# Delta Neutral Options Trading

## Introduction

In order to understand Delta Neutral options trading, a trader should first be familiar with the Options Greeks of Delta and Gamma and understand the interaction between these concepts and volatility and time decay.

Definition: A Delta Neutral options position is one that is neutral in terms of relatively small movements in the price of the underlying asset (stock, commodity, currency).

## A simple Delta neutral trade

One of the simplest possible examples of a Delta neutral options position is the so-called long straddle, which consists of buying an ATM long call option and an ATM long put option. Since the Delta of the long calls is 0.5 and the Delta of the long puts is -0.5, it means that for small movements in the price of the underlying the effect on the net value of the options position is

equal to zero.

Fig. 8.31(a) below is an example of a long straddle.

What becomes immediately apparent from the chart above is that this Delta neutrality only works for very small price movements. As soon as there is a significant movement in the price of the underlying asset in one or the other direction, the Delta of that side of the position starts increasing, which means the net Delta of the position will no longer be neutral.

This is why some professional traders something called Dynamic Delta Hedging. They do this by balancing the Delta position of the trade on a continuous basis, e.g. daily.

## Example

Let us assume the trade is opened by buying 100 ATM calls with a Delta of 0.5 and 100 ATM put options with a Delta of -0.5. The net Delta of this position = 100 x 0.5 + 100 x -0.5 = 50 – 50 = 0.

If, after a certain period of time the price of the underlying asset increases to the extent that the Delta of the call options increases to 0.6 and the Delta of the put options decreases to -0.4. The net Delta of the trade will become 100 x 0.6 + 100 x -0.4 = 60 – 40 = 20.

To balance the Delta of the trade, a Delta neutral trader would buy another 50 put options with a Delta of -0.4. The net Delta of the position would then again become 100 x 0.6 + 150 x -0.4 = 60 – 60, which is once again equal to 0.

## Purpose of Delta neutral options trading

The long straddle pictured in Fig. 8.31(a) above is a good example of a position where the trader will profit from volatility, since this trade will be profitable whether the price of the underlying breaks out sharply to the upside or the downside.

The reverse of this trade, the Short Straddle, pictured below in Fig. 8.31(b), is an example of a Delta neutral trade benefiting from time decay. If the price of the underlying remains stagnant or within a relatively small range, time decay will eat away at the value of the sold options and eventually cause them to expire worthless – in which case the seller will keep the full premium income.