Corporate Risk Management
Corporate Risk Management FIN 321
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This 14 page Class Notes was uploaded by Raina Bahringer on Sunday October 25, 2015. The Class Notes belongs to FIN 321 at University of Nevada - Las Vegas taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/228622/fin-321-university-of-nevada-las-vegas in Finance at University of Nevada - Las Vegas.
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Date Created: 10/25/15
Lecture Notes for Ch 24 Hedging with Derivative Contracts A derivative asset is any asset whose payoff price or value depends on the payoff price or value of another asset The underlying or primitive asset may be ahnost anything land stock interest rates another derivative asset Derivative are typically priced using no arbitrage arguments Arbitrage is a trading strategy that is selffinancing requires no cash and which has a positive probability of positive profit and zero probability of negative profit That is you get something for nothing That is the price of the derivative M be such that there are no arbitrage opportunities Forwards and Futures A forward contract is simply a current agreement to a future transaction ie payment for and delivery of the asset occur at a future date A forward contract fixes the price of the future transaction aka the forward price A futures contract is similar with the following differences 1 Futures contracts are standardized for exchange trading 2 Gains and losses on futures contracts are recognized daily marking to market EX Consider a farmer with a crop of wheat in the ground The change in the value of the wheat crop in the ground as a function of the change in the price of wheat is shown in the Figure As the price rises falls the farmer s wheat becomes more less valuable Since the farmer owns the wheat we say he has a long position in the wheat Increase in f A Long position in pro 1t wheat Price increase r Suppose the farmer agrees to sell the wheat under a forward contract at a forward price the current spot price with delivery upon harvest Since the farmer sold the wheat forward the farmer has a short position in the forward contract It should be obvious that future changes in the price of wheat no longer affect the farmer because he has fixed the amount of money he will receive for his crop It is useful however to recognize the changes in value of the crop and the contract separately even though in this case they offset The separate gains and losses are shown below Increase In Long position in pro t wheat Price increase A V Forward pos1tion v As the price rises the crop is more valuable But there are offsetting losses in the short position the farmer sold in the forward contract Vice versa when prices fall The net result is profits are constant as prices change Recognizing the separate effects on the value of the crop and contract is relevant in cases where the offsetting effect is not perfect ie when there is basis risk Forward prices have the following relation to spot prices F S1 cT where F forward price S spot price 0 carrying cost per period T number of periods Carrying costs include opportunity costs of holding the asset ie what you could have earned investing the proceeds from a current sale storage costs of holding the asset if any less any gains from holding the asset e g benefit of an inventory buffer yield on a financial instrument which are called convenience yields The relationship between the spot and forward prices in is an example of a No Arbitrage condition You can t make a riskfree profit To see this think about what happens if does not hold suppose F gt S1 cT You can sell at F buy on the spot market for S and deliver in T periods Further this requires no money it is selffinancing In theory if does not hold you can make an infinitely large profit But buying on the spot market drives S up selling on the futures market drives F down Options Terminology An option is a contract in which the writer of the option grants to the Mr of the option the right to purchase from or sell to the writer a designated asset at a specified price within a specified period of time writer seller short buyer long Option is sold for a price called the premium The specified price of the underlying instrument is the exercise or strike price The end of the specified period of time is the expiration date An American option can be exercised at any time up to the expiration date A European option can be exercised only on the expiration date When the option grants the buyer the right to purchase sell the asset it is called a 11 put option The buyer has a right but not an obligation to perform The writer is obligated to perform if buyer exercises Only option writers must maintain margin The underlying instrument can be Virtually anything stocks bonds indexes currencies commodities or futures contracts Option Strategies Naked Strategies Buying a call long call Call option on an asset with an exercise price of 100 and a premium of 3 The profit on the transaction at expiration as a function of the asset price can be depicted Pro t 100 103 The payoff at expiration is maxS K 0 Writing a call short call Assuming the same exercise price and premium the profit on the transaction at expiration as a function of the asset price can be depicted Pro t 3 l 103 I s 100 The payoff at expiration is maxS K 0 minK S 0 Buying a Put long put Put option on an asset with an exercise price of 100 and a premium of 2 The profit on the transaction at expiration as a function of the asset price can be depicted Graph Pro t 98 The payoff at expiration is maxK S 0 Writing a put shortput Assuming the same exercise price and premium the profit on the transaction at expiration as a function of the asset price can be depicted Pro t 2 l 98 I S 100 98 The payoff at expiration is maxK S 0 minS K 0 Naked Strategy Circumstance Buy call Expect P to rise r to fall Write put Expect P won t r won t rise Write call Expect P won t rise r won t fall Buy put Expect P to fall r to rise Covered Positions These combine a position in the asset with a position in an option Covered Call Writing Long in asset ShOIt in call write call Pro t Long39Asset I Covered 3 x Call 39 S 39 x lOO 10339 z l I I Short Call 100 I Protective Put Strategy Long in asset Long in put Pro t LongAsset 1 I Protectwe 39 Put 39 28 1 S I I X100 102 z 2 I Long Put II 100 Other possibilities include Spread combine long and short positions in the same type of option eg buy a call with a low strike price and write a call with a high strike price Combination combine long or short positions on different types of options e g buy a call and a put with the same strike price Combining these assets into portfolios allows you to achieve a wide variety of cash flow patterns Equivalent Positions and PutCall Parity Cash Flow at Expiration from Buying a Call I SltK SK SgtK ICMI 0 0 57K Cash Flow at Expiration from Buying a Put Buying the Asset and Borrowing the PV of the Exercise Price S lt K S K S gt K Put K i S 0 0 Asset S S S Loan 7 K i K i K Portfolio 0 0 S i K These two positions have the same payoff in each state of the world and in the absence of arbitrage must sell for the same price Thus we have PutCall Parity C P SiK1r We can rewrite this as P CiS KIr In this form it is known as the synthetic put relationship This relationship holds for European options and American options if the asset pays no interim cash ows If the stock pays dividends then the putcall parity relationship for European options is CPS7D7K n where D is the PV of dividends received before the option expires We can use putcall parity to examine the relationship between forwards and options A newly written forward contract is equivalent to a portfolio of a long European call and a short European put with common exercise price and eXpiration equal to the delivery date of the forward contract For new forward contracts the forward price F is set so that the value of the contract is zero No money changes hands at the inception of the contract At the delivery date T the value of the contract is ST F Comparing the payoffs to the two trading strategies DeliveryExpiration Date Current Date ST lt F ST gt F Long Forward 0 ST F SF F Long Call K F C 0 ST 7 F Short Put K F P ST 7 F 0 Option Total P i C ST 7 F ST 7 F Both strategies have the same payoff at time T They must have the same value at time 0 or there is an arbitrage opportunity Therefore P C 0 The forward price must equal the strike price that equates C and P From the putcall parity relationship CiPSiKK1mT Then using we have FKamprwf If the stock pays dividends replace S with S D Intrinsic Value and the Time Value of an Option Intrinsic value economic value of exercised immediately For a call I S K For a put I K i S If I gt 0 we say the option is in the money Time value excess value is the value of the option above its intrinsic value Ex For a call Time Value I I 4 I time T expiration The time value of an option derives from the probability that the option will be in the money prior to expiration The greater the probability the greater the time value The result is that the value of the option is greater than its intrinsic value
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