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November 26, 2018
(1) Assignment No. 10 is now posted and will be due on Monday, December 3.  Please remember to bring your handout from last class with you to class this evening.



November 9, 2018

(1) Assignment No. 9 is now posted and will be due on Monday, November 26.  Please note that you will need market information as of the close of trading on Tuesday, November 13.  Please note that you will need to do this after the market closes on Tuesday, but before it opens for trading Wednesday morning as the price information is not stored historically.

(2) In our next class, following our review of the second mid-term exam, we will continue with our discussion of options. We will discuss boundary conditions and delve into various pricing models including the binomial and Black-Scholes models. As time permits, we will discuss (a) historical and implied volatility estimation, and (b) how to make adjustments to pricing models to accommodate dividends, both discrete and continuously paid dividends. Please remember to bring your option handout from the Monday, November 5 class to our next class.



October 24, 2018

(1) Assignment No. 8
is now posted and will be due on Monday, November 5.  Please note that you will need market information as of the close of trading on Tuesday, October 30.

(2) In our next class on Monday Oct. 29 we will review assignment 7 and then have a concluding discussion of swaps.  With the remaining time, we will then move into options--our second derivatives building block.  Initially, we will look at option payoff diagrams and associated strategies, look at how to read price quotations and option chains, and discuss other institutional arrangements.

(3) Please familiar yourself with the website (formerly and how to read an option quote and option chain. To practice, go to the website, look for "Quotes", then enter a stock symbol and click "Go." Then click and look around to see the variety of information presented.

(4) The second mid-term exam will be on Monday, November 5 and will cover material up to and including the October 29 class.

(5) Finally, next week I will send the class a copy of the Option! software for pricing options using different models.


October 10, 2018

(1) Assignment No. 7 is now posted and will be due on Monday, October 29.  Please note that you will need market information as of the close of trading on Tuesday, October 16.

(2) During our next class we will spend the entire time discussing swaps.  We will discuss various institutional dimensions of the market as well as how to both price and value a swap.  The initial focus will be on interest rate swaps.  As time permits, we will also get into bootstrapping techniques for constructing the zero discount curve.  Discussion of currency and commodity swaps will be covered later depending on progress.

(3) I have emailed you a teaching note on "The Pricing and Valuation of Swaps" that you should read carefully before coming to class.  (This can also be found on the course website under Syllabus/Readings and also in Chapter 28 of Financial Derivatives: Pricing and Risk Management, Kolb and Overdahl, editors, Wiley, 2010). I also emailed you a copy of the *SWAP* software that you can also find posted under Syllabus/Readings on course website.  Please be sure that you have your *SWAP* software fully operational and that you have turned on the appropriate "system requirements" including the required add-ins and enabled macros.



October 2, 2018

(1) On Monday Oct. 8, we will discuss currency futures and forwards including their valuation, institutional arrangements, and some applications. I will also email the class a pre-read on the topic.

(2) We will also review the first mid-term exam. 

(3) Homework 6 is now posted and is due on Monday, October 15.



September 25, 2018

(1) In our next class we will continue our discussion of stock index and single stock futures. We will focus on how market professionals use these products in both active and passive strategies. We will also discuss institutional issues such as performance bonds and circuit breakers. Please remember to bring with you the handout from our last class "SIF Pricing and Arbitrage".

(2) Follow the above discussion, we will use the remaining time for exam 1.

(3) Mini-Lecture 7

***Please carefully study the following illustration to convince yourself that the arguments hold.

        Assume that you are in a world with the following current market conditions:

S (a stock or stock index) = $100; L (Libor) = 6%; d (div yield) = 2%; and you have a 1 year (360-day) investment horizon.

Thus, based on this information, we know that the one-year futures price should be:

F = S*[1 + (L-d)*(T-t)/360]

F = 100*[1 + (.06-.02)*360/360] = 104

Now, consider the following two investment strategies, which I argue are equivalent or that you would be indifferent between choosing:

1. Invest $100 in the stock, or

2. Invest $100 in a money market account and go long one futures based on that stock (at 104).

Scenario A:

Suppose that after 1 year the stock is now at $120. Your ending wealth from each of the two strategies are:

1. Wealth = 120 + .02*100 = 122 (stock value plus dividends received)

2. Wealth = 100*(1+.06) + (120-104) = 106 + 16 = 122 (money market investment plus gain on the futures)

Therefore, both strategies produce the same terminal wealth.

Scenario B:

Suppose that after 1 year the stock is now at $80. Your ending wealth from each of the two strategies are:

1. Wealth = 80 + .02*100 = 82 (stock value plus dividends received)

2. Wealth = 100*(1+.06) + (80-104) = 106 -24 = 82 (money market investment plus loss on futures)

        Again, both strategies produce the identical ending wealth.


September 18, 2018

(1) Assignment No. 5 is now posted and will be due on Monday, October 1.  Please note that you will need market information as of the close of trading on Monday, September 24.

(2) In our next class, we will conclude for now our discussion of interest rate futures and risk management, which we will resume at a later date when we will discuss interest rate swaps. During the remaining time in class, we will begin our discussion of stock index and single stock futures, with our initial focus being on institutional details, valuation, and hedging. Please be sure to read in advance the assignment reading in Chapters 7 and 8 of your text if you have one.

(3) Our first mid-term exam will be on Monday, October 1.

(4) Mini-Lecture 6

Reading Corporate Bond quotations

Corporate bond quotations are typically quoted in points and one hundreds of par (whereas government securities such as Treasury bonds and notes are quoted in points and thirty-seconds of par). To illustrate, suppose you saw a corporate bond quoted at say 108.93. This simply means its price is 108.93% of par. Thus, if you are working with a par or face amount of $1,000, then the price would be $1,089.30. alternatively, the quote may be reported with a $ sign in front; e.g., $108.93. This price would be interpreted the same and would mean $108.93 per $100 of par or $1089.30 per $1000 of par.  Similarly, a quote of 97.500 would translate into a price of $975.00 per $1000 of par.

Also, in contrast to equities, the secondary market for most corporate bonds is not very liquid (and feature relatively large bid-ask spreads). This problem has been further exacerbated by Dodd-Frank that has diminished the role of banks as liquidity providers in this market.

Sometimes when computing the yield to maturity on a bond, you may or may not get the same reported yield that you see on the Finra-markets quote site. If not, this could be for a variety of reasons including the fact that the bond may be callable. Some reporting agencies provide what is known as the yield to worst, which is the lower of yield to maturity and yield to call.  Regardless, you can easily calculate your own yield from the information provided.



September 11, 2018

(1) Assignment No. 4 is now posted and will be due on Monday, September 24. Please note that you will need market information as of the close of trading on Tuesday, Sept. 18 best obtained by going to the indicated site after Tuesday's close for price quotes for corporate bonds, and then accessing the online-WSJ and/or the website for your Tuesday futures prices.

(2) In our next class, we will study the hedging of interest rate risk. We will begin by discussing the construction of synthetic fixed rate and floating rate loans using futures (with some mention of how you similarly may hedge using swaps, caps, and forward rate agreements). In doing so, we will examine the merits of stack versus strip hedging strategies. These examples will then provide a nice lead-in to our exploration of more involved hedging situations in which we will introduce models that involve duration. To help you prepare for class, please read in advance of class and pay particular close attention to the examples and material on pages 211-217 and 219-229 of your text (or equivalent pages if you are using an older edition of the text).

(3) Mini-Lecture 4

Understanding Eurodollar futures

Recall that the underlying "asset" of the Eurodollar futures is actually the rate on a $1 million 3-month Eurodollar time deposit, which you can think of as the 3-month or 90-day Libor rate. However, rather than quote prices in terms of a rate or yield, the exchange uses a convention called the IMM Index. That is, the futures price is quoted in terms of a number that is equal to 100 minus the 3-month Libor rate. Thus, if you observed a Eurodollar futures quoted at 96.00, then this corresponds to a 3-month Libor rate or yield of 100.00 - 96.00 = 4.00%. Similarly a quote of 97.12 would correspond to a rate of 100 - 97.12 = 2.88%. (For more discussion, see pages 152-154 of your text or look in the index for Eurodollar futures.)

(4) Mini-Lecture 5

Understanding interest rate futures price quotes and the value of a price change

Convince yourself that the following price relations indeed hold--

a. For the T-bond, 10-year T-note, and 5-year T-note futures contracts (which each has a notional dollar contract size of $100,000), the dollar value of a 1/32nd change in the futures price is $31.25. To illustrate, assume that the reported futures price quote changes from say 104-160 to 104-170; the contract then has changed in dollar value by $31.25.

b. For the 2-year T-note, the change in value is $62.50 because the notional size of the contract is $200,000 as compared to $100,000 for the earlier three contracts.

c. Note that the last digit in a bond or note futures contract stands for a fraction of a 1/32. For example, you will see a 0, 2, 5, or a 7 (e.g., 110-160, 110-162, 110-165, and 110-167). A 2 stand for .25/32, 5 stands for .5/32 and a 7 for .75 1/32, and a 0 of course means zero fractions of a 32nd. Also, note that the T-bond futures minimum tick size is 1/32, so the last digit in its quote is always 0.

d. For the Eurodollar futures (which has a $1mm notional dollar contract size), a 1 basis point change translates to a change in price of $25. In other words, if the futures price changes from say 95.00 to either 95.01 or 94.99 (which means a change in yield from 5.00% to either 4.99% or 5.01%), the change in value of a contract is $25 (positive or negative depending on whether the position is held long or short, respectively). For this reason, we refer to the Eurodollar futures as having a DV01 (i.e., the "Dollar Value of a 1 basis point change") equal to $25. Also, corresponding to this, the Modified duration of the Eurodollar futures is .25. To see this note that $25 = MD x 0.0001 x $1mm; thus MD must equal .25. The minimum tick for the Eurodollar futures depends on the contract maturity: for the nearby contract it is .25 of a basis point and for all other maturities is .50 basis points.



August 28, 2018

(1) In preparation for our next class, please visit in advance of class the various websites that we covered (i..e., WSJ and CMEGroup) where futures price quotes can be found and be familiar with how to read and interpret prices for the following interest rate futures; specifically, the Eurodollar futures, and the T-bond, 10-year T-note, 5-year T-note, and 2-year T-note futures contracts.

(2) In our next class, we will begin by reviewing homework assignment no. 2.  To start our lecture, we will discuss an important role (in addition to hedging) that futures markets fulfill--facilitating price discovery. We will explore what is price discovery, how futures prices are used commercially for price-basing and improving resource allocation and decision-making, and whether there is a government interest in protecting markets against manipulation. We will introduce the concepts of backwardation and contango, and discuss the implications of these terms for futures prices.

Following this, we will review forward rate estimation, using both bond yield and money market conventions. We will then review contract specs for several of the interest rate futures that we will be using throughout the term (including those for Eurodollars, T-notes, and T-bonds) and begin developing an understanding of their cash market linkages.  With the remaining time, we will begin developing models for interest rate hedging.

(3) Mini-Lectures 1, 2, and 3 Below are a few mini-lectures to clarify concepts used in class.

(ML1) Using LIBOR: First, a brief note about performing calculations with LIBOR interest rates: To determine interest amounts, we will follow standard market practice. Libor uses an actual/360 day count convention, and interest is computed using a "simple" or "add-on" interest method.

For example, if you were to borrow $1mm today and were to repay the loan in 18 days based on a hypothetical Libor rate of 4%, the amount you would repay is computed as $1,000,000*(1+L*days/360) or $1,000,000*(1+.04*18/360)=$1,002,000.  (Note that in today's market environment that short-term Libor rates are more in the range of 2% to 2.50%.)

Note that all the LIBOR rates you will see reported in the WSJ, and elsewhere are already annualized, regardless of the indicated tenor or maturity (e.g., 1 month, 3 month, 6 month, 1 year).  Thus, you just need to multiply the rate by the relevant day count divided by 360.  For example, for Libor rates for Friday 8/24/2018, the reported the 6-month LIBOR rate to be 2.52300 (see either the WSJ or by scrolling down and clicking "American dollar LIBOR USD".) This means that the annualized 6-month LIBOR rate is .0252300 or 2.52300% (NOT 252%!!!).

Now, suppose you want to apply this rate and wish to know how much $1mm will grow to in 180 days.  Note that LIBOR is a money market rate, thus there is no compounding, just simple interest.  Therefore to calculate interest we multiply the rate by the day count divided by 360.  In this example, we thus have:

    $1,000,000 x {1 + .0252300 x (180/360)} = $1,012,615.

In the above, please again note carefully that I used .0252300 and not 2.52300.  Do not make that mistake in your calculations.  Also, please verify the calculation so that you understand the order of the calculations in parentheses/brackets.

Suppose instead I want to know what $1mm will grow to in say 194 days.  If I am willing to assume that the term structure is fairly flat around the 180-day maturity and thus the 6-month rate is a good approximation to the 194 day rate, we then get:

    $1,000,000 x {1 + .00252300 x (194/360)} = $1,013,596.17. 

Finally, if I was working with say a 100-day maturity, I would instead use the 3-month LIBOR rate rather than the 6-month rate because of the closer matching maturity.  That is, 100 days is closer to 90 rather than 180 days).  The two sources report the 3-month LIBOR rate for the same date at 2.31725%.  Thus, $1mm invested at this rate for 100 days will grow to:

    $1,000,000 x {1 + .0231725 x (100/360)} = $1,006,436.81.

In case you have an interest in reading how the ICE (Intercontinental Exchange) Benchmark Administration determines the daily Libor rates, please see:

(ML2) Volume versus Open Interest: For clarification and your future reference, here is a short summary explanation to help clarify the difference between Volume and Open Interest as relates to futures trading.

Volume is a measure of the number of contracts traded during some specified trading interval, e.g., a trading session, a day, a month, and so on.

Open interest is the number of contracts currently open and outstanding. Volume is related to open interest, but a change in volume can result in an increase, decrease, or leave unchanged open interest.

Consider the following example:

Assume that there are 3 traders, x, y, and z, who are each interested in trading the March 2018 natural gas futures, and which just today assume has been listed for trading for the first time. Thus, volume for the day is initially zero and open interest is also zero since the contract heretofore has never traded.

Trader x sells 1 contract to y, the long. Volume is 1 and open interest is 1.

Trader x next sells 1 contract to z, the long party to this second contract. Volume for the day is 2 and open interest is also 2. Note that x is now short 2 contracts while both y and z are long 1 contract each.

Trader y sells 1 contract to z. Volume is now 3 and open interest remains at 2. Note that z is now long 2 contracts and that y has exited the market. Trader x is still short 2 contracts.

Trader z sells 2 contracts to x. Volume for the day is 5 and open interest is zero as there are now no open contracts.

(ML3) "Production follows Sales": We spoke in class about one strategic response to ongoing currency risk that many firms follow, which is to locate operations close to the point of sale. The result of this is to push more operating costs into the same currency as to which sales are in.  (As an alternative, some firms alter their cost structure by issuing debt denominated in the same currency.)  To illustrate how this reduces cash flow volatility, consider the following additional simple example.

Assume a U.S. company has annual sales in Mexico in the amount of 100 pesos. Manufacturing is done in the U.S. where cost of goods sold is $9. The exchange rate is currently 0.10$/peso, but could fluctuate between .08 and .12$/peso. Thus, expected $ revenues are $10 and profit (net cash flow) is $10 - $9 or $1. However, if the dollar strengthens to say 0.08$/peso, $revenues fall to $8 and profit is now a loss of $1. Similarly, if the dollar weakens to say .120 $/peso, $revenues increase to $12 and profit is $3. In sum, profits are expected to be $1, but could range between -$1 and +$3.

Now assume the company produces instead in Mexico. Cost of goods sold is thus 90 pesos (=$9/.1) and profit is 10 pesos (100 - 90) before conversion to dollars. $ profits are expected to still be $1 (10*0.10), but could vary between +$0.80 and +$1.20 (calculated as 10*0.08 and 10*.120). While the expected profit (net cash flow) remains the same at $1, its volatility due to exchange rate movements has been reduced.


August 21, 2018

(1) To briefly recap our first lecture, we began by introducing an economic framework for analyzing whether a firm's engagement in financial risk management is justifiable from the perspective of its shareholders. Potential channels that we identified through which risk management can enhance firm value included "numerator effects" (that is, the potential of risk management to have effects on future expected net cash flows) due to, for example, the reduction of expected bankruptcy, financial distress, and related business disruption costs; the reduction of underinvestment and adverse selection problems; and the reduction of taxes.  Basically, this means that to the extent that the firm employs more debt, has higher growth opportunities, and has significant tax loss carry-forwards or is in the convex region of marginal tax rates, then the firm is more likely to experience greater potential benefits from hedging.

We also discussed "denominator" effects, which refers to the potential of risk management to have an effect on lowering a firm's cost of capital. I also referenced the role of executive compensation and ownership structure on the incentives of managers to engage in risk management.

Following this, we introduced a definition of a derivative, considered a number of common derivative structures (e.g., swaps, forwards, futures, and options), and identified their market venue (both OTC and exchange-trade instruments). In addition, we looked at recent BIS statistics regarding OTC market size including breakdowns according to product and instrument type, and by currency and maturity. We also looked at various market statistics for exchange traded futures.

We then discussed an early and seminal application of hedging, the Salomon Brothers/Merrill Lynch underwriting of an IBM debt offering and the accompanying T-bond futures hedge that was used to control the interest rate risk inherent in the underwriting. In our review, we did some risk analysis and applied a commonly used measure of risk often used in fixed income analysis known as duration. We will use duration, modified duration (MD) and convexity throughout the course as well as related concepts such as DV01 (an industry term that refers to the dollar value of a 1 basis point interest rate movement and is computed according to DV01 = MD x Price x .0001).

(2) At our next class we will begin by reviewing homework no. 1.  Also, in our next class, we will continue with the "why" of risk management during which we will discuss various alternatives and substitutes for reducing the demand for derivatives. Included will be a discussion of the importance of identifying natural hedges. Then, as we transition to the "how" of risk management, we will develop a understanding of the institutional environment for derivatives including their regulatory framework, documentation, margining and daily resettlement, and reporting conventions. We will continue with our discussion of the two derivative building blocks: the futures/forward contract and the option contract. We will discuss similarities and differences between futures and forward contracts. We will cover reading and interpreting futures price quotes and related terms of trade. We will conclude by discussing concepts related to the valuation of futures and forward contracts. Specifically, we will develop a useful pricing model that is based on no-arbitrage principles.

(3) Finally, please review homework No. 2 prior to the next class (see posted under "Assignments") so that you can more easily pick up on key thoughts during the lecture.  Also, please make a note to yourself that to be prepared to get the data for the assignment in a timely manner; you will need to access market information available at the on-line WSJ (see, and click on 'Market Data Center') for the close of trading on Tuesday, August 28. The WSJ and CMEGroup websites should be updated sometime late that Tuesday or early Wednesday to reflect this information.  As you work the assignment, I look forward to seeing your summaries of the risk management practices of your selected firm, its specific uses of derivatives if any, and most importantly your thoughts rationalizing or disapproving of their risk management practices based on the economic rationales that we discussed. Be sure to avoid simply saying that because your selected firm faces lots of risk that they can benefit from managing risks. This is not the necessarily so and in some cases can lead to destroying firm value. Rather, take some time to analyze the firms capital structure and get a sense for the amount of debt they have outstanding. Is the firm well-positioned to service the debt or could a shortfall in cash flow or earnings create potential problems? Also, is the firm growing or have growth opportunities that could be impaired due to adverse movements in interest rates, exchange rates, commodity prices, etc?


August 2, 2018

Welcome all to FI 4200 "Introduction to Derivative Markets"!

I hope that you will find this course to be a superb and one of your most beneficial experiences at GSU.  I am looking forward to seeing each of you at the first class on August 20.  As a reminder, our class meets at 4:30pm in Room 323 of the Aderhold Learning Center.

Please check back here for updates throughout the term.  Also, I will be communicating with you through your email account so please get in the habit of checking it regularly.  (If you prefer to receive your messages at another email address, please link your gsu student address to it as this is the only email address that is officially recognized by the university for communication to students.)

Please do the following prior to the first day of class:

(1) Review and download the Fall 2018 syllabus (see the "Syllabus/Readings" link)

(2) The textbook is entirely optional, but if you want to get one the ISBN number is 978-1-4051-5049-1.  Note that any used/older edition will also work fine.

(3) Go to, shade "Education" and click on the Education Home link.  This will take you to and you will see a set of tutorials/presentations that provide a nice introduction to derivatives, exchanges, and futures.  At a minimum please take a few minutes to watch the following video group at: 

(i) Managing Risk at CME Group - How it All Works (there are about 8 chapter videos, each only about 1-2 minutes long).

(ii) And then at , go quickly through the various links under "Get the Basics", "See the Impact", and "Explore the Marketplace".

(4) Important: Please begin to build a spread sheet that will compute duration and modified duration.  Along these lines, you should also go ahead and begin working on Assignment No. 1. I will send it to you via a separate email with instructions.  Note that I will attempt to post all homework exercises under "Assignments" on the course website.  For more information on this, I will send you an email with a couple of short articles attached that provide an excellent primer on calculating duration with examples.

As you have time, please also:

(5) Give a quick review to the assigned chapters for the first day of class and begin reading articles 2 and 3 that are posted under the Syllabus/Readings link.

(6) Here is a brief summary of what we will discuss at our first lecture:

We will begin by developing a working definition of a derivative, and then consider a number of common derivative structures as well as identify their market venue (both OTC and exchange-traded instruments).  We will look at some recently released statistics regarding global market size, including breakdowns according to product and instrument type, and maturity.

In our inspection of the various types of derivatives, we will see that basically all derivatives can be viewed as one or a combination of two basic building blocks: the futures/forward contract and the option contract.

To illustrate both types of contracts, we will review two case studies.  In the first, we will review an early case study regarding the use of financial futures for hedging--the Salomon Bros/Merrill Lynch underwriting of IBM's first public debt offering.  This event is sometimes credited with being the true motivating birth of the financial futures markets. In the second case study, we will look a structured debt security. Using basic financial engineering techniques, we will identify and value embedded options in the product and show how the overall security was priced from a yield perspective.

We will subsequently explore the "why" of financial risk management in which we examine the various channels through which financial risk management can potentially enhance shareholder value.  We will discuss how and under what conditions hedging can reduce financial distress and related business disruption costs, reduce under-investment incentives and adverse selection problems, and reduce taxes.

See all at our first class and please do not hesitate to call me or stop by at any time!


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