L1 flash cards derivatives (ss17)


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L1 flash cards derivatives (ss17)

  1. 1. Exchange Traded Derivatives Involves a Clearing House Physical Market Low Default Risk Contains standard terms and features Markets can be called futures market or options exchangeStudy Session 17, Reading 60
  2. 2. Over-the-Counter Derivatives No Physical Market (Not listed on the market) Transaction Created by Two Parties Decentralized Market and ExchangeStudy Session 17, Reading 60
  3. 3. Exchange-Traded vs Over-the-CounterExchange-Traded Physical Market Have Standard Terms andFeatures Organized FacilityOver-the-Counter No Physical Market Transaction created by twoparties Decentralized Market andExchangeStudy Session 17, Reading 60
  4. 4. Forwards Forward contract is an agreement between two parties tobuy/sell an asset at some specific future date at a specificprice determined at the initiation of the contractStudy Session 17, Reading 60
  5. 5. Futures Futures contracts are exchange traded, give thebuyer/ seller a right to buy/sell a security in thefuture at a specific priceStudy Session 17, Reading 60
  6. 6. Forwards vs FuturesForwards Contract Non-Exchange Traded No Clearing House Between Two Parties Customized Contract Higher Default RiskFutures Contract Exchange Traded Involve Clearing House Market to Market Standardized Contract Lower/Minimal Default RiskStudy Session 17, Reading 60
  7. 7. Options A Contingent Claim An option/right, not an obligation to buy/sell an asset if acertain threshold is reached Option premium must be paid to acquire the rightStudy Session 17, Reading 60
  8. 8. Swaps Swap is equal to a series of forward contracts Private transactions that are not directly regulated Payments payments can be fixed and floating Swaps can be on interest rates, exchange rates, stockprices, commodity prices etc.Study Session 17, Reading 60
  9. 9. Purpose of Derivative Markets Improve market efficiency for the underlying asset Provide price discovery Mechanism for hedging against risk Reduce market transaction cost Require a high degree of transparencyStudy Session 17, Reading 60
  10. 10. Purpose of Derivative Markets The price of the contract with the shortest time to expirationoften serves as a proxy for the underlying asset The price of all future contracts serve as prices that can beaccepted by those who trade the contracts Options also aid in price discovery in the way the marketparticipants view the volatility of the marketsStudy Session 17, Reading 60
  11. 11. Criticism of Derivative Markets Very complex instruments Most investors fail to understand Mistakenly characterized as legal gamblingStudy Session 17, Reading 60
  12. 12. Role of Arbitrage in Prices The market will cause the prices of two equivalent assets to beequal (i.e. eliminate the arbitrage opportunity) Risk free profit can be made if an arbitrage opportunity exists If the calculated forward price is different from the quotedprice, then an arbitrage opportunity existsStudy Session 17, Reading 60
  13. 13. Role of Arbitrage in Prices Law of one price suggests that there should be one price foridentical assets Forward price is the spot price adjusted for interest rate If the calculated forward price is different from the quotedprice, then an arbitrage opportunity existsStudy Session 17, Reading 60
  14. 14. Role of Arbitrage in Market Efficiency Efficient markets have less arbitrage opportunities Fully efficient markets have no arbitrage opportunitiesStudy Session 17, Reading 60
  15. 15. Delivery Settled vs Cash Settled Contracts Underlying asset can be delivered at the expiration date indelivery settled contract Long will pay the specified price (the forward price) Short will deliver the assetStudy Session 17, Reading 60
  16. 16. Delivery Settled vs Cash Settled Contracts Only the owed difference will be paid by the party in a cashsettled contract If the price has gone up the long the short will make a cashpayment to long or vice versaStudy Session 17, Reading 60
  17. 17. Default RiskLong If the price of the assetincreases, the long willreceive a payment Long faces the default riskthat the short will not beable to meet thecommitmentShort If the price of the assetdeclines, the long will make apayment to short Short faces default risk thatlong will not be able to makethe paymentStudy Session 17, Reading 60
  18. 18. Settling a Forward Contractat Expiration Payment made by the long at delivery, and delivery of asset is madeby the short. Long gets payment if the price has gone up Short gets a payment if the price has gone downStudy Session 17, Reading 61
  19. 19. Termination Before Expiration And Effect OnCredit Risk New contract can be entered by either party in order to cancelthe existing position Eg. If long, can take a short position in an identical forwardcontract to cancel positionStudy Session 17, Reading 61
  20. 20. Termination Before Expiration And Effect OnCredit Risk Credit risk can arise from entering into new contract with adifferent counterparty Credit risk can be minimized by re-entering in the contractwith the same party Both parties can agree to cancel the both contracts to cancelthe positionStudy Session 17, Reading 61
  21. 21. Dealers Facilitate contracts for end users A big network of financial (banking and non-banking)institutions act as dealersStudy Session 17, Reading 61
  22. 22. Dealers Each dealer has a quote desk. Dealers are ready to take either side of the transaction, whichis usually completed over the phone.-shift risk from parties as they take on transaction-lay off risk by dealing with other dealers-make profit from offloading risk to other dealersStudy Session 17, Reading 61
  23. 23. End Users End users usually want to manage the risk End users include corporations, non-profit organizations andgovernments-Eg. A corn producer can buy/sell a forwards contract if he isunsure about future corn pricesStudy Session 17, Reading 61
  24. 24. Equity Forward Contracts A contract to buy one stock, a portfolio of stocks, or a stockindex at a specific price in the future A single stock or a portfolio can be sold or bought at a futuredate by locking in the price todayStudy Session 17, Reading 61
  25. 25. Equity Forward Contracts Index forward contracts behave identically to a single or aportfolio of forwards contracts When underlying stocks pay dividends, forward priceadjustments will be neededStudy Session 17, Reading 61
  26. 26. Bond Forward Contracts Similar to forwards contracts on equities Different than forwards contracts on interest rates Forward price needs to be adjusted for coupon paying bonds Zero coupon bonds act similar to non-dividend paying stocksStudy Session 17, Reading 61
  27. 27. Bond Forward Contracts Forward contract on a bond must expire before the maturity ofthe bond Forward contract should clearly define default risk.-Eg. how default will affect the parties, should beclearly mentioned in the contract.Study Session 17, Reading 61
  28. 28. Eurodollar Time Deposits Any deposit in US dollars outside the US Banks borrow funds by issuing Eurodollar time deposits Eurodollar time deposits are short term unsecured loans. The Eurodollar time deposits market, primarily centred inLondon, is relatively less regulated.Study Session 17, Reading 61
  29. 29. LIBOR Lending rate between financial institutions Used for derivative pricing Rate at which London banks issue dollar loans to otherbanks, the best rate on the dollars loaned by a bank an add-on interest rate, it is added to the face valueStudy Session 17, Reading 61
  30. 30. EURIBOR Interbank borrowing rate Issued by European Central Bank Used for borrowing between financial institutionsStudy Session 17, Reading 61
  31. 31. Forward Rate Agreement A Forward Rate Agreement is a forward contract on interestrates FRA is different from a forward contract on a bond Only the interest differential on the notional amount of thecontract is paidStudy Session 17, Reading 61
  32. 32. Forward Rate Agreement The parties to the contract will exchange a fixed rate for avariable rate If rates rise then the long will get a differential payment (ielong interest rates). If the interest rates decline then the shortwill get a differential payment (ie short interest rates). Atexpiration the present value of interest rate differential is paid.The rate is called a forward contract rate.Study Session 17, Reading 61
  33. 33. Calculation Payment is the difference between the rate at expiration andforward rateCompany X enters into an FRA with Company Y. Company X will receive afixed rate of 5% for one year on a principal of $1 million in three years.Company Y will receive the one-year LIBOR rate, determined in three yearstime, on the principal amount. The agreement will be settled in cash inthree years. After three years time, the LIBOR is at 5.5%. Company X willpay Company Y, as the LIBOR is higher than the fixed rate.Study Session 17, Reading 61
  34. 34. CalculationMathematically, $1 million at 5% generates $50,000 of interestfor Company X while $1 million at 5.5% generates $55,000 ininterest for Company Y.Study Session 17, Reading 61
  35. 35. Calculating The Payoff Difference in the interest rates is paid The payoff is adjusted for the present value in the case of acash settled FRA Payoff made at maturity in the instance of a cash settledcontract- Long gets a payoff if the interest rates go up.- Short gets a payoff if the rates go downStudy Session 17, Reading 61
  36. 36. Formula and Component Terms Notional principal is agreed upon at the initiation of thecontract Underlying rate is the rate at expiration, usually LIBOR Forward contract rate is the agreed rate Days in underlying rate are the days to maturity of theinstrumentStudy Session 17, Reading 61
  37. 37. Currency Forward Contracts Used by banks and corporations to manage foreign exchangerisk Eliminates uncertainty about future exchange rates Forward rate can be locked in without any upfront costStudy Session 17, Reading 61
  38. 38. Futures Contracts Standardized contracts Traded on exchanges Marked to market Limited default riskStudy Session 17, Reading 62
  39. 39. Futures vs ForwardsFutures Contract Standardized Settled daily Involves Clearing House No/Minimal Default Risk Terms set by Exchange(Market to Market)Forwards Contract Non-standardized Not settled daily No Clearing House Considerable Default Risk Terms set by the partiesStudy Session 17, Reading 62
  40. 40. Margin and its Role A percentage of the contract value is initially deposited intothe margin account by each party. The margin allows each party to avoid paying the full amountof the contract value at the initiation of the contractStudy Session 17, Reading 62
  41. 41. Margin in Stock and Future Market Margin in stock market means a loan is made but a margin infutures market means a percentage of the contract value hasbeen paidStudy Session 17, Reading 62
  42. 42. Initial Margin It is the margin required to set up an account and buy thecontract Investor deposits the initial margin into her account beforestarting futures trading. The deposit can be likened to a downpayment.Study Session 17, Reading 62
  43. 43. Maintenance Margin The minimum balance required to be maintained in themargin account The maintenance margin requirement is lower than the initialmargin.Study Session 17, Reading 62
  44. 44. Variation Margin When the account balance falls below the maintenancemargin requirement, the investor need to deposit money inthe account to bring it back to initial margin. The amount deposited in the account to bring it back to theinitial marginStudy Session 17, Reading 62
  45. 45. Settlement Price The official price of the futures contract, designated by theclearing house, which usually represents the average of thefinal few trades of the day eliminates the biases from the pricing of the futuresStudy Session 17, Reading 62
  46. 46. Price Limits Price limits are imposed on some futures where the pricecannot move beyond those limits.Study Session 17, Reading 62
  47. 47. Limit Move If the transaction is made at a price beyond the price limitthen the price freezes and it is called a limit move In case of price being stuck at upper limit it is called “limit up”and “limit down” in case of price being stuck at the lower limitStudy Session 17, Reading 62
  48. 48. Locked Limit If the price is beyond limit such that the transaction cannottake place, then it is called a locked limit. The settlement price is one of the limits if the price has notmoved back within the limits by the end of the dayStudy Session 17, Reading 62
  49. 49. Margin: ExampleThe prices of a futures contract for fiveconsecutive trading days is provided inthe table. The initial marginrequirement is set at $4.00 per contractand the maintenance margin is $3.60per contract.Study Session 17, Reading 62
  50. 50. Margin: Example On day 0, a trader enters into a short position for 15 contracts.Study Session 17, Reading 62
  51. 51. Margin: ExampleOn day 0, the trader mustdeposit an initial margin of$60 (= $4 x 15).Subsequent gains andlosses on the short positionare reflected in the endingmargin balance for the day.The ending balance on day4 is $45, which is below themaintenance margin of$54 (= $3.60 x 15).Study Session 17, Reading 62
  52. 52. Margin: Example On any day in which theamount of money in themargin account at theend of the day falls belowthe maintenance marginrequirement, the trader mmust deposit sufficientfunds to bring thebalance back up to theinitial margin.requirement.Study Session 17, Reading 62
  53. 53. Margin: Example Therefore, the tradermust deposit $45 on day 5to bring the marginbalance up to $90. Afterreflecting a gain of $15,the ending balance onday 5 is $105. requirement.Study Session 17, Reading 62
  54. 54. Terminating Futures Contract Futures contracts can be settled either during or beforeexpiration. Termination terms are determined when thecontract is initiated. They specify whether the contract issettled by physical delivery or cash. Most futures contracts are exited before expiration. Anoffsetting contract needs to be entered for an investor to closea position before expiration.Study Session 17, Reading 62
  55. 55. Delivery and Cash SettlementsDelivery-Settled Contracts Clearing house matchesthe long position partywith the short positionparty in the same asset Long gets the deliveryfrom the short and paysthe contract price tothe shortCash-Settled Contracts The investor’s account willbe marked to the marketon the final day and theposition is closed Cash settlement contractshave lower transactioncostsStudy Session 17, Reading 62
  56. 56. Treasury Bill Futures Short term interest rate futures While the contract is trading, the price is quoted as 100 minusthe rate quoted as a percentage into the contract by thefutures market Expiry may be the current month, next month, or the nextquarter (eg March, June, September and December) For treasury futures, the contract with the nearest expirationtends to have the highest trading volume Study Session 17, Reading 62
  57. 57. Eurodollar Futures Eurodollars futures are based on the LIBOR Final settlement is made on the final day based on theEurodollar rate determined by British Bankers Association Contracts do not permit the actual delivery of Eurodollar timedepositsStudy Session 17, Reading 62
  58. 58. Treasury Bond Futures Medium or long term interest rate futures Very actively traded futures contracts A vast universe of bonds with differing maturities makes thefutures on bonds very complex A conversion factor is used to determine the health of thedeliverable bonds and which bonds can be delivered by theshort Cheapest to deliver bonds are identified by the shortStudy Session 17, Reading 62
  59. 59. Stock Index Futures Futures on stock indices have a multiplier which is multipliedby the quoted futures price typically expire in March, June, September or December, butthe trading volumes are highest in the nearest two or threeexpiration futuresStudy Session 17, Reading 62
  60. 60. Currency Futures Market is not as active as the currency forwards market Each contract has a designated size and quotation unit Typically expire in March, June, September and December Currency futures contracts call for actual delivery of theunderlying currencyStudy Session 17, Reading 62
  61. 61. Call and Put Options An option is a derivative contract which gives the owner a right butnot the obligation to exercise it in future. It is a right, not anobligation.Study Session 17, Reading 63Call Option right to buy an asset in thefuture at a specific price buyer expects the prices to goup option is exercised if the priceof the asset is greater than thestrike pricePut Option right to sell an asset in thefuture at a specific price buyer expects the price todecline option is exercised if the priceof the asset is below the strikeprice
  62. 62. Call and Put Option: Terms Exercise price is a price at which the option can be exercised(also called the strike price) The option premium is the amount paid to buy the right Payoff is the amount which option buyer receives uponexercise of the option (it may be negative)Study Session 17, Reading 63
  63. 63. European and American OptionsEuropean Options Can only be exercisedat expiry Easier to value Trade at a discountAmerican Options can be exercised at any timeduring the life of the option Difficult to value due to optimalexercise time consideration Trade at a premium due toflexibility on exercise datesStudy Session 17, Reading 63
  64. 64. Moneyness of an Option Moneyness is the relationship between the price of theunderlying asset and the strike price An option can be characterised as: in the money, at the moneyand out of the money An option is in the money, when it has a positive payoff (eglong call = price > strike)Study Session 17, Reading 63
  65. 65. In the Money “In the money” Options: cash inflow s > cash outflowStudy Session 17, Reading 63For Call Options: price of the asset > optionsstrike priceFor Put Options: price of the asset < optionsstrike price
  66. 66. At the Money An option is “at the money” when the exercise price is equalto the market price of the underlying asset The definition for an at the money option is the same for bothput options and call options At the money options are usually not exercised because theyresult in neutral cash flow at maturity (but a loss to optionholder given the option premium already paid)Study Session 17, Reading 63
  67. 67. Out of the Money Outflow > Inflow Option results in a loss and is allowed to expire worthless.Study Session 17, Reading 63For Call Options: options strike price > marketprice of the underlying asset.For Put Options: options strike price <market price of theunderlying asset.
  68. 68. Exchange-Traded vs Over-the-CounterOptionsExchange-Traded Undertaken by bothinstitutional and individualinvestors Credit risk does not exist Options exchange fixes allthe terms of the optionscontract Public contractsOver-the-Counter Undertaken by largeinstitutions, not individualinvestors Credit risk exist Participants choose andagree on the terms of theoption Private party contractsStudy Session 17, Reading 63
  69. 69. Over the Counter Options Over the counter market is much like a forwards market There are no guarantees in the over the counter markets More flexible Dealers marketStudy Session 17, Reading 63
  70. 70. Exchange Traded Options The options exchange fixes all the terms of the optionscontract, whether the option is European/American or deliverysettled/cash settled Fairly short term expirations for exchange traded options LEAPS (Long Term Equity Anticipatory Securities) are long termoptionsStudy Session 17, Reading 63
  71. 71. Types of Options by UnderlyingInstruments Financial Option – Option when the underlying asset is afinancial asset(i.e. stock options, interest rate options, bond options) Commodity Option – Option when the underlying asset is acommodity,Study Session 17, Reading 63
  72. 72. Financial Options: Stock Options The most popular form of option contract Typically exchange traded and available on most widely tradedstocks. Can also be created in the over the counter market Equity Options - options on individual stocks Index Options - options on a stock market indexStudy Session 17, Reading 63
  73. 73. Financial Options: Bond Options Options on bonds Primarily traded in over the counter markets Can be delivery settled or cash settled Exchanges have not been successful with bond options Bond options are mostly on government bondsStudy Session 17, Reading 63
  74. 74. Interest Rate Options Underlying is an interest rate Option to borrow/lend in the future Effective tool to hedge against interest rate uncertainty When the contract expires, the payoff is made immediatelyStudy Session 17, Reading 63
  75. 75. Out of the Money Exercise rate is used for interest rate options, instead of exerciseprice Payoff is the differential between the underlying rate and the strikerateStudy Session 17, Reading 63Call holder: right to make a fixedrate payment and receive avariable rate payment-“In the money”: unknown rate >strike rate-“Out of the money”: unknownrate < strike ratePut holder: right to make a variablerate payment and receive a fixedrate payment-“In the money”: unknown rate <strike rate-“Out of the money”: unknown rate> strike rate
  76. 76. Interest Rate Cap A limit on the upward movement of interest rates A set of interest rate call options Each option is independent of the other option Each call option is called a capletStudy Session 17, Reading 63
  77. 77. Interest Rate Floor A limit on the downward movement of interest rates A series of interest rate put options Options are independent of each other Each option is called a floorletStudy Session 17, Reading 63
  78. 78. Interest Rate Floor and Interest Rate CapInterest Rate Cap A limit on the upward movement ofinterest rates A set of interest rate call options Each option is independent of theother option Each call option is called a capletInterest Rate Floor A limit on the downward movement ofinterest rates A series of interest rate put options Options are independent of each other Each option is called a floorletStudy Session 17, Reading 63
  79. 79. Collars A combination of caps and floors-Long cap and short floor-Short cap and long floor Hedging can be undertaken at zero cost by matching the longcall and short floor Underlying can be any interest rateStudy Session 17, Reading 63
  80. 80. Option Payoff The option value at expiration is called an option’s “payoff”Study Session 17, Reading 63Payoff For Calls Payoff is the maximum of 0 or“spot price minus strike price” Max (0, (Underlying Price -Strike Price)) Upside potential is unlimited Loss is limited to optionpremium.Payoff For Puts Payoff is the maximum ofeither 0 or the “strike priceminus the underlying price” Max (0, (Strike Price -Underlying Price)) Downside potential is limited For a long put position, theloss is limited to optionpremium
  81. 81. Payoff for Calls: Long PositionStudy Session 17, Reading 63
  82. 82. Payoff for Calls: Short PositionStudy Session 17, Reading 63
  83. 83. Payoff for Puts: Long PositionStudy Session 17, Reading 63
  84. 84. Payoff for Puts: Short PositionStudy Session 17, Reading 63
  85. 85. Components of Option Price Option price have two components:-Intrinsic value: Difference between the actual price and thestrike price-Time value: Depends on the remaining time in optionexpiration and volatility Option value = Intrinsic value + Time value Prior to expiry, Option value exceeds its Intrinsic value. Thedifference is Time value. As the option reaches expiry, Time value decreases andIntrinsic value increases. At expiry, Time value is 0 and Intrinsic value is at maximum.Study Session 17, Reading 63
  86. 86. Intrinsic Value For a Call: 0 or “spot price minus strike price” For a Put: 0 or “strike piece minus spot price” Before expiration, an option will normally sell for more than itsintrinsic value “At the Money” or “Out of the Money” Option: Intrinsic Value= 0 “In the Money” Option: Intrinsic Value > 0Study Session 17, Reading 63
  87. 87. Time Value The difference between the market price and intrinsic value At expiration, Time value = 0 Given European options cannot be exercised early, all theoption value is “time value”Study Session 17, Reading 63
  88. 88. European and American Options:Minimum and Maximum Values All options have a floor value of zero American options are more valuable than European options giventhe flexible exercise regimeStudy Session 17, Reading 63European Option:Call Option: 0≤co≤ So, min. value for calloption is 0 and the max. value isthe spot price of the underlyingPut Option: po≥0, min. value po≤ X/(1+r)t, max. ValueAmerican Option:Call Option: 0≤Co≤ So, min. value forAmerican call will be zero andmax. value can be spot pricePut Option: Po≥0, min. value Po≤ X, max. value
  89. 89. European Options Given the lack of exercise option, the European put option needs tobe discountedExampleGiven: So= 28, X=25, r= 5% t=1/2 yearsSince, 0≤co≤ So0≤co≤28, minimum and maximum values for a European call optionSince, po≥0, min. value po≤ X/(1+r)t, max. value0≤po≤24.4~ (25/(1.05).5), minimum and maximum value for Europeanput optionStudy Session 17, Reading 63
  90. 90. American Options Given the option of early exercise, the American put option does notneed to be discounted.ExampleGiven: So= 28, X=25Since, 0≤Co≤ So0≤Co≤28, minimum and maximum values for a American call optionSince, Po≥0, min. value Po≤ X, max. Value0≤Po≤25, minimum and maximum value for American put optionStudy Session 17, Reading 63
  91. 91. Lowest Prices of European Options Option Price is between 0 and the maximum Lower bound = 0 or current price [of underlying]- exerciseprice (present value), whichever is higher To get a lower bound, options can be combined with risk freebonds. An investor needs to buy a bond with a Face value =Exercise price & a Current value = Exercise price (Presentvalue). This involves borrowing and lending money equal tothe present value of exercise priceStudy Session 17, Reading 63
  92. 92. European Call Lower bound combination for European calls. co ≥ Max*0,So-X/(1+r)T]Study Session 17, Reading 63Transaction Current Value Value at ExpirationST ≤ X ST > XBuy Call C0 0 ST - XSell Short Underlying -S0 -ST -STBuy Bond X/(1+r)^T X XTotal C0 - S0 + X/(1+r)^T X-St≥0 0
  93. 93. European Put Lower bound combination for European Puts. Lower bound = 0 or exercise price (present value) - price of theunderlying po≥ Max*0,X/(1+r)T-So]Study Session 17, Reading 63Transaction Current Value Value at ExpirationST ≤ X ST > XBuy Put P0 X - ST 0Sell Short Underlying S0 ST ≤ X STBuy Bond -X/(1+r)^T -X0 -XTotal P0 - S0 + X/(1+r)^T 0 ST - X ≥ 0
  94. 94. Lowest Prices of American Options American options are exercisable immediately Lower bound = current intrinsic value-Co ≥ Max(0, So-X)-Po ≥ Max(0, X-So) Option price will be at least intrinsic value, otherwise anarbitrage opportunity exists. The lower bound for American puts is higher than the lowerbound for European putsStudy Session 17, Reading 63
  95. 95. Effects of Exercise Price onOption Values Put options with a higher exercise price, have higher option prices Call options with a higher exercise price, have lower option prices A call option with higher exercise price cannot have a higher value than anoption with lower exercise price Call option buyers are willing to pay less for an option with a higher exerciseprice The value of a put with a higher exercise price must be as much, if not morethan, the lower exercise price optionStudy Session 17, Reading 63
  96. 96. Effects of Time to Expiration onOption Values Additional time to expiry is an advantage for an American put holders since it canbe exercised at any time, but it can be a disadvantage for a European put holderdue to the loss of interest More time to expiry, the more valuable an option For the options deep in the money or deep out of money, the time value of theoption may be diluted. For a European put, longer or shorter time to expiry can be worth moreStudy Session 17, Reading 63
  97. 97. Put-Call Parity for European Option A premium on the call option corresponds to the fair value of a put option havingthe same exercise price and expiration date and vice versa Arbitrage opportunity will exist if the prices diverge C+X/(1+r)t= So + PStudy Session 17, Reading 63
  98. 98. Put-Call Parity for European Option C+X/(1+r)t= So + PThe left hand side of the equation consists of a European call and risk free bond-If price of underlying < strike price, then the option is worthless at expiryand the bond = X-If price of underlying > strike price, then the call expires as S-XStudy Session 17, Reading 63
  99. 99. Put-Call Parity for European Option C+X/(1+r)t= So + PThe right hand side of the equation comprises of a European put and theunderlying asset-If price < strike price, the put expires as X-S-If price > strike price then the put expires worthless and the value of theunderlying is STStudy Session 17, Reading 63
  100. 100. Put-Call Parity Used to Arbitrage Right hand side of the equation is called a synthetic call An “in the money” synthetic call will give the underlying value minus the payoff of abond Right(?) hand side of the equation is called the synthetic put Prices not conforming to put call parity will result in an arbitrage opportunityStudy Session 17, Reading 63
  101. 101. Effects of Cash Flows onPut-Call Parity In the case of stocks, present value of dividends is deducted from the underlying’sprice In the case of bonds, present value of coupon payments is deducted from theunderlying asset’s priceco+X/(1+r)T= Po + [So-PV(CF,0,T)]Study Session 17, Reading 63
  102. 102. Effects of Cash Flows onthe Lower bounds In the case of stocks, present value of dividends is deducted from the underlyingasset’s price In the case of bonds, present value of coupon payments is deducted from theunderlying asset’s priceco ≥Max{0,*So-PV(CF,0,T)]-X/(1+r)T}po ≥Max{0,X/(1+r)T-[So-PV(CF,0,T)]}Study Session 17, Reading 63
  103. 103. Effects of Interest Rate Changeon an Option’s Price Higher interest rates :-increase the call option price-decrease the put option price When interest rates are high, investors forfeit more interest when interest rates arehigher while waiting to sell the underlying. (i.e. the opportunity cost of waiting tosell in a higher interest rates is more significant) When the underlying asset is an interest rate or bond, the interest rates do nothave a strong effect on the option pricesStudy Session 17, Reading 63
  104. 104. Effects of Volatility Changeon an Option’s Price Higher volatility of the underlying asset value increases the value of both put andcall options Higher volatility increases the possible upside value and downside value of theunderlying asset-Upside advantage helps calls but at the same time does not hurt the puts-Downside effect helps the puts but does not hurt callsStudy Session 17, Reading 63
  105. 105. Swap Contracts Swaps are a series of fixed or variable payments, otherwise described as a series offorward contracts No upfront payment and has zero value at the initiation Customized contracts and are typically over the counter instruments Only the net payments between parties are made. The difference owed by oneparty is paid to the other since the payments are made in the same currency.However, currency swaps are an exception to this rule as full interest payments aremade in currency swaps.Study Session 17, Reading 64
  106. 106. Termination of Swap Contracts Termination date is specified Usually the final payment is the termination Original time to maturity is also called the tenor of the swapStudy Session 17, Reading 64
  107. 107. Termination of Swap Contracts Termination can be undertaken by paying or receiving the market value from thecounter party. This can only be undertaken if specified by both parties in advance. A swap can also be sold to another party in order to terminate the position A swaption is also a way to terminate the swap. It is an option to enter into a swapin the future.Study Session 17, Reading 64