1 Introduction

In the fast-paced world of finance, traders are constantly seeking innovative strategies to cap italize on market opportunities and manage risk effectively. Among the several of financial instruments available, options trading has emerged as a powerful tool for investors to achieve their financial goals.

Options, a type of derivative security, offer traders the flexibility to profit from market movements in various asset classes, including stocks, indices, currencies, and commodities, without the need for substantial capital outlay. By providing the right, but not the obligation, to buy or sell an underlying asset at a predetermined price within a specified timeframe, options empower traders to leverage market insights and execute sophisticated trading strategies.

One of the key advantages of options trading is the leverage effect, which magnifies the impact of market movements on the value of options contracts. Leveraging options allows traders to control a larger position in the underlying asset with a relatively small investment, amplifying both potential gains and losses. This ability to achieve significant returns with limited capital outlay is a defining feature of options trading, making it an attractive avenue for traders seeking enhanced profitability.

In an ever-evolving financial landscape, options trading offers a dynamic approach to navi gating market uncertainties and seizing lucrative opportunities. By mastering the art of options trading, traders can unlock new dimensions of profitability and achieve their financial aspira tions.

2 Leverage Effect

The leverage effect in options trading allows investors to amplify their returns compared to investing directly in the underlying asset. For example, consider a trader who purchases a call option for $1 on a stock with a strike price of $50. Each option contract typically represents 100 shares of the underlying stock. If the stock price increases to $60 at expiration, the option would be worth at least $10 ($60- $50), representing a 900% return on the initial investment of $1. In contrast, if the trader had invested $50 directly in the stock, the same $10 increase in price would result in only a 20% return. However, it’s important to note that leverage cuts both ways, as options can also lead to significant losses if the market moves against the trader’s position.

Traders seeking to exploit the leverage effect can consider the following strategies:

1. Buying OTM Options: by purchasing OTM options, traders can leverage small invest ments to control larger positions in the underlying asset. While the probability of these options expiring in the money may be lower, the potential returns can be substantial if the underlying asset experiences significant price movements.

2. Building Quasi Zero-Option Strategies: certain multi-leg options strategies, such as spreads or combinations, can be structured to mimic the payoff profile of a zero-cost 1 option position. These strategies allow traders to benefit from the leverage effect while minimizing upfront capital outlay and potential losses.

3. Selling/Buying Options with High/Low Implied Volatility: options with high implied volatility tend to have higher premiums, reflecting increased market expectations for price movements in the underlying asset. Contrary, options with low implied volatility tend to have lower premiums. These market conditions may also amplify the leverage effect a trader may gain from trading options.

4. Buying Near-Term Options: options with shorter expiration periods usually have lower premiums compared to those with longer expiration periods. By purchasing near term options, traders can leverage market opportunities with reduced upfront capital and capitalize on short-term price movements to maximize the leverage effect.

By strategically implementing these strategies, traders can exploit the leverage effect in op tions trading to amplify potential returns while managing risk effectively. However, it’s essential to carefully assess market conditions, volatility levels, and risk tolerance before executing any trading strategy. In the subsequent sections, we will delve deeper into specific trading strategies that tend to have low cost and further exploit the leverage effect.

3 Ratio Spread Strategies

3.1 Call Ratio Spread Strategy

The call ratio spread option strategy is a complex options trading strategy that involves buying and selling call options with different strike prices and/or expiration dates to create a position that benefits from moderate bullish or bearish price movements in the underlying asset. This strategy aims to generate profits while minimizing upfront capital outlay.

In a call ratio spread option strategy, traders typically execute the following actions:

1. Buy Call Option ITM: the trader purchases one call option on the underlying asset with a specific strike price that is in-the-money (ITM) and aligned with their bullish outlook.

2. Sell Call Options OTM: Simultaneously, the trader sells ”N” call options on the same underlying asset with higher strike prices that are out-of-the-money (OTM). The number of call options sold is typically greater than the number of call options bought.

The payoff profile of a call ratio spread option strategy depends on various factors, including the strike prices, expiration dates, and the number of options bought and sold. Next, we will deal with some possible scenario that comes from the stock price’s movement and its value at the option’s expiration.

• Strong Bullish Scenario: if the price of the underlying asset increases significantly, going beyond the highest strike price, the option strategy’s payoff will start to decline from its maximum, risking to incur in a high negative payoff.

• Moderate Bullish Scenario: if the price of the underlying asset increases moderately, without going beyond the highest strike price, the option strategy’s payoff will be positive. In addition, it reaches its maximum if the stock price reaches the value of the highest strike price.

• Neutral to Bearish Scenario: if the price of the underlying asset remains relatively unchanged, the call options sold by the trader may expire worthless, allowing the trader to keep the premiums received. Meanwhile, in case of a bearish scenario, the option payoff will be capped at the option strategy’s cost.

Hence, traders may consider implementing a call ratio spread option strategy in the following scenarios:

• Moderate Bullish Outlook: when the trader expects the price of the underlying asset to increase moderately but wants to limit upfront capital outlay and downside risk.

• Neutral Outlook: When the trader is neutral to slightly bearish on the underlying asset but wants to profit from premiums received from selling the call options.

In Figure 1 an example of this strategy is reported. To draw it has been used a Python code in which a function has been built to compute the payoff of the strategy given certain inputs. Then, for some values of the stock underlying, the payoff has been plotted, highlighting which were the strikes’ values.

3.2 Put Ratio Spread Strategy

The put ratio spread option strategy is a versatile options trading strategy that involves buying and selling put options with different strike prices and/or expiration dates to create a position that benefits mainly from moderate bearish in the underlying asset. This strategy aims to generate profits while minimizing upfront capital outlay.

In a put ratio spread option strategy, traders typically execute the following actions:

1. Buy Put Option ITM: the trader purchases one put option on the underlying asset with a specific strike price that is in-the-money (ITM) and aligned with their bearish outlook.

2. Sell Put Options OTM: simultaneously, the trader sells ”N” put options on the same underlying asset that are out-of-the-money (OTM). The number of put options sold is typically greater than the number of put options bought.

The payoff profile of a put ratio spread option strategy depends on various factors, including the strike prices, expiration dates, and the number of options bought and sold.

• Strong Bearish Scenario: if the price of the underlying asset decreases significantly, going beyond the lowest strike price, the put options sold by the trader may be assigned, resulting in potential losses.

• Moderate Bearish Scenario: if the price of the underlying asset decreases moderately, without going beyond the lowest strike price, the option strategy’s payoff is for sure positive. In addition, it reaches its maximum if the underlying price reaches the lowest strike price at the option’s expiration date.

• Neutral to Bullish Scenario: if the price of the underlying asset remains relatively unchanged, the put options sold by the trader may expire worthless, allowing the trader to keep the premiums received. Meanwhile, in case of a bullish scenario, the option strategy’s payoff will be capped to the option strategy’s initial cost.

Hence, traders may consider implementing a put ratio spread option strategy in the following scenarios:

• Moderate Bearish Outlook: when the trader expects the price of the underlying asset to decrease moderately but wants to limit upfront capital outlay and downside risk.

• Neutral Outlook: when the trader is neutral on the underlying asset but wants to profit from premiums received from selling the put options.

In Figure 2 an example of this strategy is reported. To draw it, a Python code was utilized to develop a function that computes the payoff of the strategy based on user-defined inputs. Subsequently, the payoff was plotted for various values of the underlying stock, with the strike prices prominently marked.

4 Risk Reversal Strategies

4.1 Long Risk Reversal Strategy The long risk reversal strategy is a versatile options trading strategy that allows traders to profit from strong bullish price movements in the underlying asset while minimizing upfront capital outlay. This strategy involves a combination of buying and selling options to create a position that mimics the payoff profile of owning the underlying asset, typically with reduced cost and risk.

In a long risk reversal strategy, traders typically execute the following actions:

1. Buy Call Option: the trader purchases a call option on the underlying asset with a strike price above the current market price. This call option gives the trader the right, but not the obligation, to buy the underlying asset at the strike price on or before the expiration date.

2. Sell Put Option: simultaneously, the trader sells a put option on the same underlying asset with a strike price below the current market price. By selling the put option, the trader receives a premium, which helps offset the cost of buying the call option.

The payoff profile of a long risk reversal strategy could be different based on different sce narios:

• Bullish Scenario: if the price of the underlying asset increases significantly, the call option will increase in value, resulting in potential profits. Specifically, the payoff tends to infinite when the underlying price continues to increase.

• Neutral to Bearish Scenario: if the price of the underlying asset remains relatively unchanged or decreases slightly, the call option may lose value or expire worthless. However, the put option sold by the trader will increase in value, offsetting some or all of the losses on the call option. The downside risk is not fully limited, since the more the underlying price decreases, the more negative will be our strategy’s payoff.

Hence, the long risk reversal strategy could be a good trading strategy for the following reasons:

• Low-cost replicating strategy: it allows the trader to replicate a long position in the underlying price but with a low-cost initial price.

• Unlimited Reward: the potential profit is theoretically unlimited if the price of the underlying asset increases significantly, as the trader profits from the appreciation in the value of the call option.

Traders may consider implementing a long risk reversal strategy when he/she has strong bullish expectations on the underlying. The following image may better represent the strategy and when it is maximized the payoff. In Figure 3 an example of this strategy is reported. To draw it, a Python code was utilized to develop a function that computes the payoff of the strategy based on user-defined inputs. Subsequently, the payoff was plotted for various values of the underlying stock, with the strike prices prominently marked. In the subsequent sections, we will explore additional options trading strategies and their applications in different market scenarios.

4.2 Short Risk Reversal Strategy

The short risk reversal strategy is a versatile options trading strategy that allows traders to profit from strong bearish price movements in the underlying asset while minimizing upfront capital outlay. This strategy involves a combination of selling and buying options to create a position that mimics the payoff profile of shorting the underlying asset, typically with reduced cost and risk. In a short risk reversal strategy, traders typically execute the following actions:

1. Sell Call Option: the trader sells a call option on the underlying asset with a strike price above the current market price. This call option obligates the trader to sell the underlying asset at the strike price at the expiration date if assigned. 6 Figure 3: Long Risk Reversal Payoff

2. Buy Put Option: simultaneously, the trader purchases a put option on the same under lying asset with a strike price below the current market price. By buying the put option, the trader gains the right to sell the underlying asset at the strike price at the expiration date.

The payoff profile of a short risk reversal strategy is as follows:

• Bullish Scenario: if the price of the underlying asset increases significantly, going be yond the strike connected to the call option, the option’s payoff will start to decrease, until becoming negative.

• Neutral Scenario: if the price of the underlying asset remains relatively unchanged, both the sold call option and the purchased put option will expire worthless. The trader profits from the premiums received from selling the call option and pays the premium for the put option, resulting in a net credit.

• Bearish Scenario: if the price of the underlying asset decreases significantly, going below the value of the strike connected to the put, then the option’s strategy will start to become positive. Hypothetically, it would reach its maximum if the underlying price is zero at expiration.

Hence, the short risk reversal strategy offers respectively, the following reward risks:

• Lower sensibility to increases: it allows the trader to still have a net credit even if the underlying price moderately decreases. This thing would be not possible, in case the trader had adopted a traditional short-selling on the underlying.

• Unlimited Risk: thepotential loss is theoretically unlimited if the price of the underlying asset increases significantly. However, the risk is partially mitigated to the difference between the strike prices minus the net credit received.

Traders may consider implementing a short risk reversal strategy in the following scenarios:

• Moderate and Strong Bearish Outlook: when the trader expects the price of the underlying asset to decrease moderately or strongly and also wants to limit upfront capital outlay.

• Neutral Outlook: when the trader has neutral expectations on the underlying asset and thus, wants to profit from premiums received from selling the call option and limit potential losses if the price increases.

In Figure 4 an example of this strategy is reported. To draw it, a Python code was utilized to develop a function that computes the payoff of the strategy based on user-defined inputs. Subsequently, the payoff was plotted for various values of the underlying stock, with the strike prices prominently marked.

5 Volatility Strategies

5.1 Straddle Strategy

The straddle strategy is a popular options trading strategy that involves buying/selling both a call option and a put option on the same underlying asset with the same strike price and expiration date. This strategy is commonly used when traders expect (in case of long straddle) or not (in case of short straddle) a significant price movement in either direction but are unsure about the direction of the movement, if any. By combining a long call and a long put or a short call with a short put, the straddle strategy allows traders to profit from large price swings in the first case or to profit from price stagnation in the second one. From here, we will consider the long straddle strategy, knowing that the considerations of a short straddle strategy are simply the opposite. In a long straddle strategy, traders typically execute the following actions:

1. Buy Call Option: the trader purchases a call option on the underlying asset with a specific strike price and expiration date.

2. Buy Put Option: simultaneously, the trader purchases a put option on the same un derlying asset with the same strike price and expiration date as the call option.

The payoff profile of a long straddle strategy is as follows:

• Bullish Scenario: if the price of the underlying asset increases significantly, going above the highest strike price the call option will increase in value, resulting in potential profits. Meanwhile, the put option will expire worthless, but the losses on the put option are limited to the premium paid.

• Bearish Scenario: if the price of the underlying asset decreases significantly, going under the lowest strike price, the put option will increase in value, resulting in potential profits. Meanwhile, the call option will expire worthless, but the losses on the call option are limited to the premium paid.

• Neutral Scenario: if the price of the underlying asset remains relatively unchanged, both the call and put options will expire worthless. The maximum loss is reached in the case of the underlying price is equal to the strike price at the expiration date.

The straddle strategy offers the following risk and reward characteristics:

• Limited Risk: the maximum potential loss is limited to the total premium paid for both the call and put options. This occurs if the price of the underlying asset remains relatively unchanged at expiration.

• High Rewards: the potential profit is theoretically very high if the price of the under lying asset moves significantly in either direction. Indeed, profits increase as the price moves further away from the strike prices in either direction.

In Figure 4 an example of this strategy is reported. To draw it, a Python code was utilized to develop a function that computes the payoff of the strategy based on user-defined inputs. Subsequently, the payoff was plotted for various values of the underlying stock, with the strike prices prominently marked.

5.2 Strangle Strategy

The strangle strategy is an options trading strategy that involves buying/selling both an out of-the-money (OTM) call option and an OTM put option on the same underlying asset with different strike prices but the same expiration date. This strategy is utilized when traders anticipate a significant/neutral price movement in either direction but are unsure about the direction of the movement. By combining a long OTM call and a long OTM put or a short OTMcall andashort OTMput, the strangle strategy allows traders to profit from large/neutral price swings. From here, we will consider the long strangle strategy, knowing that the considerations of a short strangle strategy are simply the opposite. In a long strangle strategy, traders typically execute the following actions:

1. Buy OTM Call Option: the trader purchases a call option on the underlying asset with a higher strike price compared to the current market price.

2. Buy OTM Put Option: simultaneously, the trader purchases a put option on the same underlying asset with a lower strike price compared to the current market price.

The long strangle strategy is similar to the long straddle strategy since both involve buying both a call and put option. However, the key difference lies in the strike prices of the options. In a straddle strategy, both the call and put options have the same strike price, while in a strangle strategy, the call and put options have different strike prices. As a result, the strangle strategy typically has a lower upfront cost compared to the straddle strategy, but it requires a larger price movement in the underlying asset to be profitable. According to the scenarios at expiration, the payoff profile of a long strangle strategy is as follows:

• Bullish Scenario: if the price of the underlying asset increases significantly, going above the call’s strike, the OTM call option will increase in value, resulting in potential profits. Meanwhile, the OTM put option will expire worthless, but the losses on the put option are limited to the premium paid.

• Bearish Scenario: if the price of the underlying asset decreases significantly, going below the put’s strike, the OTM put option will increase in value, resulting in potential profits. Meanwhile, the OTM call option will expire worthless, but the losses on the call option are limited to the premium paid.

• Neutral Scenario: If the price of the underlying asset remains within a certain range, both the OTM call and put options will expire worthless, resulting in a maximum loss equal to the total premium paid for both options.

The strangle strategy offers the following risk and reward characteristics:

• Limited Risk: the maximum potential loss is limited to the total premium paid for both the OTM call and put options. This occurs if the price of the underlying asset remains within the range of the strike prices at expiration.

• High Rewards: The potential profit could be very high if the price of the underlying asset moves significantly in either direction. Profits increase as the price moves further away from the strike prices in either direction.

In Figure 6 an example of this strategy is reported. To draw it, a Python code was utilized to develop a function that computes the payoff of the strategy based on user-defined inputs. Subsequently, the payoff was plotted for various values of the underlying stock, with the strike prices prominently marked.

## Comments