Perhaps a “trigger” warning is in order concerning next Tuesday’s meeting of Finance 4366. Since we’ll be covering the topic of Ito’s Lemma, it will be a bit on the “mathy” side. We will introduce Ito’s Lemma and use it to accomplish (among other things) the following tasks: 1) derive the parameters of the probability distribution for continuously compounded rates of return, and 2) determine the stochastic process for forward contracts. Our class meeting tomorrow will begin with a quiz based upon the assigned readings, which include Hull’s textbook chapter entitled “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“.
As we segue from discrete-time to continuous time pricing models in Finance 4366, you will surely find this topic to be quite challenging. But it is essential, since a basic understanding of the continuous time framework is, as Hull puts it, “central to the pricing of derivatives”. As you read the readings assigned for Tuesday, March 20 (consisting of Hull’s textbook chapter entitled “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“), keep the following exhortation by Hull in mind (this appears as the third paragraph on the first page of the textbook chapter assigned for next Tuesday):
“Many people feel that continuous-time stochastic processes are so complicated that they should be left entirely to ‘‘rocket scientists.’’ This is not so. The biggest hurdle to understanding these processes is the notation. Here we present a step-by-step approach aimed at getting the reader over this hurdle. We also explain an important result known as Ito’s lemma that is central to the pricing of derivatives.”
Here’s the list of assigned readings for next Tuesday’s class meeting:
- Hull Chapter 13 (“Binomial Trees”)
- Binomial Option Pricing Model (single-period)
- Multiple Period Binomial Option Framework
- Dynamic Delta Hedging Numerical Example (calls and puts)
- Dynamic Replicating Portfolio Numerical Example (calls and puts)
- Convergence of the Cox-Ross-Rubinstein (CRR) Binomial Option and Black-Scholes-Merton (BSM) Option Pricing Formulas
The two most important readings for next Tuesday’s Finance 4366 quiz and class meeting are Hull’s “Binomial Trees” chapter and my teaching note entitled “Binomial Option Pricing Model (single-period)”. Tuesday’s class meeting will be primarily devoted to covering the latter reading in particular, although the other readings are also quite important for the next few Finance 4366 class meetings.
… are available at http://fin4366.garven.com/spring2018/ps2solutions.pdf…
Problem Set 2 consists of two problems. The first problem requires calculating expected value, standard deviation, and correlation, and using this information as inputs into determining expected return and standard deviation for 2-asset portfolios. We covered these concepts during last Thursday’s statistics tutorial; also see pp. 10-20 of the http://fin4366.garven.com/spring2018/lecture3.pdf lecture note. The second problem involves using the standard normal probability distribution to calculate probabilities of earning various levels of return by investing in risky securities and portfolios. We will devote next Tuesday’s class meeting to this and related topics.
Problem Set 1 is due at the beginning of class on Tuesday, January 16. Here is a hint for solving the 4th question on problem set 1.
The objective is to determine how big a hospital must be so that the cost per patient-day is minimized. We are not interested in minimizing total cost; if this were the case, there would be no hospital because marginal costs are positive, which implies that total cost is positively related to the number of patient-days.
The cost equation C = 4,700,000 + 0.00013X2 tells you the total cost as a function of the number of patient-days. This is why you are asked in part “a” of the 4th question to derive a formula for the relationship between cost per patient-day and the number of patient days. Once you have that equation, then that is what you minimize, and you’ll be able to answer the question concerning optimal hospital size.
At any given point in time during the upcoming semester, you can ensure that you are on track with Finance 4366 assignments by monitoring due dates which are published on the course website. See http://fin4366.garven.com/readings/ for due dates pertaining to reading assignments, and http://fin4366.garven.com/problem-sets/ for due dates pertaining to problem sets. Also keep in mind that short quizzes will be administered in class on each of the dates indicated for required readings. As a case in point, since the required readings entitled “Optimization” and ” How long does it take to double (triple/quadruple/n-tuple) your money?” are listed for Thursday, January 11, this means that a quiz based upon these readings will be given in class on that day.
Important assignments due on the second class meeting of Finance 4366 (scheduled for Thursday, January 11) include: 1) filling out and emailing the student information form as a file attachment to email@example.com, 2) subscribing to the Wall Street Journal, and 3) subscribing to the course blog. A completed Student information form is graded as a problem set and receives 100 points; if you don’t turn in a Student information form, then you will receive a 0 for this “problem set”. Furthermore, tasks 2 and 3 listed above count toward your class participation grade in Finance 4366.
A course blog has been established for Finance 4366 at the address http://derivatives.garven.com; it is also linked from the “Course Blog” button located on the course website. I recommend that you follow the options, futures, and other derivatives course blog regularly via email, RSS, Facebook, and/or Twitter.
The options, futures, and other derivatives course blog provides me with a convenient means for distributing important announcements to the class. Topics covered on the course blog typically include things like changes in the course schedule, clarifications and hints concerning problem sets, information about upcoming exams, announcements concerning extra credit opportunities, and short blurbs showing how current events relate to many of the topics which we cover in Finance 4366.
If you already are familiar with RSS, this is a great way to subscribe to the options, futures, and other derivatives course blog. By going to the http://derivatives.garven.com/feed webpage, you can subscribe by using Firefox’s Live Bookmarks feature, Internet Explorer’s RSS feed subscription feature, or an RSS reader. If you are either a Facebook or Twitter user, everything that is posted on the options, futures, and other derivatives course blog is automatically posted to Facebook and “tweeted”, so you can also subscribe by “liking” the Finance 4366 Facebook page or by “following” @fin4366 on Twitter. Finally, you can also subscribe via email. The remainder of this blog entry explains how to subscribe to the options, futures, and other derivatives course blog via email.
Email Subscription Instructions:
Email Subscription Instructions: If you would like to receive the risk management course blog via email, you can do this by going to http://derivatives.garven.com and entering your email address in the form provided on the right hand side of that webpage:
After clicking “Subscribe”, the following information will appear on your screen:
Next, check for an email from “Options, Futures, and Other Derivatives <firstname.lastname@example.org>”:
Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:
From that point forward, whenever I post to the course blog, you will immediately receive a nicely formatted version of the blog posting via email. Also, you can opt to change your delivery preferences, or even cancel your subscription.
A subscription to the Wall Street Journal is required for Finance 4366. In order to subscribe to the Wall Street Journal (WSJ) for the Spring 2018 semester, go to http://r.wsj.net/j73NM. Your WSJ subscription includes access to print, online, tablet and mobile editions, and only costs $1 for a 15 week subscription. At your option, you may choose to receive both the digital and paper versions of WSJ or only the WSJ digital version.
Throughout the semester, I will often reference specific WSJ articles in class and on the course blog. Finance 4366 topics (as well as topics in many of your other business school courses) come to life in the world outside the Baylor bubble when you read make a habit of reading the WSJ on a regular basis. Furthermore, if you expect to interview for jobs or internships anytime soon, reading the WSJ will give you a leg up on the competition, since you will be better informed and have more compelling ideas and insights to share with recruiters.
In closing, the following (2 minute) video provides a helpful introduction to the WSJ, providing time-saving tips to help you get the most from WSJ and succeed not only in Finance 4366, but also your other courses and careers: