FINA 2322: Derivatives - Fall 2022 PDF

Chapter 1: Introduction Chapter 1: Introduction Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 1 / 19  Chapter 1: Introduction Basics of Derivatives What is a Derivative? Definition A derivative is a financial instrument w...

Chapter 1: Introduction Chapter 1: Introduction Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 1 / 19  Chapter 1: Introduction Basics of Derivatives What is a Derivative? Definition A derivative is a financial instrument whose value depends on or derives from the value of an underlying asset or variable. Limited time to maturity Payoffs on or before maturity are a function of an observable underlying variable Key ingredients that determine the value before maturity: Characteristics of underlying variable: current level, volatility, etc Time to maturity Risk free interest rate Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 2 / 19  Chapter 1: Introduction Basics of Derivatives Examples of Derivative Payoffs: Forward (I) A forward contract is an agreement to trade the underlying asset in the future (at maturity T ) for a fixed price specified today (forward (T ) price Ft at the current time t) Party that agrees to buy the underlying (long position) makes a profit if at maturity T the price of the underlying ST is higher than the (T ) pre-specified forward price Ft , and makes a loss if at maturity (T ) (long forward) (T ) ST < Ft –> PayoffT = ST − Ft Party that agrees to sell the underlying (short position) makes a profit if at maturity T the price of the underlying ST is lower than the (T ) pre-specified forward price Ft , and makes a loss if at maturity (T ) (short forward) (T ) ST > Ft –> PayoffT = Ft − ST (T ) Typically, Ft is chosen such that no money is exchanged between long and short position at time t Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 3 / 19  Chapter 1: Introduction Basics of Derivatives Examples of Derivative Payoffs: Forward (II) On the 4th of June, the treasurer of a corporation enters into a long forward contract with a bank to buy £1 million in six months at an exchange rate of 1.55 £$ Do the corporation and the bank have an obligation? If so, what is it? Corporation: A long position obligates the corporation to pay $1’550’000 to the bank and it receives in exchange £1 million on the 4th of December Bank: A short position obligates the bank to pay £1 million to the corporation and it receives in exchange $1’550’000 on the 4th of December Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 4 / 19  Chapter 1: Introduction Basics of Derivatives Examples of Derivative Payoffs: Forward (III) What is the payoff of the forward contract if the exchange rate on the 4th of December is 1.45 £$ , 1.5 £$ , 1.55 £$ , 1.6 £$ or 1.65 £$ ? Corporation: a long position in the forward pays off      current ex-  ∗ £1million − $1’550’000   change rate  | {z }   | {z } pay $1’550’000 receive £1million or −$100’000, −$50’000, $0, $50’000, $100’000 Bank: a short position in the forward pays off     current ex-    $1’550’000 − ∗ £1million   change rate   | {z }  receive $1’550’000 | {z } pay £1million or $100’000, $50’000, $0, −$50’000, −$100’000 Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 5 / 19  Chapter 1: Introduction Basics of Derivatives Importance of Derivatives Derivatives play a key role in transferring risks in the economy Many financial transactions have embedded derivatives In corporate finance, the concept of real options is essential for the assessment of capital investment decisions Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 6 / 19  Chapter 1: Introduction Derivatives Markets Exchanges HKEX (www.hkex.com.hk) Hong Kong Futures Exchange (HKFE, www.hkex.com.hk) Hong Kong Stock Exchange (HKSE, www.hkex.com.hk) London Metal Exchange (LME, www.hkex.com.hk) China China Financial Futures Exchange (CFFEX, www.cffex.com.cn) Dalian Commodity Exchange (DCE, www.dce.com.cn) Shanghai Futures Exchange (SHFE, www.shfe.com.cn) Zhengzhou Commodity Exchange (ZCE, www.czce.com.cn) USA: CME Group (www.cmegroup.com) Chicago Board of Trade (CBOT, www.cbot.com) Chicago Mercantile Exchange (CME, www.cme.com) Chicago Board Options Exchange (CBOE, www.cboe.com) Many others (NYSE Euronext, American Stock Exchange, Philadelphia Stock Exchange, etc) Europe: Eurex (www.eurexchange.com); many others (Euronext, OMX, ICE, etc) Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 7 / 19  Chapter 1: Introduction Derivatives Markets Size of OTC and Exchange-Traded Markets 2010 GDP: World = $66tn, USA = $15tn, China = $6tn 2010 Stock Market Capitalization: World = $55tn, USA = $17tn, China = $4tn Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 8 / 19  Chapter 1: Introduction Derivatives Markets Size of OTC Market: Notional Amount vs Market Value 2010 GDP: World = $66tn, USA = $15tn, China = $6tn 2010 Stock Market Capitalization: World = $55tn, USA = $17tn, China = $4tn Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 9 / 19  Chapter 1: Introduction Derivatives Markets OTC Market: Notional Amount 2010 GDP: World = $66tn, USA = $15tn, China = $6tn 2010 Stock Market Capitalization: World = $55tn, USA = $17tn, China = $4tn Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 10 / 19  Chapter 1: Introduction Derivatives Markets OTC Market: Market Value 2010 GDP: World = $66tn, USA = $15tn, China = $6tn 2010 Stock Market Capitalization: World = $55tn, USA = $17tn, China = $4tn Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 11 / 19  Chapter 1: Introduction Derivatives Traders How do Investors use Derivatives? Managing risk "Hedgers": hedging risk Changing the nature of a liability Changing the nature of an investment without incurring the costs of selling one portfolio and buying another "Speculators": bet on a view on the future direction of the market "Arbitrageurs": locking in an arbitrage profit Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 12 / 19  Chapter 1: Introduction Derivatives Traders: Hedging Hedging Risk Hedging reduces or eliminates risk associated with potential (unknown) future movements in a market variable e.g., the price of an asset that we own Payoff of derivative is risky which at first may seem undesirable, i.e., it looks like gambling BUT: the uncertain payoff of a derivative is strongly correlated with the uncertain payoff of the underlying, and an appropriate (long or short) position in the derivative can offset the risk in the underlying, and thus, reduce risk e.g., forwards neutralize risk by fixing the price Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 13 / 19  Chapter 1: Introduction Derivatives Traders: Hedging Hedging Risk: Examples A firm which does business abroad may find it useful to trade foreign exchange rate derivatives - hedge risk in FX market An airline may find it useful to trade oil derivatives - hedge risk in jet fuel prices A stock trader may find it useful to trade derivatives on stock indices - hedge market risk A producer of electricity may find it useful to trade heating degree days (HDD) or cooling degree days (CDD) derivatives - hedge risk of demand shocks A farmer, a holiday resort or a theme park may find it useful to trade weather derivatives - hedge against unfavorable weather conditions Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 14 / 19  Chapter 1: Introduction Derivatives Traders: Speculation Speculation Taking risk by betting on a view on the future direction of a market variable and use derivatives to get extra leverage Speculation on the gold price: A view: The price of gold is likely to increase in the near future One approach is to purchase gold in the spot market and sell it later hoping the price goes up Another approach is to trade in the derivatives market → take a long position in a forward or futures contract to lock in a price in the near future The second approach needs no down payment (or only a small amount of cash as collateral or deposited in a “margin account”) instead of a large investment to buy gold to take a speculative position Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 15 / 19  Chapter 1: Introduction Derivatives Traders: Arbitrage Arbitrage Definition An arbitrage is a strategy that generates (today or in future) a positive payoff with non-zero probability and a negative payoff with zero probability In other words: locking in a riskless profit by taking offsetting positions simultaneously Arbitrage across markets: In market A, 1 ounce of gold is traded for $1’640 In market B, 1 ounce of gold is traded for $1’630 –> Buy gold in market B and sell it in market A –> Receive instantly $10 for every ounce of gold traded Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 16 / 19  Chapter 1: Introduction Derivatives Traders: Arbitrage Arbitrage: Illustration in the Forward Market (I) The current stock price of Apple is $571.5 Apple has a market beta of 0.93 and an expected return of 7.5% → its stock price is expected to increase to $614 next year (assuming Apple does not pay dividends) Suppose you could enter a forward contract (long or short position) to buy in 1’000 shares of Apple for $600’000 1 year (assume no counter-party risk) The one year risk free interest rate offered by a bank to you (lend or borrow) is 1% Is there an arbitrage opportunity? What do you do? Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 17 / 19  Chapter 1: Introduction Derivatives Traders: Arbitrage Arbitrage: Illustration in the Forward Market (II) Today: Borrow $594’000 from the bank for 1 year at 1% interest Buy 1’000 shares of Apple for $571’500 Enter a short position in the forward contract - that is, agree to sell 1’000 shares for $600’000 in one year Cash flow today: $594’000 − $571’500 = $22’500 In 1 year: Deliver 1’000 shares of Apple and receive $600’000 in cash (short position in forward contract) Pay back loan of ($594’000 ∗1.01 =) $600’000 from bank Cash flow in 1 year: $600’000 − $600’000 = 0 (for sure) Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 18 / 19  Chapter 1: Introduction Derivatives Traders: Arbitrage Principle of Asset Pricing Assumption In asset pricing we usually assume that there exist no arbitrage opportunities in the economy. If two investment strategies always have the same payoffs (or value) in the future, then they must have the same price today, otherwise there exists an arbitrage opportunity Pricing by No Arbitrage The payoff of a derivative depends on the payoff of the underlying Use derivative, underlying and risk free asset and build strategy which has zero payoff (or value) in the future, and thus, must cost nothing today Recover price of derivative from price of underlying and risk free interest rate Thomas Maurer (HKU) FINA 2322: Derivatives Fall 2022 19 / 19