Assignment 5 FIN 421-SPRING 2024

Assignment 5 FIN 421

Assignment 5

Due: Thursday, 04.11.24 at 11:59 pm

In this assignment you will apply the binomial tree model to determine the fair value of an Asian option.

Valuing an Exotic Option

The payoff of an Asian option is a function of the underlying’s average price over the life of the option. These average price options are most commonly written on exchange rates and interest rates. For example, an exporter such as Mercedes Benz may have a fairly steady monthly foreign currency income stream from it’s car sales abroad. In order to hedge it’s currency exposure over the next year, Mercedes may acquire an option whose payoff is dependent on the average exchange rate over the next 12 months.

At maturity, an Asian call option has a payoff of max(0; S — A}, where S is the average price of the underlying asset over the option’s life. This implies that the option’s payoff is path dependent, i.e. it’s payoff does not only depend on the price of the underlying at maturity, but instead on the entire price path. To price the option, we have to rely on a tree that is non-recombining:

Note that while the price of the underlying is identical for the two paths “ud” and “du” (since udSo = duS$), the payoff of the Asian call differs across the two states. For “ud”, the average price equals S(ud) =         + uS$ + udS$), whereas for “du” is equals S(du) =

| (So + dS₀ + duS$) (a different value). In general, for a tree with n periods, there will be 2n final payoff states.

For the example we will consider, the underlying has a current price of $100 and an annual volatility of 20%. The (continuously compounded) risk free rate is 2% p.a. Your task is to value an Asian call with a strike price of X = 95 that has 3 months to maturity and cannot be exercised early.

Steps:

1. You will need 4 trees: (1) underlying S (2) Asian call C (3) hedge ratio A (4) cash account

B.

2. Begin by setting up the tree for the While it is possible to write this tree as recombining (as in the examples we considered in lecture 10), it will be easier for the subsequent analysis to write the tree of the underlying as non-recombining (as in the illustration above).
3. Next, set up the tree for the Asian call and compute its’ payoffs in the final
4. Then, set up trees for the hedge ratio and the cash account and work your way from the last period back as usual.
5. All trees should be non-recombining as in the illustration

Questions:

1. Based on a 2-period tree, what is the no arbitrage price of the Asian call?
2. Based on the same tree, describe in detail the trades necessary for implementing the dynamic trading strategy that replicates the Asian call’s payoff. How many shares of the underlying to you buy/sell at each point in time and in each state (at each node in the tree)? What cash flow (in dollars) is generated by these trades? How much risk-free debt do you take out or repay at each point in time and in each state?

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• Discussion Questions (DQ)

Initial responses to the DQ should address all components of the questions asked, including a minimum of one scholarly source, and be at least 250 words. Successful responses are substantive (i.e., add something new to the discussion, engage others in the discussion, well-developed idea) and include at least one scholarly source. One or two-sentence responses, simple statements of agreement or “good post,” and responses that are off-topic will not count as substantive. Substantive responses should be at least 150 words. I encourage you to incorporate the readings from the week (as applicable) into your responses.

• Weekly Participation

Your initial responses to the mandatory DQ do not count toward participation and are graded separately. In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies. Participation posts do not require a scholarly source/citation (unless you cite someone else’s work). Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.

• APA Format and Writing Quality

Familiarize yourself with the APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in Loud-cloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required). Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation. I highly recommend using the APA Publication Manual, 6th edition.

• Use of Direct Quotes

I discourage over-utilization of direct quotes in DQs and assignments at the Master’s level and deduct points accordingly. As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content. It is best to paraphrase content and cite your source.

• LopesWrite Policy

For assignments that need to be submitted to Lopes Write, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me. Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes. Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own? Visit the Writing Center in the Student Success Center, under the Resources tab in Loud-cloud for tips on improving your paper and SI score.

• Late Policy

The university’s policy on late assignments is a 10% penalty PER DAY LATE. This also applies to late DQ replies. Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances. If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect. I do not accept assignments that are two or more weeks late unless we have worked out an extension. As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.Assignment 5 FIN 421

• Communication

Communication is so very important. There are multiple ways to communicate with me: Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class. Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours. Assignment 5 FIN 421

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