Financial Services Lecture 4 Derivatives：金融服务讲座4衍生物.doc

Financial Services Lecture 8: DerivativesGeneral:1) Derivatives are financial contracts whose value is based on the value of some underlying asset. The value is usually a function of asset price, and the contract always has a predetermined lifespanit expires at some point. This is called expiration.2) There are two basic types of derivative contracts: Forward or Futures contracts, and Options. Forwards and Futures are an agreement to buy an asset at a predetermined price, some time in the future. Option contractions give the holder the “option” to buy that asset at a predetermined price. But do not create an obligation.3) Derivatives may be used for speculative purposes, e.g. gambling, or for insurance purposes, e.g. hedging. The contracts permit us to bet on the occurrence of an event, or buy protection against it. For example: we could make a bet on, or buy insurance against, the S&P tumbling 500 points.4) We can also use derivatives to fix the price of an asset several months (or years) in advance. This can be enormously valuable if youre a wheat farmer, are about to by seed, and wish to lock in (with certainty) your profit. Derivatives, in this example, can allow a farmer to minimize his risk.5) From hereon, we will focus on financial derivativesderivatives on financial assets. However, most of what we will talk about is also applicable to commodities, or other underlying parameters.Futures and Options Markets: Statistical Data Futures and Options provide virtually unlimited trading volume potentialo Contracts are written by investors, not issued like shares of stock or bondso The value of the contract is based on value of an underlying asset, index, commodity, or interest rateo Thus, investors can write as many contracts as they wish based on that valuethe fixed quantity of the asset and requirements to deliver an asset do not constrain the writing of contracts Growth of the Futures and Options Marketo Chicago Board of Trade (CBOT), the worlds oldest futures and options exchange, was established in 1848o Over twenty major futures and options exchanges, trading 4.7 Billion contracts over the first six months of 2005o Links to world-wide futures and options exchanges:/ofor/resource.htmhttp:/www.wu-wien.ac.at/usr/h92/h9208766/seit3.htmlGlobal Trading Volume Jan-May 2005:Contracts (Millions)Futures1,584.8Options2,290.3Chief Sectors (Jan-Jun 2005):Equity Indices1,780.1Interest Rates1,320.0Individual Equities1,157.2Energy 131.2Agriculture 163.6FX/FX Index 74.3Precious/Non-Precious Metals 71.4Top Six Exchanges (Jan-Jun 2005):Korea Exchange1,096.6Eurex 639.2Chicago Mercantile Exchange 524.2Euronext.liffe Group 421.5Chicago Board of Trade 358.0Chicago Board Options Exchange 216.5Data taken from Futures Industry Magazine, 2005 ()Forwards and Futures:1) We can think of any asset as having a probability distribution associated with its future price for simplicity, we will choose the normal distribution. 2) The idea is that sometime in the future, say three, six, or nine months, there is a probability that an asset will attain a given price. Notethis distribution is not for the current price, it is for a price sometime in the future.3) This distribution cannot be observed. The distribution is in your mind, or, more accurately, represents the perceptions of the market.4) The Forward Rate (Forward) is what the market thinks that price of an asset will be: its Expected Value, or the cumulative sum of the probabilities for each potential price (realization) multiplied by that price. 5) This stock price might not occur, in fact, it probably wont occur exactly, but given its price today, and all the other information that the market has about this stock, that this is what “on average” the market thinks the price will be.6) A forward contract is where you agree to buy or sell the asset (a share of stock) at a preset price on a predetermined date. If you agree to buy the asset, you in the long position, and if you sell you are in the short position. 7) So if you are long a forward (have agreed to buy the stock) and the price of the asset increases, you have made money because you have agreed to buy the asset at the lower price. Likewise, if the stock price goes down, you have lost money.8) If you are on the opposite end of the contract, the “short position”, you lose if the price goes up, and gain if the price goes down. Why?- If youre short, you have to sell the asset no matter what. - If the price increases, you must either part with a share of stock that you could otherwise sell at a higher price, or if you dont own it, purchase a share from the market at the (higher) current price, and sell it to the contract holder at the (lower) predetermined price.9) What are the risks in a forward contract?- Obviously, share prices moving the wrong way. What else?- Counter-party Risk. Remember, there are two players in this game: a buyer and a seller. One of these parties may default.10) How much does it cost to get into a forward contract?- The forward is what the market “expects” the asset price to be at some fixed time in the future: its Expected Value.- So, at the time the contact is created, there is an Equal Dollar-Weighted Probability that the asset price will be above or below the forward. Your potential losses equal your potential gains.- Thus, the contract costs nothing to enter into.11) Who enters into forwards?- Individuals with banks, banks with banks, and so on.- The key point is that these are often highly customized contracts, which means that they are illiquid. The contracts are not an asset that can be easily traded.- Unless your counter party wants to get out of it, you may have a hard time liquidating this contract until it matures.- For this and other reasons, we have futures.12) Futures contracts are standardized exchange-traded contracts with a couple twists.a. The contract is with the issuing exchange. This feature standardizes the credit of the counter-party, because the counter-party is the exchange.b. The contract is “marked to market” daily. That is the contract is liquidated on a daily basis, whoever has lost money on the contract must pay the difference between the current contract price, and the contract is then re-written so that the contract price equals the current futures price.c. A “margin account” must be maintained by the investor. This is essentially a deposit (from the investor) held by the exchange to assure daily settlement. It keeps an investor from walking away from a contract at the end of a bad trading session without settling his account.d. Further, the number of shares in a contract, the maturity dates, and a number of other features are standardized. Hence, the contracts are liquid.13) How can you use futures to lock in the price of a share of stock, or lock in the exchange rate for a currency? Simple:- Assuming you want to buy the asset, you assume a long position, just as you would for a forward contract.- At the end of each day, the contract will be marked to market, and gains will be posted to your margin account or losses withdrawn from it.- At maturity, the cumulative sum of gains and losses will exactly equal the difference between the current market price of the asset and the contract price. Hence, when you add the gains (or losses) to the asset price on maturity, you will get an amount exactly equal to the original futures price. Therefore, you can lock in the future price of an asset using futures.14) How do firms get in trouble with futures?- Not having the cash to pay for losses prior to contract maturity. Remember you must maintain a margin account to cover potential losses. If the account cannot be maintained, the contract is terminated.- The reason this creates a problem is due to the timing of the payments. For example: suppose that you are agreeing to sell oil for a fixed price that will be paid six months from now, but do not have the oil on hand. You could lock in the purchase price of oil with a long position on a six-month futures contract, thus fixing you profits on the exchange. Suppose the price of oil begins a steep decline, every day you have a cash-outflow. You will recoup it in the end, because in six months the oil price will have dropped to exactly offset your losses, but until that time, you will have a significant cash outflow.- You might think that you could cut your losses and earn greater profits by closing the contract if futures prices fall, because the price of oil will have dropped. Whats wrong with this picture?- The day you closet that contract, prices head northsignificantlyand, they remain there. You will now have to purchase the oil at the higher price, and have locked in existing losses.15) Example: Suppose that you agree to deliver 100,000 barrels of oil for $31 per barrel, in six months. The current 6-month futures price for oil is $29.50, so you can lock in a profit of $150,000 today by going long on oil futures.Futures Price$29.50$12$17.50$15.50123456Time (Months)- If you maintain your position for the entire six months, you would have a cumulative loss of $12 per barrel on the contract, totaling $1.2M.- However, you would be able to purchase oil at that time for $17.50 per barrel, yielding a profit of 13.50 per barrel, or $1.35M.- Ignoring the interest lost on margin account settlements (remember, as the price declined, you kept paying out cash), your net profit is $150,000. The hedge works.- If you unable to sustain your position due to insufficient funds (remember, your losing money all the way up to the third month), and you closed in month 3 at $15.50, you lose $1.4M. If the oil recovers to $17.50, you net a loss of $50,000.16) Hedging with Forwards and Futuresa. Each futures (or forward) contract has a specified value.b. For example, a T-bond futures contract will cover $100,000 in T-bond futures.c. To determine the number of contracts needed to hedge a T-bond position, simply divide the position amount by contract value. E.g. If T-bonds and futures contracts are currently selling at par, and you need to hedge a long position in T-bonds of $8,000,000, how many corresponding T-bond futures contracts do you need sell? Note: We are assuming that the T-bond futures contracts are for exact same T-bonds. If not, we have to consider the differences in duration.Options:1) Call Option: The right to buy (but not the obligation) an asset at a predetermined price (the Strike or Exercise price), on (a European style option), or up to (an American style option), a preset maturity date.2) Put Option: The right to sell (but not the obligation) an asset at the strike price on, or up to, the maturity date.3) An Option contract can be viewed as making a bet on the likelihood of an event, and the degree to which it is likely to occur, during some fixed period of time. Further, the payoff from holding such a contract may be fixed, or related to the degree to which the event has occurred.4) As a result, an option contract has two major components contributing to its value:- The probability that the event will occur, or degree of the event will occur- The payoff from the contract when the event occurs, or occurs to a degree5) Payoff diagrams versus Profit and Loss diagrams for Long Positions on Calls and Puts- The profit-loss diagram is the downward shift of the payoff diagram at every point by the cost of the option.- This represents the total payoff from holding an option given a realization for the spot.- Notice that even when an option is “in the money” this is paying-off; an option-holder can lose money. The reason is that the pay-off must first cover the cost of the option.6) Payoff and Profit/Loss Diagrams for Short Positions on Calls and Puts- The opposite payoff / profit-loss of the long position- The short position on a Call can have potentially unbounded losses. Why?- What bounds the potential losses for a short position on a put?- So why would you short a Call or Put?7) What is the issue with Volatility?- What happens to the value of the option as the PDF spreads out? (That is as volatility .)Swaps:1) Exchange of Cash-flowsa. Interest Rate Swap: One firm borrows floating, the other Fixedb. Currency Swap: Exchanging Debt in two different currenciesc. Credit Swap: Same as above, but different credit levels driving deald. Usually done to reduce the Cost of Financing2) Structurea. One firm borrows floating (say LIBOR) one borrows fixedb. They Swap Payments, one firm may pay a premium (or take a discount)Libor 100bpFixedLiborFirm BFirm AFixedc. The agreeme