Questions: The Greeks and Hedging Applications in Practice

Question 1

A stock is trading with 20% implied volatility. A trader believes the stock will actually move at 30% realized volatility over the next month. What position should this trader take to express this view?

• A. Short options (short gamma), because the trader wants to collect theta while the stock moves
• B. Long options (long gamma), because when realized vol exceeds implied vol, gamma profits from delta-rebalancing will outpace theta costs
• C. Long the underlying stock to capture the large expected moves
• D. Short the underlying stock to profit from increased volatility

Answer: (B)

Volatility trading is about the spread between implied and realized volatility. If realized vol (30%) exceeds implied vol (20%), options are cheap relative to how much the stock will actually move. A long gamma (long options) position profits from realized moves through delta-rebalancing gains — each time you rebalance the delta hedge, you lock in a small profit because the stock moved more than the hedge assumed. If realized > implied, these rebalancing profits accumulate to more than the theta you pay, making long gamma profitable.

Question 2

A delta-hedged long call position is initiated at market open. By midday, the stock has risen significantly. What must the trader do to restore delta neutrality, and why?

• A. Buy more calls, because the position has gained value and needs to be scaled up
• B. Sell additional shares (or equivalent), because the call's delta has increased as the stock rose, making the position net long
• C. Do nothing — a delta hedge only needs adjustment when time passes, not when price changes
• D. Close the original hedge and re-enter with a new position at the current stock price

Answer: (B)

Delta is not constant — it increases as the underlying rises (this is gamma). When the stock rises, the long call's delta increases, meaning the position is now net long delta relative to the original hedge. To restore delta neutrality, the trader must sell additional shares. This is the cost of gamma: maintaining delta neutrality requires frequent rebalancing, and these trades are how a long gamma position accumulates P&L from actual price movements.

Question 3

A long options position increases in value if implied volatility rises, even if the underlying stock price has not changed.

• T. True
• F. False

Answer: True

This is the vega effect. Vega measures an option's sensitivity to changes in implied volatility — the market's expectation of future price swings. Long options are long vega: if implied vol rises (e.g., due to market uncertainty or an approaching catalyst), option prices increase even with no movement in the underlying. This is why buying options before earnings announcements can be profitable purely from a vega perspective, regardless of which direction the stock moves.

Question 4

Once a position is delta-hedged, the trader has eliminated most meaningful risk and no further risk management is required.

• T. True
• F. False

Answer: False

Delta hedging eliminates only first-order directional risk. It leaves the trader exposed to gamma (delta changing as price moves, requiring costly rebalancing), vega (exposure to changes in implied volatility), theta (time decay eroding option value each day), and rho (sensitivity to interest rate changes). A sophisticated options trader must monitor all five Greeks simultaneously. Delta neutrality is the starting point of risk management, not the end.

Question 5

Explain the fundamental tension between gamma and theta in options trading, and what question a trader must answer to decide whether to be long or short gamma.

Model answer: Long gamma positions (long options) profit from realized price moves through delta-rebalancing gains — each market move lets you rebalance at a profit. But they cost theta: the option loses value each day simply due to the passage of time. Short gamma positions (short options) collect theta but are exposed to large moves that cause rebalancing losses. The central question is whether implied volatility (the vol priced into the option) is higher or lower than the realized volatility that will actually occur. If realized > implied, long gamma wins: gamma profits exceed theta costs. If realized < implied, short gamma wins: time decay collected exceeds rebalancing losses from smaller-than-expected moves.

This is the essence of volatility trading: not a directional bet on the stock but a bet on the spread between two measures of volatility. The Greeks are instruments for measuring and managing this exposure — a language for describing which risks you are taking and which you are hedging.