Knock in option

What Is a Knock-In Option?

A knock-in option is a type of exotic option that only becomes active, or "knocks in," if the price of its underlying asset reaches or crosses a predetermined barrier level before or at its expiration date. Until this barrier is touched, the knock-in option has no value as a traditional option and cannot be exercised. These financial derivatives are conditional and are often used by investors seeking to capitalize on specific price movements while potentially paying a lower premium compared to a standard option.

History and Origin

The concept of options, including various forms of conditional contracts, has a long history, with roots tracing back to ancient times, such as Thales of Miletus's olive press contracts around 600 BC.¹¹ However, modern, standardized options trading began with the establishment of the Chicago Board Options Exchange (CBOE) in 1973.¹⁰ Before the CBOE, options were primarily traded in an unstructured over-the-counter (OTC) market with complex and non-standardized terms.

The formal introduction of barrier options, including knock-in options, came later as financial engineering advanced. As the options market matured and computational capabilities improved, particularly after the widespread adoption of the Black-Scholes model for pricing, more complex structures like barrier options became feasible.⁹ Academic research into these more intricate derivative instruments gained prominence in the late 20th century. For instance, the term "exotic options" was coined in a 1990 paper by Professor Mark Rubinstein.⁸ The development of sophisticated pricing models, often utilizing methods like Monte Carlo simulation, has been crucial for valuing these conditional derivatives.⁶, ⁷

Key Takeaways

• A knock-in option activates only if the underlying asset's price touches or crosses a specific barrier level.
• They typically cost less than standard options because of their conditional nature, offering potential cost savings.
• Knock-in options can be either call options or put options, and the barrier can be above or below the current price.
• They are primarily used for targeted speculation and hedging strategies.

Formula and Calculation

The pricing of knock-in options, like other barrier options, is more complex than that of plain vanilla options due to the path-dependent nature of their payoff. The value of a knock-in option depends not only on the underlying asset's price at expiration but also on whether the barrier was triggered during the option's life.

For continuous monitoring of the barrier, the pricing formulas for knock-in options are often derived from the Black-Scholes framework, with adjustments to account for the barrier condition. For a down-and-in call option, for example, where the barrier (H) is below the current stock price (S) and must be touched for the option to activate, the formula would involve terms related to the probability of hitting the barrier. Similarly, for an up-and-in call option, the barrier would be above the current stock price.

Where:

• (C_{KI}) = Price of the knock-in option
• (C_{Vanilla}) = Price of a comparable plain vanilla option (without a barrier)
• (C_{KO}) = Price of a comparable knock-out option

This relationship holds because a plain vanilla option can be seen as the sum of a knock-in option and a knock-out option with the same strike price and barrier. If the barrier is hit, the knock-in activates, and the knock-out ceases to exist. If the barrier is not hit, the knock-in never activates, and the knock-out behaves like a vanilla option.

More detailed analytical formulas for specific types of barrier options exist, but they are often complex and involve cumulative normal distribution functions and several parameters, including the volatility of the underlying asset. For discretely monitored barrier options or those with more complex features, numerical methods like Monte Carlo simulations or finite difference methods are frequently employed for valuation.⁵

Interpreting the Knock-In Option

Interpreting a knock-in option involves understanding its conditional nature. Unlike standard American options or European options, a knock-in option has no inherent rights until its barrier is breached. If the barrier is never reached, the option expires worthless, and the investor loses the entire premium paid.

The key to interpretation lies in the relationship between the current underlying price, the barrier level, and the investor's market view.

• For a "down-and-in" option (barrier below current price): The investor expects the price to fall to the barrier, then potentially reverse or continue in a favorable direction (for a call, reversal; for a put, continuation down). This is often used when an investor believes there will be a dip before a rally, or to initiate a position after a significant price decline.
• For an "up-and-in" option (barrier above current price): The investor expects the price to rise to the barrier, and then the option activates. This might be used if an investor anticipates a strong upward momentum that will carry the price through the barrier, leading to a profitable activated option.

The decision to use a knock-in option reflects a precise market expectation about price trajectory and levels. Investors are effectively betting on a specific price path rather than just the directional movement of the underlying asset.

Hypothetical Example

Consider an investor, Alex, who believes that Company XYZ's stock, currently trading at $105, will temporarily fall to $100 before resuming an upward trend. Alex wants to buy a call option but wants to pay a lower premium than a standard call, and only wants the option to become active if their prediction of a dip is correct.

Alex decides to buy a down-and-in call option on Company XYZ with the following terms:

• Current Stock Price: $105
• Barrier Level: $100 (down-and-in)
• Strike Price: $102
• Expiration Date: Three months from now
• Premium Paid: $1.50 per share (lower than a comparable standard call)

Scenario 1: Barrier is Hit
Two weeks later, Company XYZ's stock price falls to $99, touching the $100 barrier. At this moment, the knock-in option "knocks in" and becomes a standard call option. The price then rebounds and reaches $108 by the expiration date. Since the activated call option has a strike price of $102, Alex can exercise it to buy shares at $102, which are currently worth $108. The intrinsic value is $108 - $102 = $6. After accounting for the $1.50 premium, Alex's profit is $6 - $1.50 = $4.50 per share.

Scenario 2: Barrier is Not Hit
Suppose Company XYZ's stock price never falls to $100. It hovers between $101 and $107 for the next three months. Since the barrier was never touched, the knock-in option never activates and expires worthless, even if the stock price is above the strike price at expiration. Alex loses the $1.50 premium paid.

This example illustrates that the activation condition is crucial for a knock-in option.

Practical Applications

Knock-in options serve various purposes in financial markets, primarily within risk management and targeted speculation strategies.

• Cost-Effective Exposure: Investors can gain exposure to an underlying asset at a lower premium than a vanilla option. This is particularly attractive when an investor holds a specific view on price action, such as expecting a brief pullback before a significant move.
• Anticipating Market Corrections or Rallies: A down-and-in call option might be used by an investor who anticipates a market correction but believes the long-term trend remains bullish. If the market dips to a certain level (the barrier), their call option activates, allowing them to participate in the subsequent rebound. Conversely, an up-and-in put option could be used if a large rally is expected to falter after reaching a certain high, providing a cheaper way to establish a bearish position.
• Hedging Conditional Exposures: While less common for simple portfolios, sophisticated traders might use knock-in options to hedge conditional risks. For example, if a company has a contractual obligation that only triggers if a commodity price hits a certain level, a knock-in option on that commodity could provide a tailored hedge against that specific, conditional exposure.
• Structured Products: Knock-in options are often components of more complex structured products designed by investment banks. These products can offer customized payoffs linked to various market scenarios, with knock-in features managing the activation of different components. For instance, a structured note might offer enhanced returns only if a stock index reaches a specific barrier, using embedded knock-in options to achieve this payoff profile. Academic research continues to explore efficient methods for pricing and managing these intricate options, especially in volatile market conditions.³, ⁴

Limitations and Criticisms

Despite their advantages in tailoring specific market views and potentially reducing upfront costs, knock-in options come with notable limitations and criticisms:

• Complexity: Knock-in options are more complex than standard call options or put options, making them harder for retail investors to understand and price. Their path-dependent nature requires more sophisticated analytical tools and a deeper understanding of derivatives.
• All-or-Nothing Risk: The primary drawback is the binary nature of their activation. If the barrier is never touched, the option expires worthless, resulting in a total loss of the premium, regardless of how close the underlying asset came to the barrier or its price at expiration date. This "near miss" scenario can be frustrating and lead to significant losses if the market does not move precisely as anticipated.
• Liquidity: Knock-in options, being a form of exotic option, typically trade over-the-counter (OTC) rather than on organized exchanges. This can lead to lower liquidity compared to vanilla options, resulting in wider bid-ask spreads and potentially making it difficult to enter or exit positions at favorable prices.
• Model Risk: Pricing these options accurately relies on complex mathematical models that assume certain market behaviors, such as constant volatility or specific jump processes. If the real-world market deviates significantly from these assumptions, the theoretical price may not reflect the actual market value, leading to potential mispricing and unexpected outcomes. Research highlights the challenges in pricing barrier options, especially under stochastic volatility models.²
• Lack of Control: Once activated, a knock-in option becomes a standard option, but until then, the holder has no control over its activation; it's entirely dependent on the underlying asset's price hitting the barrier.

Regulators, such as the U.S. Securities and Exchange Commission (SEC), oversee the trading of options and other derivatives to ensure market integrity and investor protection.¹ However, the customized nature of exotic options means investors must exercise extreme due diligence when considering them.

Knock-In Option vs. Knock-Out Option

Knock-in options and knock-out options are both types of barrier options, but they function in opposite ways regarding their activation or deactivation based on a predetermined barrier level.

The confusion between the two often arises because both are "barrier" options and share the goal of reducing premium costs compared to vanilla options. However, their conditional nature is inverted. A knock-in option requires a specific price movement to "come alive," while a knock-out option is "alive" from the start but dies if a certain price level is reached. Understanding this fundamental difference is crucial for selecting the appropriate option for a given market outlook and risk management strategy.

FAQs

What happens if the underlying asset never hits the barrier for a knock-in option?

If the underlying asset price never touches or crosses the specified barrier level before the expiration date, the knock-in option remains dormant, never activates, and expires worthless. The investor loses the entire premium paid for the option.

Why would an investor choose a knock-in option over a regular option?

Investors choose knock-in options primarily to reduce the upfront cost (premium) compared to a standard option. They are suitable when an investor has a strong conviction that the underlying asset will hit a specific price point, but wants the option to activate only under that precise condition, or when they believe there will be a temporary price movement to a certain level before a favorable long-term trend.

Can a knock-in option be a put or a call?

Yes, knock-in options can be structured as either a call option or a put option. For a knock-in call, the investor gains the right to buy if the barrier is triggered. For a knock-in put, the investor gains the right to sell if the barrier is triggered. The barrier can be either above or below the current market price, depending on the desired trigger.

Are knock-in options traded on exchanges?

Typically, knock-in options are traded in the over-the-counter (OTC) market, directly between two parties (e.g., an investor and an investment bank) rather than on a centralized exchange like the CBOE. This customization allows for tailored terms but can lead to lower liquidity compared to standardized exchange-traded options.

What are the main risks of trading knock-in options?

The primary risk is that the barrier might never be triggered, causing the option to expire worthless and leading to a complete loss of the premium. Additionally, their complex structure and often lower liquidity can make them challenging to understand, price accurately, and exit when desired.