Introduction, Forwards and Futures - Baruch College

1 introduction , Forwards and FuturesLiuren WuOptions Markets(Hull chapters: 1,2,3,5)Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets1 / 31 Outline1 Derivatives2 Forwards3 Futures4 forward pricing5 Interest rate parityLiuren Wu(c ) introduction , Forwards & FuturesOptions Markets2 / 31 DerivativesDerivative securities are nancial instruments whose returns are derived fromthose of another nancial instrument, which is often referred to as the\underlying security."Acall optionon IBM stock: IBM stock is the underlying security. Thecall option is the : Forwards , Futures , swaps, options ..Cash markets or spot markets forprimary securitiesThe sale is made, the payment is remitted, and the good or security isdelivered immediately or shortly of primary securities: stocks , Wu(c ) introduction , Forwards & FuturesOptions Markets3 / 31 Derivatives MarketsExchange-traded instruments (Listed products)Exchange traded securities are generally standardized in terms ofmaturity, underlying notional, settlement procedures.

2 By the commitment of some market participants to act asmarket-maker, exchange traded securities are usually very makers are particularly needed in illiquid exchange traded derivatives require "margining" to limitcounterparty some exchanges, the counterparty is the exchange itself yielding theadvantage of Wu(c ) introduction , Forwards & FuturesOptions Markets4 / 31 Derivatives MarketsOver-the-counter market (OTC)OTC securities are not listed or traded on an organized OTC contract is a private transaction between two parties(counterparty risk).A typical deal in the OTC market is conducted through a telephone orother means of private terms of an OTC contract are usually negotiated on the basis ofan ISDA master agreement (International Swaps and DerivativesAssociation).Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets5 / 31 Derivatives ProductsForwards (OTC) Futures (exchange listed)Swaps (OTC) options (both OTC and exchange listed)Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets6 / 31 Review: Valuation and investment in primary securitiesThe securities have direct claims to future cash is based onforecastsof future cash ows and risk:DCF (Discounted Cash Flow Method): Discountforecastedfuture cash ow with a discount rate that is commensurate with : Buy if market price is lower than model value; sell valuation and investment depend crucially on forecasts of future cash ows (growth rates) and risks (beta, credit risk).

3 Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets7 / 31 Compare: Derivative securitiesPayoffs are linked directly to the price of an \underlying" is mostly based on replication/hedging a portfolio that includes the underlying security, and possiblyother related derivatives, to replicate the payoff of the target derivativesecurity, or to hedge away the risk in the derivative the hedged portfolio is riskfree, the payoff of the portfolio can bediscounted by the riskfree of this type are called\no-arbitrage" :No forecasts are involved. Valuation is based on is not about whether the underlying security price will go up or down(given growth rate or risk forecasts), but about the relative pricingrelation between the underlying and the derivatives under all Wu(c ) introduction , Forwards & FuturesOptions Markets8 / 31 Arbitrage in a Micky Mouse ModelThe current prices of asset 1 and asset 2 are 95 and 43, , one of two states will come trueA good state where the prices go up orA bad state where the prices go downAsset1 = 95 Asset2 = 43 PPPPA sset1 = 100 Asset2 = 50 Asset1 = 80 Asset2 = 40Do you see any possibility to make risk-free money out of this situation?

4 Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets9 / 31 DCF versus No-arbitrage pricing in the Micky Mouse ModelDCF: Both assets could be over-valued or under-valued, depending on ourestimates/forecasts of the probability of the good/bad states, and thediscount model: The payoff of asset 1 is is twice as much as the payoffof asset 2 inallstates, then the price of asset 1 should be twice as much asthe price of asset price of asset 1 is too highrelative toto the price of asset price of asset 2 is too lowrelative toto the price of asset do not care whether both prices are too high or low given forecastedcash asset 1 and buy asset 2, you are guaranteed to make money | asset 1 alone or buying asset 2 alone is not : DCF focuses on time-series forecasts (of future ). No-arbitrage modelfocuses on cross-sectional comparison (no forecasts)!Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets10 / 31 Keys to understand primary versus derivative securitiesPrimary securities:Understand the major determinants of the future cash ows and risksDerivative securities:Understand thepayoffsas a function of the underlying securityWhat's the payoff of (a portfolio of) common derivative contracts?

5 Understand the replication strategy of different payoff structures:How to replicate a certain desired payoff with the underlying securityand/or other derivatives?When replication is difficult, what assumptions do you need to make tomake it possible? What's the potential cost/harm in case yourassumption is wrong?Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets11 / 31 forward contracts: De nitionAforward contractis an OTC agreement between two parties to exchangean underlying assetfor an agreed upon price (theforward price)at a given point in time in the future (theexpiry date)Example: On June 3, 2003, Party A signs a forward contract with Party B tosell 1 million British pound (GBP) at USD per 1 GBP six month (June 3, 2003), sign a contract, shake hands. No moneychanges 6, 2003 (the expiry date), Party A pays 1 million GBP toParty B, and receives million USD from Party B in (June 3), thespot pricefor the pound (the spot exchangerate) is Six month later (December 3), the exchange rate canbe anything (unknown).

6 Is theforward Wu(c ) introduction , Forwards & FuturesOptions Markets12 / 31 Foreign exchange quotes for GBPUSD June 3, forward prices are different at different or time-to-maturityrefers to the length of time between nowand expiry date (1m, 2m, 3m etc).Expiry (date)refers to the date on which the contract : forward priceF(t;T):t: today,T: expiry, =T t: timeto spot priceS(t) =F(t;t). [orSt;Ft(T)] forward contracts are the most popular in currency and interest Wu(c ) introduction , Forwards & FuturesOptions Markets13 / 31 forward price revisitedThe forward price for a contract is the delivery price (K) that would beapplicable to the contract if were negotiated today. It is the delivery pricethat would make the contract worth : Party A agrees to sell to Party B 1 million GBP at the priceof per GBP six month later, but with an upfront payment million USD from B to is NOT the forward price. Why?If today's forward price is , what's the value of the forwardcontract with a delivery price (K) of party that has agreed to buy has what is termed along position.

7 Theparty that has agreed to sell has what is termed the previous example, Party A entered a short position and Party Bentered a long position on since it is on exchange rates, you can also say: Party A entered along position and Party B entered a short position on Wu(c ) introduction , Forwards & FuturesOptions Markets14 / 31 Terminal payoffs from forward investmentsBy signing a forward contract, one can lock in a priceex antefor buying orselling a expiry, whether one makes or loses money from exercising the contract, , one'spayoff from the contract, depends on the spot price at the previous example, Party A agrees to sell 1 million pound at $ perGBP at expiry. If the spot price is $ at expiry, what's thepayoffor partyA?On Dec 3, Party A can buy 1 million pound from the market at thespot price of $ and sell it to Party B per forward contractagreement at $ net payoff at expiry is the difference between thestrike price(K= 1:61) and the spot price (ST= 1:31), multiplied by the notional(1 million).

8 Hence, the spot rate is $ on Dec 3, what will be the payoff for Party A?What's the payoff for Party B?How doespayoffdiffer fromP&L?Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets15 / 31 Terminal payoffs from forward investments(K= 1:61)long forward :(ST K) from long forward , ST KSpot price at expiry, STshort forward :(K ST) from short forward , K STSpot price at expiry, STCounterpary risk: There is a small possibility that either side can default onthe contract. That's why forward contracts are mainly between of the motivations of the current regulation movement to centralclearing is to reduce counterparty to calculatereturnson forward investments?Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets16 / 31 Payoff from cash markets (spot contracts)1If you buy a stock today (t), what does the payoff function of the stock looklike at timeT?1 The stock does not pay stock pays dividends that have a present value does the time-Tpayoff look like if you short sell the stock at timet?

9 3If you buy (short sell) 1 million GBP today, what's your aggregate dollarpayoff at timeT?4If you buy (sell) aKdollar par zero-coupon bond with an interest rate ofrat timet, how much do you pay (receive) today? How much do you receive(pay) at expiryT?Liuren Wu(c ) introduction , Forwards & FuturesOptions Markets17 / 31 Payoff from cash markets: Answers1If you buy a stock today (t), the time-tpayoff ( T) is1 STif the stock does not pay +Dter(T t)if the stock pays dividends during the time period[t;T] that has a present value ofDt. In this case,Dter(T t)representsthe value of the dividends at payoff of short is just the negative of the payoff from the long position: STwithout dividend and ST Dter(T t)with you borrow stock (chicken) from somebody, you need to return boththe stock and the dividends (eggs) you receive in you buy 1 million GBP today, your aggregate dollar payoff at timeTisthe selling priceSTplus the pound interest you make during the time period[t;T]:STerGBP(T t) zero bond price is the present value ofK:Ke r(T t).

10 The payoff isKfor long position and Kfor short these Wu(c ) introduction , Forwards & FuturesOptions Markets18 / 31 Futures versus ForwardsFutures contracts are similar to Forwards , butBuyer and seller negotiateindirectly, through the risk is borne by the exchange clearinghousePositions can be easily reversed at any time before expirationValue ismarked to market : quality; quantity; short position has often differentdelivery options ; good because itreduces the risk of squeezes, bad .. because the contract is moredifficult to price (need to price the \cheapest-to-deliver").The different execution details also lead to pricing differences, , effect ofmarking to market on interest Wu(c ) introduction , Forwards & FuturesOptions Markets19 / 31 Futures versus SpotEasier to go short: with Futures it is equally easy to go short or short seller using the spot market must wait for an uptick before initiatinga position (the rule is ).