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April 5, 2018

(1) Our next meeting on Wednesday, April 18 will be our last class session--how time flies by!.  I anticipate that the final exam will start at 7:10 and you will have 2.5 hours to complete it.  We will begin the class by reviewing homework 7 and then move on to various topics with an anticipated stop time of around 7pm to allow a transition to the final exam.  In the interim, I would like to do a team study of an option pricing application to a private equity investment.  Also, and depending on time, we will discuss assorted topics related to American option pricing, currency options and futures options.

(2) As a reminder, the deadline for the submission of the financial data analytics project is 6pm on Monday, April 23.



March 22, 2018

(1) Homework 7 is now posted and is due on Wednesday, April 18.  Please note that you will need to download option prices following the close of trading on Thursday, April 5 from the website.

(2) In our next class (April 4), we will begin by reviewing the latest homework assignment no. 6.  Following that we continue our discussion of options.  We will review volatility estimation including the historic and implied volatility methods.  We will also discuss "volatility smiles".  Following that we will explore ways to make adjustments to the Black-Scholes model to accommodate dividends and will consider both discrete and continuously paid dividends.  We will then discuss the "Greeks", which refer to the various sensitivities of option prices to the model's various inputs, and we will also discuss their uses for risk management.  With any remaining time, we will discuss American option pricing and conditions for early exercise.

Please remember to bring to class your main option handouts from the prior class.



March 8, 2018

(1) Homework 6 is now posted and is due on Wednesday, April 4.  You will need to obtain market information from the website related to trading conducted on Thursday, March 22.  Please note that you will need to do this after the market closes on Thursday, but before it opens for trading Firday morning as the price information is not stored historically.

(2) On Monday, we will begin class by reviewing the swaps homework assignment no. 5 and then conclude our coverage of swaps with a discussion of currency swaps and the notion of DV01 and hedging as applies to swaps.  Please remember to bring your swaps handout from our last class with you.

(3) 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.  We will then 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.

(4) Before coming to class, please familiar yourself with the website 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.

(5) Also, I will be emailing all a copy of "Option!", which is a really nice option pricing software (I will be sending it through the university's "send a file" procedure; when you receive the notification please download asap as its availability will disappear if you do not download it soon.  After downloading, please familiarize yourself with it and be sure that it is fully functional and operational.


February 22, 2018

(1) Assignment 5 is now posted and is due on Wednesday, March 21.  You will need to remember to obtain a variety of market information related to trading as of Thursday, March 8.

(2) In our next class, we will conclude our study of stock index and single stock futures.  Following that we then move into discussing swaps.  We will consider various institutional dimensions of the market as well as how to both price and value a swap.  Our initial focus will be on interest rate swaps.  During class we will also get into bootstrapping techniques for constructing the zero discount curve and we will also explore the importance of making convexity adjustments when pricing and valuing swaps.  Our discussion of currency and commodity swaps will likely be covered in the subsequent class depending on progress.

(3) I will email each of 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 will also email 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.



February 9, 2018

(1) Assignment No. 4 is now posted (due on Wednesday, March 7). Please note that you will need to collect market information as of the close of trading on Thursday, February 22 obtained from among various sources, e.g., the WSJ, WSJ online, and the website.

(2) In our next class, we will conclude for now our discussion of interest rate futures/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 discuss stock index and single stock futures.

a.  Our initial focus will being reviewing institutional details, valuation, and hedging.

b.  In our next segment we will then focus on how market professionals use these products in both active and passive strategies.

c.  Depending on time, we will also discuss events surround the "flash crash" and triple witching effects

(3) Pre-Reading: To prepare for class, please read before coming to class pages 13-14 of the "Scams, Scoundrels and Scapegoats ..." article (see the section titled "War Stories"), which can be found under the Syllabus/Readings link of the course website.  Also, for those of you with a text, please read Chapters 7 and 8.

(4) Mini-Lecture 7

(ML7) Stock versus Stock Index Futures Investing

Please carefully study the following illustration to convince yourself that the arguments hold.  The basic concepts described here will not only help your understanding of valuation and arbitrage involving stock index futures, but will also be shown in class to underlie more advanced strategies used in industry including portable alpha and enhanced indexing.

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).  (This is sometimes referred to as a fully collateralized futures position.)

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.



January 25, 2018

(1) In our next class, we will begin by reviewing Homework 2.  During this discussion, I will also say a few words about the accounting treatment of derivatives as it relates to FAS 133.

(2) The main focus of the class will be the hedging and management of interest rate risk.  We will begin with discussing the sensitivities of interest rate futures to interest rates and discuss the notion of futures duration.  We will then look at some hedging examples including 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, for this having a textbook, 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).

Following this, we will extent our discussion of interest rate risk management (with futures) by also exploring immunization strategies. We will look at the use of derivatives in facilitating both "planning period" and "asset-liability" forms of immunization.

(3) During class we will also look at a case study of the events surrounding the so-called derivatives "debacle" involving the firm Metellgesselschaft ("MG"). I will email you a couple of related handouts to this case that you should review prior to coming to class so that you will be better prepared to discuss. The MG case will nicely reinforce and tie together several concepts that we have considered recently in class including the merits of a stack and roll versus strip hedging strategy; some issues related to backwardation versus contango in futures prices; margins; and the considerations that firms should give to margining and liquidity maintenance when conducting a hedging program.

(4) Assignment No. 3 is now posted (due on Wednesday, February 21). Please note that you will need to collect market information as of the close of trading on Thursday, February 8 obtained from among various sources, e.g., the WSJ, WSJ online, and the website.

Mini-Lectures 4-6

(ML4) 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%. A quote of 99.39 would correspond to a rate of 100 - 99.39 = 0.61%.  (For more discussion, see pages 152-154 of your text or look in the index for Eurodollar futures.)

(ML5) 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.

(ML6) 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.  The issue of liquidity will come up in our next class when we discuss immunization strategies using futures.

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.



January 12, 2018

(1) Assignment 2 is now posted (due on Wednesday, February 7). Please note that you will need to obtain various pieces of market information as of the close of trading on Thursday, January 25. You can get these by going to the CME Group exchange website,, the WSJ, and/or WSJ-online.  Also, please give the assignment a quick read prior to coming to our next class so that you can more easily pick up on key thoughts during the lecture.

(2) To briefly recap our first lecture, we began by reviewing key tenets of Finance for purposes of developing a framework for understanding the value proposition of financial risk management.  Following that we introduced a more formal 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; ensuring funding to support the firm's strategic plan; 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 referred to "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 (or not 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 with a "linear" derivative such as futures.  Specifically, we looked at 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).

Following this, we looked at an application involving "non linear" derivatives such as options. Specifically, we looked at how Household Industries was able to monetize an exposure to a large holding of Time Warner preferred stock through a debt offering that had embedded option features.  This offering provided the firm with down-side risk exposure while at the same time allowing the firm to participate in some of TW's potential upside movements.  By recognizing the nature of these various exposures, we were able to use concepts based on option pricing theory to help price the debt.

Finally, we discussed the concept of natural hedges and how the recognition of natural hedges can mitigate the need to engage in hedging.

(3) In our next class, we will begin by reviewing the homework. In one of your assignments you are asked to investigate the risk management practices of your selected firm, its specific uses of derivatives if any, and most importantly developing 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?

Following the homework review, 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.

We will then continue with our discussion of the first of our two derivative building blocks: the futures/forward 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 and illustrate its robustness by applying the model to a variety of futures contracts.

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.

(4) Introduction of Mini-Lectures:

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 stated 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 60 basis points or .60%; hence in the above calculation you would use .0060 in place of .04.)

(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.  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.



December 18, 2017

Welcome all to FI 8200 "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 January 10.  As a reminder, our class meets at 5:30pm in Room 1215 of the Buckhead 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 Spring 2018 syllabus (see the "Syllabus/Readings" link)

(2) The textbook is 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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