In futures pricing, various factors influence the determination of the futures price. These factors include interest rates, dividends, carrying costs, and storage costs. Interest rates play a significant role in futures pricing because they affect the cost of carry, which refers to the cost of holding a position in the futures contract. Dividends also impact futures pricing, especially in equity futures, where the expected dividends affect the cost of carry. Carrying costs include expenses such as storage, insurance, and financing costs associated with holding the underlying asset. Thus, option (b) is the correct answer.

Option (a) is incorrect because contributing factors, such as interest rates and carrying costs, do affect futures pricing.

Option (c) is incorrect because contributing factors are relevant in both futures and options pricing.

Option (d) is incorrect because contributing factors are not solely determined by market sentiment but rather by economic and financial factors affecting the underlying asset.

When the storage costs for the underlying asset increase, it becomes more expensive to hold the asset until the delivery date. As a result, the cost of carry increases, leading to an upward pressure on the futures price. Traders and investors would demand a higher price for the futures contract to compensate for the increased holding costs associated with the underlying asset. Therefore, option (c) is the correct answer.

Option (a) is incorrect because an increase in storage costs would typically lead to an increase, not a decrease, in the futures price.

Option (b) is incorrect because changes in storage costs can influence the futures price.

Option (d) is incorrect because changes in storage costs affect the economic dynamics of the futures contract and are relevant to its pricing.

The fair value of a futures contract is determined by the cost of carry model, which considers factors such as interest rates, dividends, storage costs, and convenience yields. It represents the theoretical equilibrium price at which the futures contract should trade in the market. The fair value reflects the present value of the cost of holding the underlying asset until the delivery date. Therefore, option (c) is the correct answer.

Option (a) is incorrect because the fair value is not necessarily the same as the initial purchase price of the futures contract.

Option (b) is incorrect because although supply and demand dynamics influence the actual futures price, the fair value is determined by economic and financial factors.

Option (c) is incorrect because regulatory authorities do not set the fair value of futures contracts; it is determined by market forces and economic principles.

Option pricing models, such as the Black-Scholes model, require certain inputs to calculate the theoretical value of an option premium. The primary inputs include the current price of the underlying asset and its volatility. Volatility represents the degree of price fluctuations of the underlying asset and is a critical determinant of option prices. Higher volatility generally leads to higher option premiums. Therefore, option (b) is the correct answer.

Option (a) is incorrect because while strike price and expiration date are important parameters in option pricing, they are not the primary inputs to the model.

Option (c) is incorrect because while dividend yield and interest rates may influence option prices, they are not the primary inputs to the option pricing model.

Option (d) is incorrect because market sentiment and trading volume are not direct inputs to option pricing models but may indirectly affect option prices through supply and demand dynamics.

Delta measures the sensitivity of an option’s price to changes in the price of the underlying asset. A delta of 0.70 indicates that for every $1 increase in the underlying asset’s price, the option price is expected to increase by $0.70. Therefore, if the price of the underlying asset increases by $1, the estimated change in the option price would be a $0.70 increase, as indicated by the delta. Hence, option (b) is the correct answer.

Option (b) is incorrect because an increase in the price of the underlying asset would typically lead to an increase, not a decrease, in the option price, given the positive delta.

Option (c) is incorrect because the estimated change in the option price is determined by the delta and the direction of the underlying asset’s price movement.

Option (d) is incorrect because while the price of the underlying asset increases, the estimated change in the option price is based on the delta, which may not be equal to the increase in the underlying asset’s price.

Interest rates influence the cost of carry, which is a crucial component in the pricing of futures contracts. Lower interest rates reduce the cost of financing and, consequently, the cost of holding the underlying asset until the delivery date. This leads to an increase in the futures price to reflect the lower cost of carry. Therefore, option (c) is the correct answer.

Option (a) is incorrect because interest rates do play a significant role in futures pricing.

Option (b) is incorrect because higher interest rates increase the cost of carry, putting downward pressure on futures prices.

Option (d) is incorrect because interest rates impact both futures and options pricing, not just options.

Convenience yield is the benefit or advantage of holding the physical asset rather than a futures contract. A higher convenience yield implies a greater incentive to hold the physical asset, resulting in a lower cost of carry. Consequently, a higher convenience yield leads to a higher fair value of a futures contract. Therefore, option (b) is the correct answer.

Option (a) is incorrect because convenience yield does impact futures pricing.

Option (c) is incorrect because a higher convenience yield reduces the cost of carry, increasing the fair value of a futures contract.

Option (d) is incorrect because convenience yield primarily affects futures pricing, not just options.

An increase in expected dividends for gold mining companies implies a higher income yield for holding gold-related assets. This higher income yield increases the opportunity cost of holding a non-income-generating asset like gold. As a result, the cost of carry for gold increases, putting downward pressure on the futures price. Therefore, option (a) is the correct answer.

Option (b) is incorrect because changes in expected dividends can influence the futures price.

Option (c) is incorrect because an increase in expected dividends is associated with a higher cost of carry, leading to a decrease in the futures price.

Option (d) is incorrect because expected dividends can impact the cost of carry and, consequently, futures pricing.

The negative delta for a put option indicates that the option price is expected to move in the opposite direction of the underlying asset’s price. If the stock price decreases by $2, the estimated change in the option price would be a $1.00 increase, considering the negative delta. Therefore, option (b) is the correct answer.

Option (a) is incorrect because the change in the option price is based on the negative delta and the direction of the underlying asset’s price movement.

Option (c) is incorrect because the estimated change in the option price is determined by the negative delta and the decrease in the stock price.

Option (d) is incorrect because, with a negative delta, an increase in the stock price would result in a decrease in the option price.

Volatility represents the magnitude of price fluctuations of the underlying asset. Higher volatility implies greater potential price swings, making the option more valuable. Lower volatility reduces the likelihood of large price movements, decreasing the perceived value of the option. Therefore, lower volatility leads to higher option premiums. Option (c) is the correct answer.

Option (a) is incorrect because volatility significantly impacts option pricing.

Option (b) is incorrect because higher volatility generally leads to higher option premiums.

Option (d) is incorrect because volatility primarily affects option pricing, although it can also influence futures pricing.

Time to expiration represents the amount of time remaining until the option contract expires. Longer time to expiration provides more opportunities for the underlying asset’s price to move in favor of the option holder, increasing the probability of the option being in-the-money. Consequently, options with longer time to expiration have higher premiums to reflect the increased probability of profitability. Therefore, option (c) is the correct answer.

Option (a) is incorrect because longer time to expiration generally leads to higher option premiums.

Option (b) is incorrect because shorter time to expiration often leads to lower option premiums due to decreased time value.

Option (c) is incorrect because time to expiration is a critical factor in option pricing, influencing the time value component of the option premium.

Writing options involves taking on the obligation to buy or sell the underlying asset at a predetermined price (strike price) within a specified period. The primary risk associated with writing options is market risk, which refers to the risk of adverse price movements in the underlying asset. If the market moves against the writer’s position, they may incur losses that exceed the premium received from writing the option. Therefore, option (b) is the correct answer.

Option (a) is incorrect because credit risk pertains to the risk of default by counterparties, which may not be the primary risk for option writers.

Option (c) is incorrect because liquidity risk relates to the inability to execute trades at desired prices due to a lack of market participants.

Option (d) is incorrect because counterparty risk refers to the risk of the other party in the transaction defaulting, which may not be the primary risk for option writers.

Gamma measures the rate of change of an option’s delta in response to changes in the price of the underlying asset. If the price of the underlying asset increases by $1, the estimated change in the option’s delta would be the initial delta (0.40) plus the gamma (0.05), resulting in a total increase of 0.45. Therefore, option (c) is the correct answer.

Option (a) is incorrect because the change in the option’s delta is determined by adding the initial delta and the gamma.

Option (b) is incorrect because the gamma contributes to the change in the option’s delta.

Option (d) is incorrect because the gamma’s impact on the delta is additive, not multiplicative.

The Black-Scholes model is a widely used mathematical model for pricing European-style options. It provides a theoretical understanding of option pricing by considering factors such as the underlying asset’s price, time to expiration, strike price, risk-free interest rate, and volatility. Key assumptions of the Black-Scholes model include constant volatility, no dividends during the option’s life, and efficient markets. Therefore, option (c) is the correct answer.

Option (c) is incorrect because the Black-Scholes model is primarily used for options pricing, not futures pricing.

Option (b) is incorrect because while the Black-Scholes model is commonly applied to European-style options, it can also be adapted for other types of options.

Option (d) is incorrect because the Black-Scholes model assumes constant volatility but does not necessarily assume no dividends. It can accommodate dividend-paying stocks through adjustments to the model.

The primary difference between American-style options and European-style options lies in their exercise characteristics. American-style options allow the holder to exercise the option at any time until the expiration date, whereas European-style options can only be exercised at expiration. Therefore, option (c) is the correct answer.

Option (a) is incorrect because American-style options offer the flexibility to exercise before expiration.

Option (b) is incorrect because European-style options cannot be exercised before expiration.

Option (d) is incorrect because options cannot be exercised after expiration, regardless of their style.

The delta of a put option measures the sensitivity of the option’s price to changes in the price of the underlying asset. A higher delta indicates a stronger negative correlation between the option’s price and the underlying asset’s price. Therefore, a put option with a higher delta provides better downside protection and is more effective as a hedge against price declines in the underlying asset. Hence, option (a) is the correct answer.

Option (b) is incorrect because a higher delta, not a lower delta, generally increases the effectiveness of the hedge.

Option (c) is incorrect because delta plays a crucial role in determining the effectiveness of the hedge.

Option (d) is incorrect because hedge effectiveness depends on various factors, including the delta of the option, not solely on the stock price.

When writing (selling) a call option, the maximum profit potential is limited to the premium received from selling the option. The writer of the call option receives the premium upfront but assumes the obligation to sell the underlying asset at the strike price if the option is exercised. Therefore, the maximum profit occurs when the option expires worthless, and the writer keeps the premium. Option (b) is the correct answer.

Option (a) is incorrect because writing a call option has a limited profit potential.

Option (c) is incorrect because the writer’s profit is not limited to the strike price but rather to the premium received.

Option (d) is incorrect because it describes the maximum loss scenario for the writer, not the maximum profit potential.

The strike price of an option determines the price at which the underlying asset can be bought or sold if the option is exercised. Out-of-the-money options have strike prices that are higher than the current price of the underlying asset. This means that if the option were to be exercised immediately, it would not result in a profit for the holder. Out-of-the-money options typically have lower premiums compared to in-the-money options due to their lower intrinsic value. Therefore, option (c) is the correct answer.

Option (a) is incorrect because the strike price does impact option premiums.

Option (b) is incorrect because in-the-money options have strike prices below the current asset price.

Option (d) is incorrect because at-the-money options have strike prices closest to the current asset price, but they can be slightly above or below it.

The primary risk associated with buying options is credit risk. Credit risk refers to the risk that the counterparty, typically the option writer or seller, may default on their obligation to fulfill the terms of the options contract. If the counterparty fails to honor the contract, the option buyer may incur losses, including the loss of the premium paid for the option. Therefore, option (b) is the correct answer.

Option (a) is incorrect because market risk applies to changes in the value of the underlying asset.

Option (c) is incorrect because opportunity risk typically refers to missed opportunities rather than risks associated with options trading.

Option (d) is incorrect because liquidity risk pertains to the ability to enter or exit positions at desired prices.

Gamma measures the rate of change of an option’s delta in response to changes in the price of the underlying asset. A gamma of 0.03 indicates that the option’s delta is increasing rapidly with each unit change in the underlying asset’s price. Therefore, option (a) is the correct answer.

Option (b) is incorrect because a positive gamma implies that the option’s delta is increasing, not decreasing, with changes in the underlying asset’s price.

Option (c) is incorrect because a gamma of 0.03 suggests a relatively rapid increase in the option’s delta, rather than a slow increase.

Option (d) is incorrect because a non-zero gamma value indicates that the option’s delta is not constant but changes with movements in the underlying asset’s price.

The expiration date is the date when the option contract ceases to be valid. After the expiration date, options lose all value and become worthless if not exercised. Therefore, the expiration date is critical for options holders and writers as it sets the deadline for taking action on the options contract. Hence, option (b) is the correct answer.

Option (a) is incorrect because the strike price is predetermined and does not change with the expiration date.

Option (c) is incorrect because longer expiration periods may increase option premiums due to the additional time value, but it does not determine the expiration date.

Option (d) is incorrect because the expiration date is a fundamental factor influencing option premiums and their behavior over time.

The primary difference between futures contracts and forward contracts lies in their standardization. Futures contracts are standardized agreements traded on organized exchanges, where the terms of the contract, such as quantity, quality, expiration date, and settlement, are predetermined by the exchange. In contrast, forward contracts are customized agreements tailored to the specific needs of the parties involved and are traded over-the-counter (OTC). Therefore, option (a) is the correct answer.

Option (b) is incorrect because both futures and forward contracts can be traded over-the-counter, but futures contracts are primarily traded on exchanges.

Option (c) is incorrect because the maturities of futures and forward contracts can vary and are not inherently longer or shorter in one compared to the other.

Option (d) is incorrect because both futures and forward contracts can involve physical delivery or cash settlement, depending on the terms of the contract.

An increase in interest rates affects option premiums through changes in the cost of carry and discount rates. Higher interest rates increase the cost of carry for call options (since it’s more expensive to hold the underlying asset) and decrease the present value of potential future gains, leading to lower call option premiums. Conversely, higher interest rates increase the cost of carry for put options (since it’s more expensive to hold the underlying asset short) and increase the present value of potential future gains, leading to higher put option premiums. Therefore, option (b) is the correct answer.

Option (a) is incorrect because an increase in interest rates decreases call option premiums.

Option (c) is incorrect because an increase in interest rates does not necessarily impact both call and put option premiums in the same direction.

Option (b) is incorrect because an increase in interest rates generally decreases call option premiums and increases put option premiums.

Theta measures the rate of change of an option’s value with respect to time. A negative theta indicates that the option’s value decreases as time passes, reflecting the diminishing time value of the option. Therefore, a theta of -0.04 implies that the option’s value decreases by $0.04 per day. Hence, option (b) is the correct answer.

Option (a) is incorrect because theta measures the rate of decline in the option’s value, not its increase.

Option (c) is incorrect because theta is typically expressed in terms of days, not years.

Option (d) is incorrect because theta reflects the daily decay in the option’s value, not its annual decrease.

The primary purpose of using options in investment portfolios is to hedge against adverse price movements in the underlying assets. Options provide investors with the flexibility to protect their portfolios from downside risk by purchasing put options or to generate additional income by writing covered call options. By using options strategically, investors can mitigate the impact of adverse market movements and protect their investment capital.

Option (b) is incorrect because options do not guarantee fixed returns.

Option (c) is incorrect because while options can amplify gains, they also come with amplified risks.

Option (d) is incorrect because options, like any investment instrument, carry inherent risks that cannot be completely eliminated.

Implied volatility represents the market’s expectation of future price movements in the underlying asset. It is derived from the pricing of options and is a key input in option pricing models. Higher implied volatility leads to higher option premiums, reflecting the increased uncertainty and potential for larger price swings. Therefore, option (b) is the correct answer.

Option (a) is incorrect because implied volatility is not based on historical price movements.

Option (c) is incorrect because implied volatility significantly influences option premiums.

Option (d) is incorrect because implied volatility and historical volatility are related but distinct concepts.

Writing covered calls involves owning the underlying asset while simultaneously selling call options against it. This strategy provides a degree of downside protection since the investor already owns the underlying asset. It reduces the risk of default compared to strategies like writing naked calls, where the investor does not own the underlying asset. Therefore, option (a) is the correct answer.

Option (b) is incorrect because buying long straddles involves purchasing both call and put options, which may expose the investor to more risk.

Option (c) is incorrect because writing naked calls involves selling call options without owning the underlying asset, exposing the investor to significant risk.

Option (d) is incorrect because buying protective puts involves purchasing put options to hedge against a potential decline in the value of the underlying asset, but it does not address the risk of default.

A bull put spread involves selling a put option with a higher strike price and simultaneously buying a put option with a lower strike price. This strategy results in a net credit and provides limited profit potential and limited risk. The maximum loss is capped at the difference between the strike prices, and the maximum profit is limited to the initial credit received. Therefore, option (c) is the correct answer.

Option (a) is incorrect because a long straddle involves buying both a call and a put option, potentially resulting in unlimited risk.

Option (b) is incorrect because a short strangle involves selling an out-of-the-money call and an out-of-the-money put, exposing the investor to unlimited risk.

Option (d) is incorrect because an iron condor involves both call and put spreads, potentially resulting in unlimited risk.

An increase in the stock’s price is generally favorable for call options. The value of a call option is positively correlated with the price of the underlying stock. As the stock’s price rises, the call option becomes more valuable because it grants the right to buy the stock at a predetermined (strike) price, which may be lower than the current market price. Therefore, option (b) is the correct answer.

Option (a) is incorrect because an increase in the stock’s price typically leads to an increase, not a decrease, in the call option’s value.

Option (c) is incorrect because the call option’s value is influenced by changes in the underlying stock’s price.

Option (d) is incorrect because, in general, an increase in the stock’s price has a positive impact on the value of a call option, regardless of its delta.

Time decay, represented by the option greek theta, reflects the rate of decline in an option’s value as time passes. As an option approaches its expiration date, the rate of time decay accelerates, leading to a decrease in the option’s value. This is because the time value portion of the option premium diminishes as expiration approaches, ultimately reducing the option’s overall value. Therefore, option (b) is the correct answer.

Option (a) is incorrect because time decay decreases option value over time.

Option (c) is incorrect because time decay is a crucial factor affecting option pricing.

Option (b) is incorrect because time decay affects the value of all options, regardless of whether they are in-the-money, at-the-money, or out-of-the-money.