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ESM3007 Introduction to Financial Eng. Lecture 2 Derivatives: Introduction Kyungchul Park

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Lecture overview Reading for this lecture Hull, Chapter 1 Hand-Out: Note on Bond Valuation and Returns Subjects What is derivative ? Basic types of derivatives: Forwards, Futures, Options, and Swaps Functions of derivatives Types of traders: Hedgers, Speculators, Arbitrageurs Additional Topics: Introduction to bonds and bond valuation

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Prologue: In the News 지난해 국내 금융회사들의 파생상품 거래규모가 전년 대비 크게 증가해 4경원을 돌파한 것으로 집계됐다. 또 파생상품 거래를 통한 금융회사들의 이익은 1조4,000억원에 달했다. 금융감독원은 지난 2006년 국내 금융회사의 파생상품 거래규모는 4경4,291조원으로 전년 대비 5,864조원, 15.3% 증가했다고 18일 밝혔다. 거래잔액 역시 902조원, 52.3% 증가한 2,628조원을 기록했다. 금감원은 주가지수옵션 계약금액 및 은행의 구조화 채권 발행 증가로 금리 위험 헤지 목적의 원화이자율 스왑 거래가 늘었기 때문이라고 설명했다. 또 국내 금융사들은 지난 한해 파생상품 거래를 통해 전년 대비 3,306억원, 31.1% 증가한 1조3,941억원의 이익을 올렸다. 증권사의 주식관련 파생상품 이익이 전년 대비 2,190억원 증가한데 따른 것으로 풀이된다. 한편 은행권은 9,623 억원의 파생상품거래 이익을 남겼다. 이중 국내은행의 이익은 5,693 억원으로 전체 영업이익의 4.6%에 불과했지만 3,930 억원의 이익을 올린 외국은행 지점은 이 비율이 120.9%에 달해 파생상품 위주의 영업을 하고 있는 것으로 나타났다. <서울 경제 2007, 3, 18>

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Derivatives A derivative is an instrument whose value depends on the values of other more basic underlying variables. Interest Rate or Foreign Exchange Rate Index Values such as a Stock Index Value Price of Commodity: Grain, Oil, Food, Metal, etc Financial Assets: Stock, Bond, etc Others: Weather Note: All of the underlying variables are volatile (risky). Thus, the value of a derivative is derived from another variable.

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4 Basic Types of Derivatives Forward Contracts Futures Contracts Swaps Options cf. Many say that there are only two basic derivatives: forwards and option. (In many cases, you can show any derivative can be replicated by using a portfolio of forwards and options.)

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Derivative Markets Exchange-Traded Markets: Futures and Options Standardized products Trading floor (open outcry system) or electronic (computerized trading) Virtually no credit risk Over-the-Counter (OTC) Markets: Forwards, Options, Swaps Usually non-standard (customized) products Computer or telephone-linked network of dealers between two financial institutions between a financial institution and its client  Financial institution plays as a market maker. Some credit risk

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Size of OTC and Exchange Markets Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market

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Uses of Derivatives To hedge or insure risks  to shift risk to others To reflect a view on the future direction of the market  to speculate To lock in an arbitrage profit To change the nature of an asset or liability To change the nature of an investment without incurring cost the costs of selling one portfolio and buying another

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Why to Study Derivatives Firms and individuals face financial risks that are greater than ever Derivative markets allow participants to reduce, or hedge risk. Using derivatives allows individuals and firms to create payoff patterns that are compatible with their beliefs and degree of risk aversion at a low cost Risk management There is a vital linkage between spot market and derivative market For e.g., to fully understand stock market, you should have knowledge on derivative market for stock index (e.g., KOSPI 200 Option) Caution: Derivatives are very versatile (have large leverage effect). Derivative disasters (e.g., Barings bank in p. 15) To correctly use derivatives, you have to fully understand their risks and rewards !

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Forward Contracts Agreement to buy or sell an asset at a certain future time for a certain price (delivery price) cf. 1. Spot contract: Agreement to buy or sell an asset today 2. Forwards are very popular on currencies and interest rates A forward contract gives the buyer the right and obligation to buy a specified asset on a specified date at a specified price  Long Position The seller has the right and obligation to sell the asset on date for the price  Short Position At delivery, ownership of the asset is transferred and payment is made from the buyer to the seller. (no money changes hands on the origination date of the forward contract) If your position has a value, you face the risk that your counterparty will default.

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Forward Contracts: Example On June 3, 2003 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.6100 ($/GBP). This obligates the corporation to pay $1,610,000 for £1 million on December 3, 2003. What are the possible outcomes?

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Forward Contracts: Payoff (Delivery price = K) Profit Price of Underlying at Maturity (ST) K Long Position (ST - K) Short Position (K - ST)

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Brief Preview on Forward Price Consider a stock that pays no dividend and is worth $60 (current spot price) You can borrow or lend money for one year at 5%. What should be 1-year forward price of the stock ?

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Futures Contracts Futures are similar to forwards, except: Futures trade on futures exchanges (e.g., CME, CBOT, KRX) Futures are standardized contracts  Increased liquidity Default risk is virtually none  Guarantees by clearinghouse

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Options A call option is an option to buy a certain asset by a certain date for a certain price (the strike price or exercise price) Call option gives the holder the right to buy the underlying asset. The seller of call option (the call writer) is obligated to sell the asset if call option holder exercises his right. A put option is an option to sell a certain asset by a certain date for a certain price (the strike price or exercise price) Put option gives the holder the right to sell the underlying asset. The seller of put option (the put writer) is obligated to buy the asset if put option holder exercises his right. cf. Note the right and obligation is separated, so option should have value on the option holder (premium paid to option writer).

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Options: American vs. European An American option can be exercised at any time during its life A European option can be exercised only at maturity cf. In options markets, there are four types of participants: - Buyers of calls - Sellers (Writers) of calls - Buyers of puts - Sellers (Writers) of puts

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Profit Diagram for Call Option (European) Profit 0 K ST call premium Long Position (Buyer) Short Position (Writer)

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Profit Diagram for Put Option (European) ST Profit 0 K put premium Long Position (Buyer) Short Position (Writer)

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Types of Traders Hedgers (Risk Shifters) Speculators (Risk Takers) Arbitrageurs (Alchemists) cf. Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators (see. Barings Bank Disaster p.15)

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Hedging Example Hedging using forward contracts A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract (forward rate = 1.6192) - What if the spot rate is 1.5000 after 3 months - What if the spot rate is 1.7000 after 3 months Hedging using options An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts - What if the spot price is $28 after 2 months - What if the spot price is $25 after 2 months cf. linear vs. nonlinear instrument

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Hedging Example: Microsoft Case

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Hedging Example: Comparison Hedging using forwards vs. options Using forwards, the effect is to fix the price that the hedger will pay or receive for the underlying asset. Options provide insurance for investors.  Protect investors against adverse price movement in the future while still allowing them to benefit from favorable price movements There is virtually no cost when entering into forwards, but options involves the payment of an up-front fee (insurance premium).

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Speculation Example An investor with $2,000 to invest feels that Amazon.com’s stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of $22.50 is $1 What are the alternative strategies? Alternative 1: Buy 100 shares of Amazon.com’s stock today Alternative 2: Buy 2,000 call options (= 20 call option contracts) - What if the price of Amazon.com’s stock rises to $27 ? - What if the price of Amazon.com’s stock falls to $15 ? Compare the above alternatives. (Fig. 1.5 on p. 13) cf. Note the leverage effect of call options. (Profit/loss magnified) Q. What if the investor choose futures ?

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Arbitrage Example Arbitrage involves locking in a riskless profit by simultaneously entering into transactions in two or more markets e.g. New York and London Stock Exchanges, Spot and Futures Markets Example A stock price is quoted as £100 in London and $172 in New York. The current exchange rate is 1.7500 What is the arbitrage opportunity? cf. In general, arbitrage opportunity cannot last for long because of the law of demand and supply. cf. Many pricing models assume no arbitrage opportunity. (Pricing based on “No Arbitrage Theorem”)

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Swaps A swap contract obligates two parties to exchange, or swap, cash flows at specified future dates. A swap is like a portfolio of forwards. Each forward in a swap has a different delivery date, and the same forward price.

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Swaps Example: ‘Plain Vanilla’ Interest Rate Swap I agree to pay you 8% of $40 million each year for the next five years. You agree to pay me whatever 1-year LIBOR is (times $40 million) for each of the next five years ($40 million is the notional principal). cf. LIBOR (London Inter-Bank Offer Rate) If LIBOR > 8%, you pay me: (LIBOR - 8%) X $40 million If LIBOR < 8%, I pay you: (8% - LIBOR) X $40 million Note there are 5 payments and each of them is a forward contract. - I am long five forward contracts with delivery dates at the end of each year of the next five years. - You care short five forward contracts. cf. called forward rate agreement (FRA)

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Additional Topics 1 The following slides are for the deeper treatment of the relevant materials in this lecture.

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Discussion Topic 1: Risk and Premium – Callable Bonds Callable Bond Gives the bond issuer the right but not obligation to redeem its issue of bonds before bond’s maturity. (Bond issuer has an option !) Q1. What type of risk is shifted from the bond issuer to bondholder ? Q2. How can you determine the premium paid to bondholder ?

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Discussion Topic 2: Arbitrage and Pricing of Forwards Suppose that: The spot price of gold is US$300. The 1-year forward price of gold is US$340. The 1-year US$ interest rate is 5% per annum. Q1. Is there an arbitrage opportunity? Q2. What should be the price of 1-year gold forward ?

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Discussion Topic 3: Futures Contract and Options Show that: 1. Long forward = Buy a Call and Write a Put (having the same strike price) 2. Short forward = Write a Call and Buy a Put (having the same strike price) profit ST K Buy Call Write Put = K Underlying price profit 0 ST

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Additional Topics 2 A Brief Introduction to Bonds and Bond Valuation

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Classifying Bonds Bond Classification Factors Issuer (Domestic, International), Maturity, Coupon Rate, Redemption Features Issuer Government, Municipality, Corporation  Major factor to determine bond’s risk International Bonds - Eurobond: denominated in a currency other than that of a country where it is issued. e.g. Eurodollar bond: dollar denominated bonds sold outside U.S. Maturity Short: < 1 year, Intermediate: 1 ~ 10, Long: > 10 Principal and Coupon Rate Principal: Actual amount issued in a bond Coupon Payment: Periodic interest payment (Principal X Coupon Rate) Types: Fixed Rate, Floating Rate, Zero Coupon Redemption Features Callable Bonds: Issuer has the right to redeem its issue of bonds before maturity  call risk to bondholder  need premium to sell Putable Bonds: Bondholders have the right to sell their bonds to the issuer before maturity Convertible Bonds: Bondholders have the right to convert their bonds into predetermined number of equity shares at or before maturity

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Bond Pricing Bond Pricing Determined by present value of its expected cash flows (coupon interest + par value) Coupon Payments (C) Par Value at Maturity (M) 1 2 3 n-1 n P: Market Price, C: Fixed Coupon Payment, M: Maturity Value (Principal Amount), r1,..,rn: Discount Rates, n: # of periods cf. P = PV (coupon annuity) + PV (principal)

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Bond Pricing YTM (Yield to Maturity) Single discount rate, which, if substituted for all of the discount rates, would give the same price of the bond P: Market Price, C: Fixed Coupon Payment, M: Maturity Value (Principal Amount), y: YTM, n: # of periods cf.1. YTM is another method to quote a bond’s price. Don’t confuse it with expected return. 2. To calculate YTM, you should solve the above equation for unknown y.

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Bond Pricing Price-Yield Relationship Rising Interest Rates  Lower Bond Prices Falling Interest Rates  Higher Bond Prices Par value = $100 Maturity = 36 months (3 years) Coupon Rate = 5% (annual) Method of Payment: Annually Yield Price

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A Note on Compounding Conventions Compounding Conversion Formula YTM can be quoted in a number of different ways: 1-year yield, 6-month yield, etc. You should be able to convert one to another equivalent one. ym = yield in period m, yn = yield in period n, m, n = number of months APR (Annual Percentage Rate) APR = r X m, r: interest rate charged per period, m: number of periods in a year e.g., Credit card with 1.5% monthly interest charge  1.5 X 12 = 18% (APR) EAR (Equivalent Annual Rate) Annual compounded rate EAR = (1 + r)m – 1 e.g., Credit card with 1.5% monthly interest charge  1 - (1 + 0.015)12 = 19.56 %

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