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I understand what an option is and I know that a market maker always publishes a bid and an ask price for which it will buy or sell options on the exchange. Now I heard that market makers always hedge their positions by buying or selling the underlying assets so that whether the market goes up or down, they always make money. And this I don't understand.

So let's go with an example. On the stock exchange stock X is freely traded. If I am a market maker for options I would publish prices for buying and selling options. Let's say I published an ask price for a call option and somebody buys the call option. If I would not have a call option I would write one. So let's assume the numbers are as follows:

  • Stock X costs $100 on the exchange at time of writing the option
  • option strike price is $150
  • option expiration date is 3 months from now
  • I write/sell the option for $5

To hedge my option position I now buy the underlying asset X for $100. That means there are three possible situations:

  1. At the time of the expiration date, stock X is worth $160 (above the strike price). I sell the stock X (which I bought for $100) for $150 to the holder of the option I wrote. That means I made $5 for the option plus $50 for the price increase of X (minus the transaction costs).
  2. At the time of the expiration date, stock X is worth $125 (below the strike price but above the price at which I bought stock X). The holder of the option does not execute the option contract. So I sell stock X for $125 on the market. That means I made $5 for the option, plus $25 for the price increase of X (minus the transaction costs).
  3. At the time of the expiration date, stock X is worth $50 (below the strike price and below the price at which I bought stock X). I sell the stock X (which I bought for $100) for $50 on the market. That means I made $5 for the option minus $50 for the price decrease of X (minus the transaction costs). So in this case I actually lost money.

In case 3 above I could of course also sell the stock X if it drops below $95 and buy again if it increases above $95 again. If stock X is then $50 at the expiration date I would make no profit at all (the $5 I sold the option for is compensated by the $5 loss I made on stock X). If the price of stock X would actually pass the $95 up and down multiple times finally ending at $50, I would actually make a loss because of the transaction costs and the spread I constantly pay for buying and selling stock X at $95.

So what am I missing here? Where do I go wrong in the example I wrote? How do option market makers actually hedge their positions so that they do not have a price risk?

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    "market makers always hedge their positions by buying or selling the underlying assets" - this is not true. – D Stanley Aug 10 '17 at 19:54
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    @NathanL - Why is it not related to personal finance? I this hedging is at all possible, I might give a go at writing options and hedging them to improve my personal financial situation (i.e.: make money) – kramer65 Aug 10 '17 at 19:57
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    @DStanley - Can you explain why that is not true? Why would or wouldn't a market maker hedge it's option positions? – kramer65 Aug 10 '17 at 19:57
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    There are other ways to hedge price risk other than buying the underlying. It's not uncommon but it doesn't "always" happen. – D Stanley Aug 10 '17 at 19:58
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    You can buy/sell other options to reduce price risk, or be long a different underlying, or have a natural long/short position (e.g. refiners are naturally short crude oil and naturally long products like gasoline) – D Stanley Aug 10 '17 at 20:18
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How do option market makers actually hedge their positions so that they do not have a price risk?

You cannot complete hedge away price risk of a sold call simply by buying the underlying and waiting. As the price of the underlying decreases, the "Delta" (price risk) decreases, so as the underlying decreases, you would gradually sell some of the underlying to reduce your price risk from the underlying to match the price risk of the option.

The opposite is true as well - as the price of the underlying increases, you'd buy more of the underlying to maintain a "delta neutral" position.

If you want to employ this strategy, first you need to fully understand what "delta" is and how to calculate it. Then you can use delta hedging to reduce your price risk.

  • Thanks for your answer! I read a couple hours about the delta and that makes sense now. So as the price of the underying rises, the option can be hedged by taking a position in the underlying equal to the delta of the option. Instead of doing this, could I also hedge the risk by buying or selling another option on the same underlying asset? – kramer65 Aug 11 '17 at 7:36
  • Sure - you could but/sell options on different strikes or maturities. Note that those aren't perfect hedges either - the deltas may move differently. – D Stanley Aug 11 '17 at 15:25
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How do option market makers actually hedge their positions so that they do not have a price risk?

Greeks

Options have different "greeks", as some people like to say, as they follow greek letters (spot the exception). They sum up some of the various types risks that you have in an option position (or to some extent, a stock position).

  • Delta - How much the price of the option changes in the market when the price of the underlying security changes.
  • Gamma - How much the delta of the option changes when the price of the underlying security changes.
  • Vega - How much the price of the option changes in response to a change in the volatility of the underlying security changes.
  • Theta - How much the price of the option changes as time passes to expiration.

Delta

The biggest market risk is delta risk, so market makers try to keep their positions delta neutral. Delta not only indicates how much the value of the option will change in line with a change in the underlying security, but it also represents the probability that an option will expire in the money. If an option is deeply in the money such as a low priced call, it will have a delta closer to 100. However if the option is out of the money such as a high priced call, there is a high chance that the option will expire worthless, so will have a delta closer to zero. Importantly, this delta changes over the lifetime of the option. If for example, an option that was deeply in the money goes out-of the money (because the underlying dropped in price), then the delta on that option will change.

Delta also applies to underlying stock. A hundred shares (long) of the underlying has a delta of 100; while a hundred shares (short) of the underlying has a delta of -100.

Hedging

The options market maker will try to ensure his positions have low risk so will try to neutralise the greeks by buying options or stock reduce the size of the risks. Probably most frequently buying or selling stock to neutralise the delta of his option positions.

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Buying the underlying asset will not completely hedge you, only what lies above 155 dollars (strike + price of option) - you still have the risk of losing everything but 5.

You have a maximum earnings-potential of 55 dollars (strike of 150 - investment of 100 + option of 5) but you have a risk of losing 95$ (investment of 100 - option of 5).

Say chance of winning everything or losing everything is 50-50, your expected outcome is 0.5 x -95 + 0.5 x 55 = -20$. Is this a great investment?

Sure you don't know your odds - otherwise it would be a sure thing. You shouldn't sell the call option if you do not expect prices to go up - but in that case - why not just buy the underlying alone?

Speculating in options is a dangerous game with infinite earnings-potential but also infinite loss potential. (Consider selling a call option and not buying the underlying and the price goes from 100 to 1.000.000.000).

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Let's consider that transaction cost is 0(zero) for calculation.
In the scenario you have stated, maximum profit that could be made is 55$, however risk is unlimited.

Hedging can also be used to limit your losses, let's consider this scenario.
Stock ABC trading @ 100$, I'll buy the stock ABC @ 100$ and buy a put option of ABC @ strike price 90$ for a premium of 5$ with an expiration date of 1 month.
Possible outcomes

  1. Expiry @ 150$ i.e. Deep out of the money (with regard to my option contract) - here I make a profit of 45$ (unlimited profit, based on the price @ expiry, if price reaches 200$, profit will be 95$).
  2. Expiry @ 90$ i.e. At the money - here I end up in loss of 15$, this is the maximum loss I can incur.
  3. Expiry @ 50$ i.e. Deep in the money - even here I end up in loss of 15$.
  4. Expiry @ 100$ - here I end up in loss of 5$.

I end up in a loss in 3 out of 4 scenarios, however my loss is limited to 15$, whereas profit is unlimited.

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