge the delta exposure by shorting 50 shares of XYZ. If the underlying stock price moved higher and the delta increased to 75 percent, the investor would need to short another 25 shares of XYZ to hedge the delta of the call option. An investor could also purchase a put option which has a negative delta, or sell a call option with a different strike price to mitigate the delta of the original call on the XYZ stock.

## Hedging the Vega

The vega of a call option is the exposure of an option to implied volatility. Implied volatility is a market input that gauges expectations of the movement of an underlying stock over a specific period on an annualized basis. To hedge the vega exposure of a call option, an investor needs to sell another option, which would mitigate the exposure of the original call option to implied volatility.

## Summary

Hedging a call option requires mitigating a number of risks, which include the option delta and option vega. Delta risks change based on underlying movements in the stock price, while vega risks fluctuate with changes in implied volatility. To hedge a call option an investor needs to understand and have access to an option pricing model that produces option Greeks.