Options Hedging


Traders are generally risk-averse. To minimise the risk, the trades are often covered with additional trades in order to hedge the risk. While hedging, traders need to do a risk-reward tradeoff. The hedge reduces the risks, but it also reduces the potential gains. Traders often try to perform a perfect hedge in case an arbitrage opportunity shows up. With a perfect hedge, the hedge is 100% inversely correlated to the asset. This course will cover two types of hedging:

  • Option hedging
    Option traders are exposed to different kinds of risk. These risks will be identified. Examples will be given for hedging using options.
  • ETF hedging
    ETF traders also hedge their trades. Basic ETFs are pretty straightforward and it is easy to explain how ETF traders make use of arbitrage opportunities.

Table of Contents

Option hedging

A basic way of hedging using options is by covering a long- or short position in an asset. In case the trader has a long position in an asset, he has a unlimited potential gain (since theoretically the price can increase infinitely), but the asset could also go to zero. In that case, the trader would lose everything. However, If the trader buys a put option, it would give the trader the right to sell his assets at the strike price.

Example: A Trader take a position in stock ABC for a price of $50. He buys a put option for $2, with a strike price of $45. In case the stock price increases to $60, then the trader would not exercise his put option and his unrealised (realised when the trade is closed) gain would be Quicklatex. Com 45e6f7d6bde29a90c1e0f53c21761c22 l3 $8. In case the stock price decreases to $40, then the trader could exercise his put option. Without exercising his put option, his unrealised profit/loss would be Quicklatex. Com 7d5d746f18948024f6d5580b271efba9 l3 -$12. If the trader closes his position and exercises his put option, than his realised profit/loss would reduce to Quicklatex. Com 55988e2a8ccd3275ccc2e85ee20ebb16 l3 -$7.

Traders may decide to make their portfolio delta-neutral. Delta-neutral is a portfolio strategy in which multiple assets are combined with positive and negative delta, so that the portfolio is not sensitive for price changes in the underlying asset(s). Option traders use delta-neutral strategies to either profit from movement in the implied volatility, the time decay of options or to hedge a portfolio.

Example:
A trader sells 50 call options that mature in 3 months and have an exercise price of 120 euro. Furthermore, Quicklatex. Com 1ffec6c3d787ec73fbe912f8b7e800e3 l3. How does the traders achieve a delta neutral position?

Answer:
Step 1: The trader has to calculate Quicklatex. Com 09d70b66513deeda0838cc2d61746b25 l3 and Quicklatex. Com d4fcaa62d43f25a252b1bcab04f30202 l3 in order to compute Quicklatex. Com f6a2673272e7a53d82badab7bf249c4e l3.

(1)   Quicklatex. Com fb8caf1131924e423cf53847b6793d7b l3

(2)   Quicklatex. Com 7ba2e3260045aa57cb338d465ffb4878 l3

Step 2: Calculate Quicklatex. Com f6a2673272e7a53d82badab7bf249c4e l3.

(3)   Quicklatex. Com a514ad4b751363a37372e4718e45e614 l3

(4)   Quicklatex. Com 733e71bcf5a60bff9571fd1a7166a77f l3

(5)   Quicklatex. Com a9b563ddd9b33f72ac0d8898bb8c3248 l3

Step 3: Determine the delta of the option.

(6)   Quicklatex. Com 46b5d0545bd28309777b7ca35fe58380 l3

Step 4: Conclude the strategy
To hedge the selling of 50 call options with a delta-neutral strategy, the trader has to buy Quicklatex. Com ad90fcc275de3aac16d7ecc9b06c578a l341.75 stocks of the underlying asset.

Delta-hedging is a dynamic hedging strategy. The replicating portfolio must be managed actively, because the gamma-exposure of your portfolio causes the delta to change due to the fluctuating stock price and because the time to maturity becomes smaller. This can lead to large hedging errors if the replicating portfolio is not adjusted often enough.

Are traders in reality always risk neutral? Absolutely not. It also differs per firm how they handle the positions that they are building. Based on certain market characteristics, a traders wants to be rather long or short on certain areas of the implied volatility curve. For example, if some important news comes out that might impact the market heavily, a traders wants to be rater long in the ATM (At The Money) options, since this is where the trader can earn most on Gammas (see the previous lecture). If a traders’s position in the options are net Gamma long, then the trader will earn on his/ her position when the underlying starts to move, because long deltas will build up in the portfolio if the underlying moves up and short deltas will build up in the portfolio if the underlying moves down. The trader will earn money on these deltas, because it’s off course profitable if for example the underlying

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