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Option Greeks

Module Units

# Delta Hedging

Delta hedging is an option trading strategy that aims to reduce, or hedge, the directional risk associated with price movements in the underlying asset.

For e.g.: Imagine I hold 500 shares of XYZ Ltd @ ₹100. When the stock price will go up, I’ll gain and when the stock price will go down, I’ll lose.

To protect myself from the downside directional risk, I will try to offset my risk by creating a negative Delta (i.e. by taking a bearish position). Suppose, a call option of strike 100 is trading at ₹3 and has a Delta of 0.55.

I want to sell 300 call options. So, now Delta of my option position is-

300* (-0.55) =-165 (Delta is negative when we sell call option)

Now, when the stock price goes up by ₹20, profit on the stock position is (500*20)= ₹10000/-

Whereas loss on call option is (0.55*20*300)= ₹3300/-

So the net profit will be 10000+900-3300= ₹7600/-

If the stock price goes down by ₹20, loss on the stock will be (500*20)= ₹10000/-

So the net loss will be 10000-900= ₹9100/-

Here we can see that I have hedged myself partially against the downward price risk, where instead of losing ₹10000/- , I lost ₹9100/-. This is called Delta hedging, where I try to take advantage of my fear. This has just partially helped me cover my risk.

However, we can sell more call options to offset the risk to a larger extent or create a zero Delta position. This is called Delta neutral. A portfolio is just momentarily Delta neutral because the Gamma and Delta of an option keeps on changing. So we have to keep on adjusting Delta with different and continuous trades. We shall learn more about it in upcoming chapters.

Question to ponder over?

Have you tried to find out the Delta of an option when the volatility is 10,000%?

Answer: All Delta turns to 1 in such extreme situations.

AMAZING FACT

There is yet another way to interpret Delta.

“Delta is the probability of the option contract being in-the-money at expiration”. This is not a theoretical definition of Delta but has helped me to understand more about its behavior.

For example,

### Q) Why for ITM options, for the same strike price, the longer days to expiration, Delta is lower?

A) More time to move means less likelihood of the option still being in-the-money at expiration; this translates into a smaller Delta.

### Q) Why for OTM options, for the same strike price, the longer days to expiration, the Delta is higher?

A) If you’re buying OTM options, you need time for the stock to move up to the strike price. In other words, there’s a much higher probability of the underlying finishing ITM for the (longer to expiration) option than for the (nearer to expiration) option; Delta reflects that probability.