Lecture Notes Derivatives Securities

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Lecture NotesDerivatives SecuritiesProfessor Doron E. AvramovHebrew University of JerusalemProf. Doron AvramovDerivatives Securities1 פרופ' דורון אברמוב

Syllabus: Course DescriptionThis is a comprehensive course on the theory andpractice of derivatives securities.The course describes conceptual paradigms and theirextensive applications in practice.Prof. Doron AvramovDerivatives Securities2 פרופ' דורון אברמוב

Syllabus: Course DescriptionWe will be covering the following topics: Buying and selling put and call options Understanding futures and forward contracts Speculating with derivatives Risk management: hedging with derivatives Analyzing structures such as equity linked CD Employee stock optionsProf. Doron AvramovDerivatives Securities3 פרופ' דורון אברמוב

Syllabus: Course Description Pricing options with the Binomial Tree Understanding the B&S formula Pricing exotic options Option Greeks Constructing complex strategies with options Shortfall probability and insuring against shortfall Applying derivatives concepts to corporate decisions Credit risk modeling Pricing warrants and convertible bonds Interest rate futures such as FRAs and Eurodollars Hedging with swaps contractsProf. Doron AvramovDerivatives Securities4 פרופ' דורון אברמוב

Syllabus: ResourcesText book: The textbook for this course is Derivatives Markets byRobert L. McDonald, Second Edition. ISBN 978-0-32128030-5Case studies: The risk in stocks in the long run: The Barnstable Collegeendowment Sara’s optionProf. Doron AvramovDerivatives Securities5 פרופ' דורון אברמוב

Syllabus: Assessment Case Studies (30%) – See below. Exam (60%) - The final exam will be based on the materialand examples covered in class, assignments, and assignedreading. The exam is closed books and closed notes.However, you will be allowed to bring in one piece of paperwith handwritten notes (double-sided, A4 size). You are notallowed to use any other notes. I will allow the use of nonprogrammable calculators during the exam.Prof. Doron AvramovDerivatives Securities6 פרופ' דורון אברמוב

Syllabus: Assessment Class Participation (10%) - It is mandatory to attend thesessions. If you miss a session for good reason, make sureyou catch up on all missed material, as you are fullyresponsible for class lectures, announcements, handouts, anddiscussions. Warning: A nontrivial fraction of the final exam questionscould be based on class discussions, assigned readings, andexamples which are not necessarily covered in the lecturenotes.Prof. Doron AvramovDerivatives Securities7 פרופ' דורון אברמוב

Syllabus: Case 1 The Risk of Stocksin The Long Run - Description This case describes a scenario encountered frequently in practice: how to mix stocks andbonds in long run investments. The Barnstable College contemplates that stocksoutperform bonds in the long run and is considering two proposals consistent with thatphilosophy. The long run investment with insuring against a potential shortfall evententails using the B&S option pricing formula. The following questions are based on figures displayed in the case and are aboutcomputing quantities typically used in risk management and measurement. The case is abit confusing about the mean, expected return, as well as the risk free rate. Assume thatall the case figures reflect gross return (not continuously compounded). That means thatyou need to use the approximations displayed in the class notes for recovering the meanand variance of the stock. The continuously compounded riskfree rate rf ln(1 Rf)where Rf is the figure displayed in the case.Prof. Doron AvramovDerivatives Securities8 פרופ' דורון אברמוב

Syllabus: Case 1 The Risk of Stocksin The Long Run - Questions1. Compute the probability that stocks will underperform bonds for investment horizons of1, 2, 5, 10, 20, and 30 years.2. Compute the corresponding VaR at the 5% level for those horizons.3. Compute the expected shortfall under those circumstances – or the expected value of thestock investment given that stocks underperform bonds.4. Compute the value of a put option that insures against a shortfall for the sameinvestment horizons as in part 1.5. How would you reconcile the fact that even when the shortfall probably declines withthe investment horizon the cost of insuring against a shortfall increases?6. Assess the pros and cons of the two proposals offered to BCE. Which one would youselect?Prof. Doron AvramovDerivatives Securities9 פרופ' דורון אברמוב

Syllabus: Case 2 Sara’s Option –Description Sara Becker is about to graduate with an MBA from Harvard and is faced with threeemployment offers, each with a different compensation package. Two of Sara’s threeoffers involve stock options as a significant portion of total compensation. The thirdoffer is all cash, with large annual cash bonuses. In examining the three alternatives, thiscase provides an opportunity to analyze how executives and employees value theircompensation packages, and in particular the option based component of their pay. The clear lake option package is a more traditional plan, while the WebScale package isunusual in that it uses “index options” in which the payoff is linked – in a complex way– to the performance of the stock relative to the S&P. As Sara considers and comparesthe three compensation packages she evaluates the value of her stock options based ondifferent factors such has her risk tolerance, her probable length of stay at eachcompany, and the volatility of each company’s stock.Prof. Doron AvramovDerivatives Securities10 פרופ' דורון אברמוב

Syllabus: Case 2 Sara’s Option –Questions1.2.3.4.5.6.7.Use the B&S formula to value Sara’s Clear Lake annual options grant. How does the value of thisoption grant change with:– A 10% increase in the stock price?– A 10% increase in volatility?– An increase in the dividend rate from 0% to 3%?– A one year reduction in the “time to expiration” of the options?Give an intuitive explanation why option values change in the ways indicated by your analysis.Will Sara’s private value of these options generally be higher or lower than the value determined bythe B&S formula? Explain!What factors, not considered by the B&S formula, affect the value of Clear Lake’s options to Sara?How should Sara value three years’ worth of Clear Lake option grants (i.e., how much cash shouldshe be willing to trade off for these options?) Note: An assumption much be made about Sara’sdeparture date. Do the analysis under three assumptions: Sara departs after (i) three years, (ii) fiveyears, and (iii) 20 years.Repeat the analysis in Question 4 for WebScale’s options.Which compensation package is worth the most to Sara – Clear Lake’s package, Davis andRockefeller’s, or WebScale’s? Explain!Prof. Doron AvramovDerivatives Securities11 פרופ' דורון אברמוב

Derivative Securities:What are Derivatives?Why Using Derivatives?How big is the Market forDerivatives?Prof. Doron AvramovDerivatives Securities12 פרופ' דורון אברמוב

What are Derivatives?Primary assets:Securities sold by firms or government to raisecapital (stocks and bonds) as well as stock indexes(S&P, Nikkei), interest rates, exchange rates, creditrisk, commodities (gold, coffee, corn), etc.Derivatives assets:Options, forward and futures contracts, FRAs,Eurodollars, Swaption, CDS, etc. These financialassets are derived from existing primary assets.Prof. Doron AvramovDerivatives Securities13 פרופ' דורון אברמוב

Why using derivatives?– Risk management (e.g., hedging)– Speculation– Reduce market frictions, e.g., cost of default, taxes, andtransaction costs– Exploit arbitrage opportunities.Prof. Doron AvramovDerivatives Securities14 פרופ' דורון אברמוב

Exchange Traded Contracts Contracts proliferated in the last three decades What were the drivers behind this proliferation?Prof. Doron AvramovDerivatives Securities15 פרופ' דורון אברמוב

Increased Volatility Oil prices:1951–1999 DM/ rate:1951–1999Prof. Doron AvramovDerivatives Securities16 פרופ' דורון אברמוב

Led to New and Big Markets Exchange-traded derivatives Over-the-counter traded derivatives: even more!Prof. Doron AvramovDerivatives Securities17 פרופ' דורון אברמוב

Derivative SecuritiesOverview: UnderstandingOption and Futures ContractsProf. Doron AvramovDerivatives Securities18 פרופ' דורון אברמוב

Some Basics Option terminologyCall and put optionsOptions as insuranceStructuresEmployee stock optionsForward and futures contractsSpeculation with derivativesHedging with derivativesProf. Doron AvramovDerivatives Securities19 פרופ' דורון אברמוב

Option Terminology Buy Long HoldSell Short WriteCall - option to buy underlying assetPut - option to sell underlying assetSo we have: buy call, buy put, sell call, sell putKey Elements– Exercise or Strike Price– Maturity or Expiration– Premium or Price– Zero Sum GameProf. Doron AvramovDerivatives Securities20 פרופ' דורון אברמוב

Definition and Terminology A call option gives the owner the right but not the obligation to buy theunderlying asset at a predetermined price during a predetermined timeperiod. Strike (or exercise) price: the amount paid by the option buyer for theasset if he/she decides to exercise Exercise: the act of paying the strike price to buy the asset Expiration: the date by which the option must be exercised or becomeworthless Exercise style: specifies when the option can be exercised– European-style: can be exercised only at expiration date– American-style: can be exercised at any time before expiration– Bermudan-style: can be exercised during specified periods (e.g., on the firstday of each month. Bermuda is located between the US and Europe.Prof. Doron AvramovDerivatives Securities21 פרופ' דורון אברמוב

Examples Buying a call on an index– Today: call buyer acquires the right to pay 1,020 in six months forthe index, but is not obligated to do so– In six months at contract expiration: if spot price is 1,100, call buyer’s payoff 1,100 – 1,020 80 900, call buyer walks away, buyer’s payoff 0 Selling a call on an index– Today: call seller is obligated to sell the index for 1,020in six months, if asked to do so– In six months at contract expiration: if spot price is 1,100, call seller’s payoff 1,020 – 1,100 ( 80) 900, call buyer walks away, seller’s payoff 0Prof. Doron AvramovDerivatives Securities22 פרופ' דורון אברמוב

Payoff/Profit of a Purchased Call Payoff Max [0, spot price at expiration – strike price] Profit Payoff – future value of option premium Examples:S&P Index 6-month Call Option Strike price 1,000, Premium 93.81, 6-monthrisk-free rate 2%– If index value in six months 1100 Payoff max [0, 1,100 – 1,000] 100 Profit 100 – ( 93.81 x 1.02) 4.32– If index value in six months 900 Payoff max [0, 900 – 1,000] 0 Profit 0 – ( 93.81 x 1.02) – 95.68Prof. Doron AvramovDerivatives Securities23 פרופ' דורון אברמוב

Diagrams for Purchased Call Payoff at expirationProf. Doron AvramovDerivatives Securities Profit at expiration24 פרופ' דורון אברמוב

Payoff/Profit of a Written Call Payoff – max [0, spot price at expiration –strike price] Profit Payoff future value of option premium Example– S&P Index 6-month Call Option Strike price 1,000, Premium 93.81, 6-monthrisk-free rate 2%– If index value in six months 1100 Payoff – max [0, 1,100 – 1,000] – 100 Profit – 100 ( 93.81 x 1.02) – 4.32– If index value in six months 900 Payoff – max [0, 900 – 1,000] 0 Profit 0 ( 93.81 x 1.02) 95.68Prof. Doron AvramovDerivatives Securities25 פרופ' דורון אברמוב

Put Options A put option gives the owner the right but not theobligation to sell the underlying asset at a predeterminedprice during a predetermined time period The seller of a put option is obligated to buy if asked Payoff/profit of a purchased (i.e., long) put– Payoff max [0, strike price – spot price at expiration]– Profit Payoff – future value of option premium Payoff/profit of a written (i.e., short) put– Payoff – max [0, strike price – spot price at expiration]– Profit Payoff future value of option premiumProf. Doron AvramovDerivatives Securities26 פרופ' דורון אברמוב

Put Option Examples– S&P Index 6-month Put Option Strike price 1,000, Premium 74.20, 6-monthrisk-free rate 2%– If index value in six months 1100 Payoff max [0, 1,000 – 1,100] 0 Profit 0 – ( 74.20 x 1.02) – 75.68– If index value in six months 900 Payoff max [0, 1,000 – 900] 100 Profit 100 – ( 74.20 x 1.02) 24.32Prof. Doron AvramovDerivatives Securities27 פרופ' דורון אברמוב

A Few Items to Note A call option becomes more profitable when theunderlying asset appreciates in value A put option becomes more profitable when the underlyingasset depreciates in value Moneyness is an important concept in option trading.Prof. Doron AvramovDerivatives Securities28 פרופ' דורון אברמוב

“Moneyness”In the Money - exercise of the option would be profitableCall: market price exercise price (denoted by K or X)Put: exercise price market priceOut of the Money - exercise of the option would not beprofitableCall: market price exercise pricePut: exercise price market priceAt the Money - exercise price and market price are equalProf. Doron AvramovDerivatives Securities29 פרופ' דורון אברמוב

Call and Put Options on IBMProf. Doron AvramovDerivatives Securities30 פרופ' דורון אברמוב

Home’s Insurance is a Put Option You own a house that costs 200,000You buy a 15,000 insurance policyThe deductible amount is 25,000Let us graph the profit from this contact.Prof. Doron AvramovDerivatives Securities31 פרופ' דורון אברמוב

Home’s Insurance as a PutOptionProf. Doron AvramovDerivatives Securities32 פרופ' דורון אברמוב

Call Options are also Insurance Banks and insurance companies offer investmentproducts that allow investors to benefit from a rise in astock index and provide a guaranteed return if themarket falls. The equity linked CD provides a zero return if theindex falls (refund of initial investment) and a returnlinked to the index if the index rises.Prof. Doron AvramovDerivatives Securities33 פרופ' דורון אברמוב

Equity Linked CDs S final 10,000 1 0.7 max 0, 1 1300 Prof. Doron AvramovDerivatives Securities34 פרופ' דורון אברמוב

The Economic Value of theEquity Linked CD We paid 10,000 and we get 10,000 in 5.5 yearsplus some extra amount if the S&P500 index levelexceeds 1300. That payoff structure is equivalent to buying azero coupon bond and x call options. Why? Assuming that the annual effective rate is6%, the present value of 10,000 to be received in5.5 years is 7,258.Prof. Doron AvramovDerivatives Securities35 פרופ' דורון אברמוב

The Economic Value of theEquity Linked CD Thus, we practically paid 7,258 for a zero couponbond and 2,742 for x call options. What is x? And what is the implied value of one calloption? The component of payoff attributable to call option is7000 / 1300 max[ S final 1300,0]Prof. Doron AvramovDerivatives Securities36 פרופ' דורון אברמוב

The Economic Value of theEquity Linked CD Therefore x 5.3846. One call option is priced as 2742/5.3846 509.23 The economic value of one call option using the B&Sformula isBSCall (1300,1300, σ , ln(1.06),5.5, δ ) We will describe this formula later in this course. What if the economic value of the calls is smallerthan the implied price of the calls?Prof. Doron AvramovDerivatives Securities37 פרופ' דורון אברמוב

Employee Stock Options (Warrants) Employee stock options are call-like optionsissued by a company on its own stock When such options are exercised the companyissues new shares – thus warrants are not azero-sum game unlike regular call options. The options are often at-the-money at the timeof issue They could last as long as 10 yearsProf. Doron AvramovDerivatives Securities38 פרופ' דורון אברמוב

Typical Features of Employee Stock Options There is a vesting period during whichoptions cannot be exercised When employees leave during the vestingperiod options are forfeited When employees leave after the vestingperiod in-the-money options are exercisedimmediately and out of the money optionsare forfeited Employees are not permitted to trade theseoptionsProf. Doron AvramovDerivatives Securities39 פרופ' דורון אברמוב

Exercise Decision To realize cash from an employee stockoption the employee must exercise theoptions and sell the underlying sharesProf. Doron AvramovDerivatives Securities40 פרופ' דורון אברמוב

Drawbacks of Employee Stock Options Gain to executives from good performance is muchgreater than the penalty for bad performance Executives do very well when the stock market as awhole goes up, even if their firm does relatively poorly Executives are encouraged to focus on short-termperformance at the expense of long-term performance Executives are tempted to time announcements or takeother decisions that maximize the value of the optionsProf. Doron AvramovDerivatives Securities41 פרופ' דורון אברמוב

Accounting for Employee Stock Options Prior to 1995 the cost of an employee stockoption on the income statement was its intrinsicvalue on the issue date After 1995 a “fair value” had to be reported inthe notes (but expensing fair value on theincome statement was optional) Since 2005 both FASB and IASB have requiredthe fair value of options to be charged againstincome at the time of issueProf. Doron AvramovDerivatives Securities42 פרופ' דורון אברמוב

Nonstandard Plans The attraction of at-the-money call optionsused to be that they led to no expense on theincome statement because they had zerointrinsic value on the exercise date Other plans were liable to lead an expense Now that the accounting rules have changedsome companies are considering other typesof plansProf. Doron AvramovDerivatives Securities43 פרופ' דורון אברמוב

Possible Nonstandard Plans Strike price is linked to stock index so that thecompany’s stock price has to outperform theindex for options to move in the money Strike price increases in a predetemined way Options vest only if specified profit targetsare metProf. Doron AvramovDerivatives Securities44 פרופ' דורון אברמוב

Dilution Employee stock options are liable to dilutethe interests of shareholders because newshares are bought at below market price. Later in the course we will show how thedilution effect enters into an option pricingformula.Prof. Doron AvramovDerivatives Securities45 פרופ' דורון אברמוב

Backdating Backdating appears to have been awidespread practice in the United States A company might take the decision to issueat-the-money options on April 30 when thestock price is 50 and then backdate thegrant date to April 3 (earlier) or May 5(later) when the stock price is lower. Why would they do this?Prof. Doron AvramovDerivatives Securities46 פרופ' דורון אברמוב

Academic Research Exposed BackdatingProf. Doron AvramovDerivatives Securities47 פרופ' דורון אברמוב

Forward Contract A forward contract is an agreement made todaybetween a buyer and a seller who are obligated tocomplete a transaction at a pre-specified date in thefuture. The buyer and the seller know each other. Thenegotiation process leads to customized agreements:What to trade; Where to trade; When to trade; Howmuch to trade?Prof. Doron AvramovDerivatives Securities48 פרופ' דורון אברמוב

Futures Contract A Futures contract is an agreement made today betweena buyer and a seller who are obligated to complete atransaction at a pre-specified date in the future. The buyer and the seller do not know each other. The"negotiation" occurs in an organized future exchange. The terms of a futures contract are standardized. Thecontract specifies what to trade; where to trade; When totrade; How much to trade; what quality of good

The textbook for this course is Derivatives Markets by Robert L. McDonald, Second Edition. ISBN 978-0-3-2128030-5 Case studies: The risk in stocks in the long run: The Barnstable College endowment Sara’s option 5 Prof. Doron Avramov ב ומרבא ןורוד 'פ ורפ Derivatives Securities

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