Delta hedging?

I understand the purpose of hedging and managing risks, but what’s the purpose of entering a position if you’re just going to hedge/eliminate any movement in the position? Guess I’m just questioning some of the purpose of entering a security position in the first place if youre just gonna hedge - and therefore sacrifice the gains to avoid the losses.

Also, the text on page 209 schweser says, “we know that the delta will increase from the increase in price…” Is this always the case? That is, do increases in stock price always result in a higher delta ? Why?

thanks in advance!

Sometimes you dont want exposure in the underlying, even though you need to have the position, that is why you hedge (unless you hedge in order to gamma scalp, or some other stuff). If you hedge with options you have to adjust all the time cause delta will change with time and volatility.

On a call option, delta will increase when the underlying is moving upwards, cause the real value of the option will increase when it is more in the money, or closer to be in the money. For a put option, it will also increase, cause the real value will go down – Delta might change from -0.5 to – 0.4.

A couple of reasons you would delta hedge:

You want to temporarily adjust your exposure levels, or you have a position you are prohibited from selling, or you are considering tax implications, or you work at a firm that carries and inventory of stocks but doesnt want to take the risk of doing so, or often times you may not be looking for a delta 1 hedge as the book focuses on but may be looking to reduce a bit of the exposure for a period of time and therefore partially hedge and do so in a similar fashion, etc.

Hello BMiller. Option value is comprised by more than delta. Recall that there is “intrinsic value” and “time value”. This is a simplification, but generally speaking, you can hedge the “intrinsic value” by delta hedging. However, the “time value” represents the value of volatility, since option payoffs are assymetric. The “time value” is not hedged by delta. Therefore, even if you delta hedge the position, there is still a component of the option price that is not being hedged.

In general, this “time value” component can contribute to your return in two ways:

  1. It’s a bet on implied volatility. If implied volatility increases, the option value increases also, despite delta hedging.

  2. It’s a bet on realized volatility, because you are long gamma. Consider what happens when the stock price is volatile and you have positive gamma. If stock price goes up, your option delta goes up. So you sell stock to delta hedge. If stock price goes down again, option delta goes down, so you buy stock to delta hedge. If this cycle repeats, you are buying the stock low and selling high repeatedly. So, delta hedging itself can provide you with a positive return if you are long gamma.

Options have many nuances, not just delta!

Thank you everyone for the help. Ohai, couple questions.

1.) It’s been a couple weeks since I looked at this reading so I could easily be mistaken, but I thought if delta increased…that essentially increased the risk to the call short. I thought you bought shares in this case and if delta decreased than you sell. However your second answer states otherwise. Apologize if I’m mistaken.

2.) Is it always the case that if the stock price increases than delta increases and vice versa? Why is that?

Thanks for the help!

. If your’e short the option , you have short delta. , to offset ( delta hedge ) , you will buy equivalent underlying units.Initially you are delta neutral , but short gamma . as the stock price rises your delta will go negative again , so you buy more stock to hedge. If the stock price falls , your delta will go positive, , and you will unload stock to stay neutral .Either way you’re screwed , because you are , fighting the trend. You just hope the market loses volatility .

There is only 1 upside to delta-hedging while short the option. The option buyer is long theta. His option position loses value due to time decay.

As the option seller , you 're short theta ,so your position gains as time goes by. Who supplies this gain? Its your option buyer

As long option holder : long gamma , long theta . Good if stock is volatile , bad as time goes by.

As short option writer : short gamma , short theta , hope volatility is low and collect theta value as time goes by

Another thing to note:

Although it may appear that being delta hedged is profitable for the long option under stock volatility , it is only partly true . the gains due to long gamma are not locked in , because he still has gamma exposure If he gamma hedges , only then he can lock in gains.gamma hedging means taking a different delta position in response to change in the spot price

  1. I was assuming a long call position, or long any other position with positive gamma. If you are short a call, just assume the opposite of what I said - time decay is positive, but if you delta hedge, you lose money under volatile conditions.

  2. This is only true if you are long gamma. Gamma is the second order derivative of option price with respect to stock price. You can see this on a call or put payoff diagram. Both of these graphs are curving upwards. The positive curvature shows positive gamma.