How Can I Calculate the Delta Adjusted Notional Value?

The delta adjusted notional value is used to show the value of an option. This is different from most other derivatives, which use gross notional value or, in the case of interest rate derivatives, a 10-year bond equivalent value. Investors can calculate the delta-adjusted notional value of a portfolio by adding the options' weighted deltas together.

The delta adjusted notional value quantifies changes to a portfolio's value if it was comprised of underlying equity positions, instead of options contracts. For example, a stock is trading at $70 and the delta of the related call option is 0.8. In this case, the value of the weighted delta for the option is $56 ($70 x 0.80).

Explaining Delta

In derivatives trading terminology, "delta" refers to the sensitivity of the derivative price to changes in the price of the underlying asset. For example, an investor purchases 20 call option contracts on a stock. If the stock goes up by 100% but the value of the contracts only increases by 75%, the delta for the options will be 0.75.

Call option deltas are positive, while put option deltas are negative.

Delta measures the change in option premium generated by a change in the underlying security. Delta's value ranges from -100 to 0 for puts and 0 to 100 for calls (multiplied by 100 to move the decimal). Puts generate negative delta because they have a negative relationship to the underlying security i.e. put prices fall when the underlying rises and vice versa.

On the other hand, call options generate a positive relationship with the underlying security's price. So, if the underlying goes higher so does the call premium, as long as other variables that include implied volatility and time remaining until expiration remain constant. Conversely, if the underlying price falls, the call premium will also fall, as long as other variables remain constant.

An at-the-money option generates a delta of approximately 50, meaning the option premium will rise or fall by one-half point in reaction to a one-point move up or down in the underlying security. For example, an at-the-money wheat call option has a delta of 0.5, and wheat rallies 10 cents. The premium will increase by approximately 5 cents (0.5 x 10 = 5), or $250 (each cent in premium is worth $50).

Explaining Notional Value and Delta Adjusted Exposure

Notional value is the total amount of an option contract's underlying asset at its spot price. This term differentiates between the amount of money invested and the amount associated with the whole transaction.

Notional value is calculated by multiplying the units in one contract by the spot price. This is easy to demonstrate with an indexed futures contract. For example, an investor or trader wants to buy one gold futures contract. The contract will cost the buyer 100 troy ounces of gold. If the gold futures contract is trading at $1,300, it then has a notional value of $130,000 (1,300 x 100).

Options have a delta-dependent sensitivity so their notional value is not as straightforward as an indexed futures contract. Instead, the option's notional value needs to be adjusted based on the sum of exposures within the portfolio. The easiest way to calculate this delta adjusted notional value is to calculate the delta for each individual option and add them together.

Notional value is useful in determining exposure levels in interest rate swaps, total return swaps, equity options, foreign currency exchange derivatives, and exchange traded funds (ETFs).