Welcome to the Sharpe Two Friday Option Quiz!

Every Friday, we will challenge you with a mix of fundamental theory and real-world questions to test your options trading knowledge and get you one step closer to mastery.

Ideal for those keen to hone their skills on the art of options or prepping for a job interview, our quiz offers a concise yet insightful way to test and expand your understanding. You will find three sections:

**Theoretical Value:**Sharpen your grasp of options theory and its foundational principles.**Capital Concepts:**Apply theoretical knowledge through the lens of a retail trader navigating real market events.**7-Figures Bonus:**Step into the shoes of a professional trader and tackle complex, high-stakes scenarios on the trading desk.

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**Theoretical Value**

Which model is typically used for pricing options on dividend-paying stocks, and how does it differ from the Black-Scholes model?

Explain how Gamma and Vega interact in a portfolio consisting of long options positions with about three months before expiry. What are the implications for a trader with a long 20-delta strangle during periods of high market volatility and already declining from their peaks? How would it change if it was three weeks before expiry?

## Capital Concepts

You hold a series of long call options on TLT (iShares 20+ Year Treasury Bond ETF). The Federal Reserve unexpectedly announced a significant interest rate hike. Describe the immediate effect on your options' value and its rationale.

As a retail trader, you have executed a short volatility strategy by selling straddles on SPY (SPDR S&P 500 ETF Trust). One straddle expires in 20 days, and another in 50 days. Suddenly, the market experiences a steepening of the implied volatility skew. How does this affect your position, and what adjustments, if any, should you consider?

## 7-Figures Bonus

You're a trader at an options desk, and a client seeks to hedge interest rate risk in their bond portfolio. They're interested in an exotic derivative involving a swap of bonds, potentially linked to the performance of a bond index or specific credit events. Describe the structure of such a derivative, including the key risks and how you would manage them. Consider the implications of recent changes in interest rates and credit spreads in your explanation.

## Theoretical Value

### Question 1

The model typically used for pricing options on dividend-paying stocks is the Black-Scholes-Merton model, a modification of the original Black-Scholes model. The key difference is the inclusion of dividends; the Black-Scholes-Merton model discounts the stock price by the present value of expected dividends during the option's life, reflecting the impact of dividend payments on option pricing.

### Question 2

**The second question will be divided into three parts to clarify the explanations.**

**Part 1: Gamma and Vega Interaction in a Long Options Portfolio (3 Months to Expiry)**

**Gamma:**Gamma measures the rate of change in an option's delta for a unit change in the underlying asset's price. In a long options position, a positive gamma indicates that the delta increases as the underlying price moves favorably, making the position more sensitive to further price changes in the same direction. This effect is generally more pronounced in options closer to expiration, but with three months to expiry, gamma's impact is moderate yet still significant.**Vega:**Vega measures the sensitivity of an option's price to changes in the underlying asset's implied volatility. In long options positions, positive vega means that the value of the options increases as volatility rises. With three months to expiry, the options have substantial vega, making them sensitive to changes in market volatility.

**Part 2: Implications for a Trader with a Long 20 Delta Strangle (High Volatility, Declining from Peaks)**

**In High but Declining Volatility:**The trader's long strangle will initially benefit from high volatility due to positive vega. However, as volatility starts declining from its peak, the value of both the call and put options may decrease. The long strangle is most sensitive to this decline in volatility because of its high vega exposure.**Gamma Effects:**With three months to expiry, the gamma effect is present but not as sharp as it would be closer to expiration. This means that while the deltas of the call and put options will adjust as the underlying asset's price moves, these adjustments will be less dramatic. The strangle will benefit from large swings in the underlying price, but not as much as it would closer to expiration.

**Part 3: Change in Dynamics (3 Weeks to Expiry)**

**Increased Gamma:**As the expiry date approaches, gamma rises, especially for at-the-money options. In the case of a long 20 delta strangle, any significant move in the underlying asset's price could lead to more substantial changes in the options' deltas. The strangle becomes more sensitive to the underlying price movements.**Higher Vega Risk:**With less time to expiry, the vega of the options remains significant, but the impact of changes in volatility becomes more pronounced. A further decline in volatility could rapidly erode the value of the strangle.**Time Decay (Theta):**Another critical factor now is time decay, which accelerates as expiration approaches. This decay can negatively impact the value of the strangle, particularly if the underlying asset's price does not exhibit significant movement.

**Conclusion**

Managing this long 20-delta strangle for the trader becomes more challenging as expiry nears. While opportunities for capitalizing on price movements due to gamma increase, the risks associated with declining volatility and time decay also rise. The trader needs to be nimble, possibly adjusting the position or considering hedging strategies to mitigate these risks. This scenario requires a delicate balance between responding to market movements (gamma) and managing the decline in volatility (vega), all while keeping a close eye on the accelerating time decay (theta).

## Capital Concepts

### Question 1

An unexpected interest rate hike would likely lead to a decrease in the value of long call options on TLT. Higher interest rates generally lead to lower bond prices, and TLT, a long-term Treasury bond ETF, would decrease in value. Since call options give the holder the right to buy the underlying asset, a decrease in TLT's price would make these options less valuable.

### Question 2

The second question will be divided into three parts to clarify the explanations.

**Part 1: Impact of the Steepening Implied Volatility Skew**

**Effect on Straddles:****Straddle Expiring in 20 Days:**The short straddle with 20 days to expiry is more sensitive to changes in implied volatility, particularly for the at-the-money options that make up the straddle. A steepening skew typically means that the implied volatility of out-of-the-money (OTM) options (both puts and calls) is increasing relative to at-the-money (ATM) options. Since this straddle is closer to expiry, the increase in implied volatility of OTM options may not significantly affect its overall value, as short-dated options are less sensitive to changes in skew.**Straddle Expiring in 50 Days:**The longer-dated straddle is more affected by the skew change. The increase in implied volatility for OTM options makes this straddle more expensive to buy back, potentially leading to unrealized losses on the position.

**Market Interpretation:**A steepening of the implied volatility skew without a corresponding move in the market can signal that traders anticipate increased risk or uncertainty in the future, possibly expecting larger-than-usual movements in the underlying asset.

**Part 2: Potential Adjustments to the Position**

**Managing the 20-Day Straddle:**For the short straddle expiring in 20 days, the trader may consider closely monitoring the position due to its proximity to expiry. If the implied volatility continues to rise, the trader might decide to close or roll the position to a later date to avoid potential losses.**Adjusting the 50-Day Straddle:**Given the greater sensitivity to the steepening skew, the trader might consider hedging this position. Possible strategies include buying OTM options to offset the increased risk or adjusting the strikes of the straddle.**Overall Portfolio Management:**The trader should assess the overall risk profile of their portfolio in light of the market signal implied by the skew steepening. This might involve rebalancing or diversifying their positions to mitigate potential risks.

**Part 3: Interpreting the Market Signal**

**Risk Anticipation:**The quick steepening of the skew suggests that the market is pricing greater risk, particularly for tail events (significant up or down movements). This could be due to various factors, including macroeconomic changes, geopolitical events, or other market dynamics.**Strategic Response:**The trader should interpret this as a warning sign to reassess their market view and the assumptions underlying their current positions. It may be prudent to adopt a more defensive strategy, particularly for positions with longer-dated expiries that are more exposed to changes in the implied volatility skew.

**Conclusion**

In this scenario, the trader must balance the immediate concerns associated with the short-dated straddle with the broader implications of the steepening skew on the longer-dated position. The key lies in actively managing the positions in response to the evolving market conditions and reassessing the overall trading strategy in light of the potential for increased market volatility or major price movements in the future.

The steepening of the implied volatility skew in a short volatility strategy, like selling SPY straddles, implies that out-of-the-money options (both puts and calls) are getting pricier than at-the-money options. This could lead to losses on the sold straddles if the market moves significantly, as the more expensive out-of-the-money options would result in higher costs to close the positions. The trader might consider adjusting the position by rolling the straddles to different strikes or expirations or hedging the position with other options or underlying assets.

### 7-Figures Bonus

An exotic derivative involving a swap of bonds for hedging interest rate risk might be structured as a total return swap. In this swap, one party agrees to pay the total return of a bond or a bond index (including interest payments and capital gains/losses) in exchange for a regular fixed or floating payment from the other party. This derivative can effectively transfer the bond's interest rate risk and credit risk to the counterparty. Key risks include credit risk (risk of default by the bond issuer or the counterparty) and market risk (risk due to changes in interest rates). Managing these risks involves regular monitoring of credit conditions, interest rate movements, and potentially using hedges like interest rate swaps or options. The recent changes in interest rates and credit spreads can significantly affect the valuation of this swap, requiring active management and revaluation of the positions.

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