### Important information about Finance 4366 assignments for Thursday, March 30, and Tuesday, April 4

I posted the American Options problem set (Problem Set 8) on the course website earlier this evening.  It is due at the beginning of class on Tuesday, April 4.

The readings assigned for Thursday, March 30 include the “Wiener Processes and Ito’s Lemma” chapter in the Finance 4366 textbook, along with two other readings which I have authored: 1) Applying Ito’s Lemma to determine the parameters of the probability distribution for the continuously compounded rate of return, and 2) Geometric Brownian Motion Simulations. While Quiz 8  (due via Canvas by 2 pm on Thursday, March 30) is based primarily on the textbook chapter, we will also rely on these other readings as we cover some of the most important foundational principles for continuous time finance during the next few class meetings.

Regarding Thursday’s Finance 4366 class, unfortunately, I cannot meet with you that day.   However, I have uploaded a recording of the introductory lecture for the “Wiener Processes and Ito’s Lemma” topic at https://bit.ly/itoslemma, which you are required to watch and report on.   In your report, provide a brief (1-2 page) synopsis of the topics presented in the recorded lecture. Email your summary as an attached Word or PDF file to fin4366@gmail.com by no later than 2 p.m. on Tuesday, April 4. By complying with these requirements, you will receive attendance credit for Thursday’s class; if not, then you will be marked absent from Finance 4366 for that day.

I hope everyone enjoys Diadeloso tomorrow, and I will look forward to seeing all of you in class on Tuesday, April 4!

### Lecture notes for tomorrow

The lecture notes we’ll be covering in class tomorrow include Early Exercise of American Call and Put Options on Non-Dividend Paying Stocks and Dividends and American Options. The first note addresses American options for non-dividend paying stocks. The second note illustrates the pricing implications of (discrete) dividend payments for European options, and also shows how dividend payments affect incentives for early exercise of American call options.

### Change in plans for tomorrow

I have decided to not start the “Wiener Processes and Ito’s Lemma” topic until Thursday, March 30, so the quiz based on the following 3 readings: 1) Hull, Chapter 14 (“Wiener Processes and Ito’s Lemma”), 2) Applying Ito’s Lemma to determine the parameters of the probability distribution for the continuously compounded rate of return, and 3) Geometric Brownian Motion Simulations, will become available on Canvas beginning at 2 pm on Wednesday, March 29.

Tomorrow will be devoted to coverage of the “Early Exercise of American Call and Put Options” topic.  I’ll soon post Problem Set 8 (based on this topic), the due date for which will be Thursday, March 30.

### Cox, Ross, and Rubinstein Class problem for tomorrow

Here’s a class problem (linked below) we’ll work on during tomorrow’s class meeting which is designed to help students understand how to apply the Cox, Ross, and Rubinstein binomial option pricing model. Between now and then, if time permits, I’d like to encourage all of you to try to complete this problem prior to coming to class tomorrow. Essentially, this is a simpler version of Problem 2 on Problem set 7.

We’ll also delve tomorrow into the topic of American versus European options. Looking forward to seeing all of you tomorrow!

Cox, Ross, and Rubinstein Class problem

### Problem Set 7, problem 2 helpful hints…

Here is a Q&A I just had with a Finance 4366 student about Problem Set 7, problem 2:

Student: Dr. Garven, I am a bit confused about problem 2 for PS7. Do you want us to write out a huge binomial tree table with 15 steps and have that over the 6-month period of the call? Or do just want us to use an equation to get the price of the call?  Thanks, Student

Dr. Garven: With the Cox-Ross-Rubinstein (CRR) model, there is no need to determine the entire binomial tree for a large number of timesteps. Since European options cannot be exercised prior to expiration, only the terminal nodes at which the call ends up in-the-money matter for pricing purposes.  The subset of in-the-money terminal nodes is identified by first calculating the minimum number of up moves required to end up in the money.  To do this, use the following equation (derived and explained on p. 36 of the Binomial Trees lecture note ): $b= ln(K/S{d^n})/\ln (u/d)$, and round b up to the nearest integer (“a“) greater than b. Once a‘s value has been determined, there will be   (+ 1 – a) in-the-money terminal nodes and a out-of-the-money terminal nodes.  For example, suppose the exercise price in this problem is $80 rather than$120.  With n = 15 timesteps, the minimum number of up moves required for that call option to expire in the money is a = 5; such an option would end up with 11 in-the-money terminal nodes and only 5 out-of-the-money terminal nodes 6 months from now.

Next, calculate each of the call option payoffs (given by ${u^j}{d^{15 - j}}S - K$) at each of + 1 – a in-the-money terminal nodes.  Once you know these payoffs, then you can calculate the risk neutral expected value of the call option 6 months from now by multiplying each payoff by its risk-neutral probability and adding the product given by $\left( {\frac{{15!}}{{j!\left( {15 - j} \right)!}}} \right){q^j}{\left( {1 - q} \right)^{15 - j}}\left( {({u^j}{d^{15 - j}})S - K} \right)$ for the + 1 – a in-the-money terminal nodes.  This sum corresponds to the (risk neutral) expected value of the call option 6 months from now.  The final step in determining the arbitrage-free price of the call option simply involves calculating the present value of this sum, for 6 months and at the riskless rate of interest (2%).

Once you know the arbitrage-free price for the call option, you can obtain the price of an otherwise identical put option by simply invoking the put-call parity equation!

### This week in FInance 4366: Important Announcements

1. Problem Sets 7 and 8 are now due on March 23 and March 28 respectively (both moved back from March 21 and March 23).
2. Be sure to read my 5-page “Early Exercise of American Call and Put Options on Non-Dividend Paying Stocks” prior to coming to class tomorrow. This way, you will get much more out of the lecture – I promise!. However, there won’t be a quiz on this reading prior to our Tuesday class meeting.
3. Prior to our class meeting on March 23, read Hull Chapter 14 (“Wiener Processes and Ito’s Lemma”) and my teaching notes entitled Applying Ito’s Lemma to determine the parameters of the probability distribution for the continuously compounded rate of return and Geometric Brownian Motion Simulations and take the Canvas quiz based on these readings.

# Overview:

Baylor has two student-managed investment funds: A large-cap stock fund currently valued at approximately $14.2 million, and a small-cap stock fund currently valued at approximately$1.1 million. Students in the Portfolio Practicum courses are directly responsible for managing the portfolios, while learning the techniques used by professionals to analyze and select individual stocks. Each student will also learn how to use Bloomberg, FactSet, Thomson Eikon and other resources commonly used in the investment management industry.

# The Classes:

Small-Cap: Mondays, 2:30-4:00pm, for a total of 16 weeks spread across both the Fall and Spring semesters
Large-Cap: Mondays, 5:00-7:30pm, for the Fall Semester only
Location: Hodges Financial Markets Center (Foster 116)
Structure: Designed after the format of an investment management firm and built around student participation.

Designed to cover two-semesters, the Small-Cap Practicum gives students experience researching, analyzing, and managing a portfolio of small capitalization (small-cap) stocks. The Fall course introduces equity research methods, including valuation, modeling, fundamental analysis, and cultivating resources. Student analysts, in teams, complete an initiation-of-coverage research report on a firm. Their research may include the team talking to company management and utilizing various information sources including financial documents, trade associations, and competitors, customers, and suppliers of the firm. In the Spring, one team will compete in the CFA Investment Research Challenge, while other student teams will continue to research and present new opportunities for the portfolio.

The Large-Cap Practicum is a one-semester course. The class structure is designed after the operational format of a funds management firm and is built around student participation. Specifically, two-person teams are assigned to cover each sector of the S&P 500. Although there are course readings, the course primarily consists of teams preparing and presenting to the class detailed reports on stocks in their sector. Every class member is involved in a discussion of each stock. Following the presentation and discussion, the team makes a recommendation on each stock. The class votes and the recommendations of the class are implemented.

For a better understanding of either course, you are welcome to attend all or part of a class session this semester! Both classes meet on Monday. The Small-Cap class begins this semester at 2:30 pm and the Large-Cap class begins at 5:00. The available Mondays this semester are March 20 (Large-Cap) and 27 (Small-Cap and Large-Cap).

# Professors (Small Cap):

• David Morehead, CFA, Chief Investment Officer at Baylor University – Office of Investments.
• Renee Hanna, CFA, Managing Director of Investments at Baylor University – Office of Investments.

# Professors (Large Cap):

• Brandon Troegle, CFA, CAIA, Senior Portfolio Advisor at Northern Trust Corporation.
• Taylor Finch, CFA, Managing Member at Finch Capital Management.

How to Apply:

Complete the online application at https://www.baylor.edu/business/financialmarkets/apply. The application will be open beginning at 8:00 am on Monday, March 20.

In addition to the usual grades, contact, and background information you will need to provide:

1. Statements of why you wish to take the course and your career plans/goals
2. Description(s) of any investment and/or finance-related experience

The deadline for submission is Midnight, Monday, March 27.

Each course is open to both graduate and undergraduate business students with a minimum 3.2 GPA, a strong academic record, and an interest in investments*. Applicants will be evaluated by a Finance faculty committee.

### Investor Anxiety Hits a Fever Pitch After Silicon Valley Bank Collapse

This WSJ article provides quite a bit of detail about how investors are hedging their exposure to bank risks using a wide variety of different types of financial derivatives.  This article notes, among other things, that trading volumes in put options, especially puts written on the SPDR S&P Regional Banking ETF (exchanged traded fund), are quite popular, with trading volumes on the Chicago Board Options Exchange (CBOE) hitting near record daily volumes.  Other popular strategies mentioned in this article include shorting bank stocks, buying credit default swaps on bank stocks, and buying call options on the VIX index in hopes of protecting investors against further stock declines.

### Solutions (and Spreadsheet) for Solving the 1-timestep Delta Hedging, Replicating Portfolio, and Risk Neutral Valuation Class Problem Set

1. Here are the (fully written out) solutions for this class problem.  Pages 1-3 explain (correctly as well as in considerable detail) the delta hedging approach for 1 timestep calls and puts.

2. Here is the spreadsheet we used in class today; while it only provides solutions for the replicating portfolio and risk neutral valuation methods, the worksheets contained therein also carry out 2 timestep calculations for both of these methods.

Click to access OneTimestepSolutions.pdf