Lecture 1 – Introduction Zonghe Guo Sep 11, 2022 FINS3635 Hull Chapter 1-2 Basic information 2 Lecturer Zonghe Guo Contact information: [email protected] Week 1-5 Lecture in Charge Mathieu Fournier Contact information: [email protected] Week 7-10 No tutorials! About the subject 3 Objective Introduction to pricing principle and hedging techniques in derivative markets Focus on Standard derivative instruments: Forward, Futures, Swap, and Options Topics covered Pricing principle of derivatives Hedging with derivatives Trading with derivatives Assessment 4 Group Assignment 1 (10%) Midterm exam(35%) Group assignment 2 (15%) Final exam(40%) Assessment 5 Group Assignment 1 (10%) Excel About Margin Calls (from Week 1) Minimum Variance Hedge (from Week 2) 1-4 students Release in Week 3 (Wed, 28 Sep) Due in Week 4 (Sun 11:59pm, 9 Oct) More information will be given in class in week 2 Assessment 6 Midterm (35%) Open book Two-hours Week 6 (20 Oct 12pm-2pm) Covers materials in week 1-5 Similar to textbook exercise questions Assessment 7 Group assignment 2 (15%) Excel About Binomial trees (from Week 5) Black Scholes (from Week 7) 1-4 students, not necessary the same group for assignment one Release in Week 7 (Wed, 26 Oct) Due in Week 8 (Sun 11:59pm, 6 Nov) More information will be given after midterm Assessment 8 Final (40%) Time: School exam time Open book Similar to textbook exercise questions Moodle 9 Course announcements Assumed to be common knowledge Lecture notes Released at least one week before class Coverage of Hull Exercise questions General forum Try my best to reply in 48 hours Email me if it is personal Textbook 10 Hull, Options, Futures And Other Derivatives, 8th edition If you use an old edition, make sure to adjust the references There is a solutions manual available I will follow the book fairly closely and the exercise questions are taken from the book, so you’re strongly recommended to get it Special Case for Lecture 2! 11 Pre-recorded video will be in use Released on Wed (21 Sep) If you have questions, join the lecture at 2:30 What are derivatives 12 Financial assets whose value depend directly on some underlying variable or assets The underlying is typically a commodity (such as wheat and orange juice) or a financial asset (such as stocks and bonds or other derivatives) Some derivatives are written on non-tradable variables, such as weather futures. a New York daily weather futures, the delivery price is 25°. If at maturity, the weather is 23°, you will gain or loss $200 ($100 per degree) based on your position. The derivatives market 13 Some derivatives are exchange traded Standardized High liquidity Low counterparty risk Other derivatives are traded on the over-the-counter (OTC) market Bilateral agreements, typically between an investment bank and a customer Tailor made Lower liquidity Higher counterparty risk The derivatives market 14 Largest derivatives exchanges worldwide in 2021, by number of contracts traded(in millions) The derivatives market 15 By December 2009, the over-the-counter market had grown to $614.7 trillion and the exchange-traded market had grown to $73.1 trillion. The notional value of outstanding OTC derivatives reaches $610 trillion at end-June 2021. Who’s trading all this stuff 16 Hedgers use derivatives as insurance Companies hedging currency and interest rate risk Investors limiting portfolio risk Fund managers hedging market risk Speculators use derivatives to place bets Useful to increase leverage Often lower transaction costs, e.g. when betting on commodity prices Arbitrageurs exploit mispricing to make profits Central in this course Companies frequently use derivatives to set up executive incentive programs Small part of market cap, but important application Two approaches to pricing 17 Fundamental pricing Prices are set in a supply-demand equilibrium The properties of an asset tell us what that price is likely to be. Examples: CAPM Arbitrage pricing This is what we will be doing in this course What is arbitrage 18 An arbitrage is a (set of) trades that generate zero cash flows in the future, but a positive and risk free cash flow today This is the proverbial “free lunch” A simple example exploits violations of the law of one price, e.g. an identical assets selling for two different prices Simultaneously buying the cheap asset and selling the expensive asset would be an arbitrage trade (buy low & sell high) Derivatives are priced based on the same principle, but the trades are (slightly) more complex Replicating portfolios 19 We typically rely on a portfolio of assets that exactly mimic the cash flows of some other asset We call such portfolios replicating portfolios or synthetic assets Arbitrage pricing is all about constructing replicating portfolios using assets with known prices Example of replicating portfolios 20 How would you price the risk-free one-year zero-coupon bond below, assuming the interest rate is 10% Example of replicating portfolios 21 Suppose the price of Bond A was actually $80.9, i.e. lower than what we found on the last slide We know that the bond is mispriced. How do we exploit this We want to make a synthetic version of the bond, i.e. some investments that mimic its cash flows exactly In this simple example we can just put some amount of money, M, in the bank After one year in the bank account earning 10% interest, it should have grown to match the bonds cash flow of $100 Example of replicating portfolios 22 The $90.9 bank deposit replicates the bonds cash flow (is a synthetic bond) but has a different price We buy the cheap instrument and sell the expensive (in this case the synthetic) instrument “Selling” a bank deposit means borrowing the money. Our synthetic instruments will commonly involve such short positions. Today we borrow $90.9 and buy the bond for $80.9. We are left with $10 In one year the bond pays us $100 which is exactly enough to repay the loan. We have zero net cash flow Our “free” $10 is an arbitrage profit and the entire scheme is an arbitrage trade Arbitrage pricing 23 In practice smart people will identify arbitrage opportunities and trade on them This will increase the demand for underpriced security and raise its price until no further arbitrage trades are possible, i.e. until prices are in equilibrium In this course we are interested in finding those equilibria, e.g. arbitrage-free prices Assumption of arbitrage-free markets 24 We will commonly make the following assumptions, such as Ignoring default risk so that everyone face the same interest rate Interest rates are constant There are no taxes Markets are complete, e.g. everything can be traded without frictions No transaction costs Can trade any claim, e.g. fractions of stocks and bonds with any maturity Can take cost-less short positions Can trade in continuous time and at continuous prices Remember that the model and the world is not the same 25 Transaction costs In practice many apparent arbitrage opportunities will be prevented by transaction costs Liquidity risk Arbitrageurs risk not to be able to trade out of their positions Leg risk When Arbitrageurs wish to execute their trades, during the time it takes to complete may potentially leaving them in an unhedged position Model risk There is always a risk that your model neglected some crucial real-world feature What is a forward contract 26 An agreement to trade some underlying asset in the future at a price set today The buyer is said to take a long position and the seller a short position The agreed price (or settlement price), K (or F), is known as the delivery price The underlying could be stocks, currencies, commodities etc. The agreed upon trade, the delivery, takes place at the contract’s time- of-maturity, T What is a forward contract 27 The value of the long position, , varies with the price of the underlying By convention the delivery price, K, is set so that the value at the start of the contract , , is zero The spot price 28 The market of the underlying is known as the spot market and the price of the underlying is known as the spot price, The value of the long position, f, varies with the spot price Example of forward 29 Suppose, at maturity (June 24, 2010), spot bid is 1.5000, spot offer is 1.5010. Long position K (1.4413) Short position K (1.4408) T (1/12) t (0) (0) Long position 0 (1.4411) Short position 0 (1.4407) Long position T (1.5010) Short position T
(1.5000) Long position (1.4413) (1.5010) why Example of forward 30 Suppose, at maturity (June 24, 2010), spot bid is 1.5000, spot offer is 1.5010. If > T , Arbitrage opportunity (buy low & sell high): Sell (short) the contract Buy (long) the asset in spot market Make delivery Lock a risk-free profit Convergency of forward price to spot price 31 At maturity, T, a forward contract is an agreement to trade the underlying today That’s just an ordinary trade, so the spot price and forward price converge (T = T ) The prices are generally not equal at t < T Is it possible that the T is below or above the range The forward contract payoff function 32 At time T the buyer gets an asset worth $ and pays the delivery price, K The payoff for the long position is $ – The payoff for the short position $ Example of forward 33 Suppose, at maturity (June 24, 2010), spot bid is 1.5000, spot offer is 1.5010. Gain or loss of long position (1.5000-1.4413) Gain or loss of short position (1.4408-1.5010) Counterparty risk 34 Counterparty risk is the risk that the counterparty, i.e. the other part in a forward agreement, will be unable to meet their obligations This is sometimes referred to as credit risk or default risk Futures contracts 35 Like a forward contract, a futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price Unlike forward contracts, futures contracts are normally traded on an exchange Standardized contract Close out position 36 Unlike forward, the vast majority of futures contracts do not lead to delivery Most traders choose to close out their positions prior to the delivery period specified in the contract Close out a position means entering into the opposite trade to the original one For example, the New York investor who bought a July corn futures contract on March 5 can close out the position by selling (i.e., shorting) one July corn futures contract on, say, April 20. In this case, the investor’s total gain or loss is determined by the change in the futures price between March 5 and the day when the contract is closed out. Futures contracts 37 As the two parties to the contract do not necessarily know each other, the exchange also provides a mechanism that gives the two parties a guarantee that the contract will be honored. Futures contracts are settled daily You pay (or receive) the change in f every day (image you close out position) K (settlement price) is then updated to set f = 0 again This process is known as marking to market Think of futures as a series of one-day forwards Margins 38 To ensure that you can cover unfavorable moves in f, you have to deposit some money, the initial margin, in marginal account to enter a futures contract Gains and losses from the futures are covered by the margin account You must always maintain some minimum margin balance, the maintenance margin, which is typically 75% of the initial margin If your balance falls below the maintenance margin, you’ll get a margin call and must deposit additional money to the initial margin level or have your position closed out by brokers. Together, margin requirements and daily settlements almost eliminate counterparty risk Example of Margins 39 Futures v.s. forwards 40 Futures v.s. forwards 41 If the interest rate is deterministic, the forward price and futures price are equal We will typically assume that this is true We will denote both the forward and the futures price by F How are futures quoted 42 Gold 100 oz is the underlying asset June 2010 is the maturity (delivery date) Settlement is the price for calculating margin requirement (1:30 pm for gold) Change is the change in F. This is typically the daily change in Settlement. Open/High/Low are the daily opening/highest/lowest F How are futures quoted 43 Volume is the number of contracts traded for the day Open interest is the number of live contracts (just long or just short position) at the end of previous day Anything interesting here How are futures quoted 44 Trading volume can be greater than both the beginning-of-day and end-of- day open interest. (This was the case for June 2010 gold on May 26, 2010.) How Suppose A own 2 long position, B own 2 short position yesterday, Open interest (2) A long 2 & then close position by short 2, A’s counterparty is C Now, the open interest is (2) But the Volume is (4) This indicates that many traders who entered into positions during the day closed them out before the end of the day. (Traders who do this are referred to as day traders.) Order types 45 When trading we are typically faced with a lower bid price (at which we can sell) and a higher ask price or offer price (at which we can buy) Investors place orders with brokers through different order types. Market orders trade at once at the best available price, e.g. buys at the current bid price Limit orders specifies a particular price. The order can be executed only at this price or at one more favorable to the investor. if the limit price is $30 for an investor wanting to buy and the spot price is $35, the order will be executed only at a price of $30 or less. There is, of course, no guarantee that the order will be executed at all, because the limit price may never be reached. Order types 46 Stop-loss or stop orders also specifies a particular price. The order is executed at the best available price once a bid or offer is made at that particular price or a less favorable price. Suppose a stop order to buy at $35 is issued when the market price is $30. It becomes an market order to buy when the price reach $35. The purpose of a stop order is usually to close out a position if unfavorable price movements take place. It limits the loss that can be incurred. Order types 47 Stop-limit is a combination of a stop order and a limit order. The order becomes a limit order as soon as a bid or offer is made at a price equal to or less favorable than the stop price. Two prices must be specified in a stop–limit order: the stop price and the limit price. Suppose that spot price is $35, a stop–limit order to buy is issued with a stop price of $40 and a limit price of $41. As soon as price reach $40, the stop–limit becomes a limit order at $41. If the stop price and the limit price are the same, the order is sometimes called a stop-and-limit order. Options 48 Options are financial contracts that give us the right, but not the obligation, to trade an underlying asset at a pre-specified strike price, K They are similar to forwards, except we can choose not to go through with the final trade Since we can always choose to ignore the options, they cannot be worth less than zero Option premium is the income received by an investor who sells an option contract Types of options 49 Options that give us the right to buy the underlying are called call options Options that give us the right to sell the underlying are called put options The holder of an option has a long position The issuer of an option has a short position Options that can only be exercised at a specific time-of-maturity, T, are called European options Options that can be exercised at any time prior to T are called American options Option payoffs 50 At time T the holder of a call option will either exercise it (if ! > ) or throw it away (if > !) Ignoring the premium, only consider cashflow at maturity The call option payoff is max(! – ; 0) The opposite is true for a put option` The put option payoff is max( – !; 0) Example of options 51 Option type (call option) Underlying asset (Google stock) Strick price Bid or offer (option price) Comparing to bid and offer in futures Any interesting trend (higher strick price, lower option price; longer maturity, higher option price) Example of options 52 How about the trend for puts (higher strick price, higher option price; longer maturity, higher option price) Swaps 53 Swaps are agreements to exchange (swap) two future cash flows Typical examples is swapping some fixed interest rate payments for floating interest rate payments, or cash flows in one currency for cash flows in a different currency Swaps typically result in a series of cash flows Example of Swaps 54 Before swap: Microsoft interest rate is LIBOR+0.1% Intel interest rate is 5.2% After swap: Microsoft interest rate is 5.1% Intel interest rate is LIBOR+0.2% Exercise questions 55 Chapter 1: 1-2, 5-6, 12, 19, 24, 26 Chapter 2: 1, 3, 5, 8, 10-12, 14, 16, 19-20, 22, 24, 25