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 $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 -$12. If the trader closes his position and exercises his put option, than his realised profit/loss would reduce to -$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, . How does the traders achieve a delta neutral position?*Answer*: **Step 1**: The trader has to calculate and in order to compute .

(1)

(2)

**Step 2**: Calculate .

(3)

(4)

(5)

**Step 3**: Determine the delta of the option.

(6)

**Step 4**: Conclude the strategy

To hedge the selling of 50 call options with a delta-neutral strategy, the trader has to buy 41.75 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