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Does a look back call become more valuable or less valuable as we increase the frequency with which we observe the asset price in calculating the minimum?

Short Answer

Expert verified
A look back call becomes more valuable with increased observation frequency.

Step by step solution

01

Understanding a Look Back Call Option

A look back call option is a type of exotic option where the payoff depends on the maximum or minimum price of the underlying asset over a certain period. For a look back call, the payoff is typically calculated as the difference between the maximum price observed during the period and the price at the end of the period. Hence, the value of this option benefits from a higher maximum asset price being observed.
02

Effect of Observation Frequency

As the frequency of observing the asset price increases, the chance of capturing a higher maximum price also increases. This is because with more observations, there are more opportunities to record a peak in the asset's price, which directly affects the calculation of the maximum price and hence the value of the look back call option.
03

Implications for the Look Back Call's Value

Given that the value of a look back call depends on accurately capturing the high points of the asset's price, increasing the frequency of observations allows for a better assessment of the maximum price. This leads to the look back call becoming more valuable, as there is a higher likelihood of recording a greater maximum price, thus increasing the payoff.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exotic Options
Exotic options are fascinating financial instruments that extend beyond traditional call and put options. They come with unique features and structures, making them versatile tools for different investment strategies.
A look back call option is a type of exotic option. Unlike standard options, the payoff for exotic options like a look back call depends on the past behavior of the underlying asset, such as its maximum or minimum price over a specific period. This feature allows investors to "look back" at the asset's price history, making these options attractive for those seeking to capitalize on favorable price movements without precisely timing the market.
  • Exotic options often come with higher risk and complexity due to their unique payoff structures.
  • Their pricing requires sophisticated mathematical models and a deep understanding of the underlying factors affecting their value.
  • These options can be customized to suit specific investment needs, leading to a wide variety of exotic options available in the market.
Understanding exotic options is essential for investors looking to diversify their portfolios and leverage advanced financial strategies.
Asset Price Observation
Asset price observation plays a crucial role in valuing look back options. Unlike standard options that typically rely on the asset's price at expiration, look back call options consider the highest or lowest price observed during the option's lifespan.
By increasing the frequency of asset price observations, investors have more opportunities to capture the peaks of the asset's price. This can significantly affect the valuation of the option.
  • Regular observations can better capture fluctuations and volatility in the asset's price.
  • A higher number of observations increases the likelihood of recording extreme price points, which are crucial for determining the option's payoff.
  • Frequent observation provides a comprehensive view of the asset's price behavior, leading to a more accurate assessment of potential maximum or minimum prices.
In the context of look back options, observing asset prices frequently enables a better estimation of potential payoffs, enhancing the option's attractiveness when peak price points are crucial for option valuation.
Option Valuation
Option valuation is the process of determining the fair value of an option, taking into account various factors such as time, volatility, and the behavior of the underlying asset.
For look back options, this valuation becomes more complex, as it includes the historical prices of the asset over the option's term.
The value of a look back call option specifically hinges on accurately capturing historical price highs, which directly influence the payoff.
  • Option pricing models for look back calls must incorporate mechanisms to account for recorded highest and lowest prices.
  • Increasing observation frequency refines the valuation model, as it increases the chances of capturing optimal price points.
  • Factors like market volatility and asset performance trends are crucial in accurately pricing these options.
For investors, understanding the dynamics of option valuation is key to gauging potential returns and risks associated with these exotic options. Accurate valuation ensures that investors can make informed decisions, maximizing their strategic benefits from using look back options.

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Most popular questions from this chapter

Use a three time step tree to value an American put option on the geometric average of the price of a non-dividend-paying stock when the stock price is $$\$ 40,$$ the strike price is $$\$ 40,$$ the risk-free interest rate is \(10 \%\) per annum, the volatility is \(35 \%\) per annum, and the time to maturity is 3 months. The geometric average is measured from today until the option matures.

Suppose that the strike price of an American call option on a non-dividend paying stock grows at rate \(g\). Show that if \(g\) is less than the risk-free rate, \(r,\) it is never optimal to exercise the call early.

Consider an "as you like it" option where the holder has the right to choose between a European call and a European put at any time during a 2 -year period. The maturity dates and strike prices for the calls and puts are the same regardless of when the choice is made. Is it ever optimal to make the choice before the end of the 2 -year period? Explain your answer.

Suppose \(c_{1}\) and \(p_{1}\) are the prices of a European average price call and a European average price put with strike \(X\) and maturity \(T ; c_{2}\) and \(p_{2}\) are the prices of a European average strike call and European average strike put with maturity \(T ;\) and \(c_{3}\) and \(p_{3}\) are the prices of a regular European call and a regular European put with strike price \(X\) and maturity \(T .\) Show that $$c_{1}+c_{2}-c_{3}=p_{1}+p_{2}-p_{3}$$

Does a down-and-out call become more valuable or less valuable as we increase the frequency with which we observe the asset price in determining whether the barrier has been crossed? What is the answer to the same question for a down- and-in call?

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