Options Hedging

The risks associated with options transactions can be significant but there are a number of ways a trader can hedge these risks.  The main risks experienced by options traders are, directional risks, implied volatility risks, second derivative or gamma risk, time erosions risk, and interest rate risk.

Directional Risk

Most investors view a call option as a vehicle to capture directional upside of a security.  In fact a call option has an imbedded risk which changes with the price of the underlying security.  As the value of a call option changes, the theoretical directional risk known as “the delta” changes.  The delta of an option tells the investor how much the value of their option will change with a notional change in the price of the security.

optioncalldelta

For example, let’s assume the delta of an Apple $500 Call Option that expires in 30 days is 50%, and that the current price of Apple stock is $500.  A delta of 50% on one call option contract would expose the owner of the options to 50 shares of Apple stock.  This is calculated by multiplying the delta by the total number of shares in each contract (100 shares * 50%). For every dollar Apple moves above $500, the value of the call option will increase by $50 dollars.

If an investor wants to hedge their directional risk they can attempt to hedge their delta with shares of a stock (or futures if the security is a commodity), by shorting the underlying security with number of shares calculated as the delta.  This process is referred to as delta hedging, and it is a repetitive process, which changes as the underlying security price changes.  As the price of the underlying security changes, so does the delta.

For example, (using the Apple Call $500 strike option) if an investor sold 50 shares at $500 dollars the delta of the trade which consists of a long $500 call and short 50 shares of Apple stock would create a delta neutral position.  If the price of Apple increased to $550 a share, the long call position would show an increased delta (say 60%) which would create a delta position of +10 shares of Apple stock (60 shares long from the call and -50 from the short Apple stock position).  If on the other hand the stock price initially declined from $500 to $450, the investor would hold a net short position as the delta of the Apple $500 call would decline to 40%, giving the investor a delta of 40 shares while holding a short position of 50 shares for an aggregate short 10 share position.

Implied Volatility Risk

Options positions are exposed to implied volatility risk known as vega risk.  Long options positions will generally hold long vega risk meaning the value of the option increases as implied volatility increases. Implied volatility is the markets estimate of how much options traders believe a security will move over the course of a specific period on an annualize basis.

To hedge vega risk, an options trader will need to either buy or sell options to offset the risk.  With long options positions a trader will need to hedge by selling options. For short vega positions a trader will need to purchase options to hedge their vega risk.

One issue associate with hedging vega risk is strike map risk.  For example, if a trader purchase an Apple $500 call and then hedges the vega when the price of Apple is $600, with an at the money call option, if the price moves back to $500 the $600 call will not offset the vega from the $500 call.

When hedging vega risk with a different strike price, the investor needs to match up the volume of vega by determining the amount to offset.  For example, a $500 strike on Apple when the price is $600 could have a vega exposure of 2,000 per 1%, and that will need to be offset with a different strike price.  The total number of contracts will likely not be the same, which will need to be adjusted by the trader.

Gamma Risk

Gamma risk is a second derivative risk and it measures the change in the delta of an option relative to the change in the underlying price of the security.  For example, on a long call position, as the price of the underlying security rises, the delta rises.  This change is computed by the option gamma.

Traders need to measure gamma as large moves in an underlying security could change the risks they hold in options positions dramatically.  Generally short gamma positions are more worrisome than long gamma positions.  With long gamma positions the investors is always on the correct side of the trade.  If the underlying security moves higher the option position will get longer and longer.  If the underlying security moves lower the gamma will make the investor shorter and shorter.

Negative gamma positions put the investor on the wrong side of the trade.  As the underlying security moves higher the investor becomes shorter and shorter and the reverse is true as the underlying security moves lower.

To hedge gamma exposure, options traders need to purchase or sell options to offset the positive or negative gamma they have.  Strike risk is also an issue with hedging gamma, as gamma shows the most strength for the closest strike prices.

Theta Risk

Time decay risk can be substantial given that nearly 70% of the options that are written expire worthless.  The reason this is the case is that generally implied volatility is higher than actual historical volatility.  If the implied volatility is higher than the actual historical volatility, the chance of an option settling in the money is low.

To hedge time decay, an investor needs to sell options to offset long options positions that are subject to time erosion.  Time decay is not a linear concept, it erodes in a geometrical way were erosion increases as the expiration date moves closer.

Interest Rate Risks

Option interest rate risk is usually very small.  To hedge exposure an investor needs to sell interest rate futures contracts or cash bond and notes.  The risk is usually too small to hedge, but an option that is far in the money can have a future value that is large enough to hedge the interest rate exposure.

Adam

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Adam is an experienced financial trader who writes about Forex trading, binary options, technical analysis and more.

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