CFA Level 1 - Derivatives

Derivative Instruments and Markets Features

• Derivatives: Definition and Features

  • A derivative's value is derived from another underlying asset.

• Basic Features of Derivative Markets

  • Exchange-traded

  • Over-the-counter (OTC)

Learning Outcome

• Define a derivative and describe basic features of a derivative instrument.

• Describe the basic features of derivative markets, and contrast over-the-counter and exchange-traded derivative markets.

Derivative Contracts

• Forwards: Customized, traded OTC.

• Futures: Standardized, traded on exchanges, require margin.

• Swaps: Commitment to exchange cash flows.

• Options: Contingent claim.

• Credit Derivatives: Based on credit risk.

Forward Contracts

• Agreement to buy or sell an asset at a specified future date and price.

• Example: Sell Gold after 1 month @ forward price = $100

• Payoff Scenarios: Market Price (MP) vs Forward Price (FP)

  • MP > FP: Long benefits, short loses.

  • MP < FP: Short benefits, long loses.

  • Example Scenarios:

    • MP = $110: Gain to short, loss to long.

    • MP = $120: value = S_{30} - FP = $120 - $100 = $20

    • MP = $90: value = S_{30} - FP = $90 - $100 = -$10

• Settlement: Physical or Net Cash

Components Specified in Forward Contracts

• Underlying Asset (commodities, stocks, bonds, currencies).

• Delivery Date.

• Forward Price.

Physical Settlement

• Example: If S_{30} = $110 physical gold is exchanged for $100. Net Cash Settlement

  • Long: (MP - FP). Example: 110-100 = $10 gain.

  • Short: -(MP - FP). Example: -(110-100) = -$10 loss

Risks Involved

• Counterparty risk arises for both sides if one party defaults.

• Derivatives are highly leveraged. Value = 0 (neither party pays anything to another on the first day).

Futures Contracts

• Standardized forward contracts traded on exchanges.

• Standardized sizes, dates, and settlement procedures.

• Require margin deposits (both long and short positions).

• More regulated than forwards.

• Guarantee against default.

• Examples of future prices over time: FP2 = 93, FP3 = 92

Sample Forward Contract

• Derivative transforms the performance of the underlying.

• Example: AMY Investments agrees to deliver 1,000 Airbus shares at €30 per share in six months.

• Transfers price risk to a counterparty.

• Settlement: Cash difference or physical delivery.

  • If S_T is €25, AMY receives €30,000 or settles the €5,000 difference in cash (1000 * (30-25)).

• Stand-alone vs. Embedded derivatives.
  Distinct Derivative contract
  * Derivatives on stocks or bonds such as Callable Bonds, Puttable Bonds, and Convertible Bonds

Derivatives and Market Opportunities

• Expand opportunities to create or modify exposure to an underlying.

• Allow short selling to profit from expected declines.

• Serve as portfolio diversification tools.

• Enable issuers to offset financial market exposure.

• Create large exposures with small cash outlays.

• Offer lower transaction costs and higher liquidity than spot markets.

• Used for hedging to offset risk exposure.

Derivatives Underlying

• Equities

  • Stocks, groups of stocks, or indices.

  • Index swaps to exchange returns on different indices or interest rates.

  • Options, futures, and swaps based on realized volatility.

  • Warrants.

• Fixed Income

  • Bonds and related derivatives (options, forwards, futures, swaps).

  • Interest rate swaps (fixed for floating).

  • Market reference rate (MRR) as the interest rate underlying (e.g., SOFR).

• Currency

  • Used to hedge foreign exchange risk.

• Commodity

  • Manage price risk via derivatives, separate from physical delivery.

  • Soft (agricultural) and hard (natural resources) commodities.

• Credit Derivatives

  • Based on default risk.

  • Credit default swaps (CDS) to manage default risk separately from bond market.

• Other Derivatives

  • Weather, cryptocurrencies, longevity.

OTC Derivative Markets

• Involve contracts between end-users and dealers (market makers).

• Dealers hedge risk through offsetting contracts.

• Terms are customized.

• Less transparency and more counterparty risk than exchange-traded derivatives.

Exchange Traded Derivatives

• Standardized contracts traded on exchanges (futures, options).

• More formal, liquid, and transparent.

• Lower transaction costs.

• Terms set by the exchange (size, type, quality, maturity).

• Market makers provide liquidity.

• Efficient clearing and settlement process.

• Both parties post collateral against default.

• Full transaction information disclosed to exchanges and regulators.

• Exhibit 5: LME Lithium Futures Contract Specifications

  • Contract Maturities: Monthly [from 1 month to 15 months]

  • Contract Size: One metric ton

  • Delivery Type: Cash settled

  • Price Quotation: USD per metric ton

  • Final Maturity: Last LME business day of contract month

  • Daily Settlement: LME Trading Operations calculates daily settlement values based on its published procedures

  • Final Settlement: Based on the reported arithmetic monthly average of Fastmarkets' lithium hydroxide monohydrate 56.5% LiOH. H20 min, battery grade, spot price cif China, Japan, and Korea, USD/kg price, which is available from Fastmarkets from 16.30 London time on the last trading day

• Exhibit 6: Exchange-Traded Derivative Markets

Central Clearing

• CCPs assume credit risk between counterparties, especially financial intermediaries.

• Maintain flexibility for end-users.

• Systemic credit risk transfer leads to centralization and concentration of risks.

• Proper safeguards are needed to avoid excessive risk in CCPs.

Forward Commitment and Contingent Claim Features and Instruments

• Define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics

• Determine the value at expiration and profit from a long or a short position in a call or put option

• Contrast forward commitments with contingent claims

Forward Contracts (Detailed)

• OTC derivative where a buyer agrees to purchase an underlying asset from a seller at a future date at a pre-agreed fixed price.

• Customized, with no active secondary market.

• Long obligated to buy, short obligated to sell.

• Specified asset and delivery location.

• Specified date in the future.

• Long gains if asset price above forward price, short gains if asset price below.

• Value is 0 at the start.

• Deliverable or cash-settled.

• Symmetric payoff profile, also referred to as linear derivatives.

Futures Contracts (Detailed)

• Standardized forward contracts traded on futures exchanges.

• Offer liquidity and protection against default.

• Exchange-traded with active secondary market.

• Require margin deposit, marked to market daily.

• Settlement price determined by clearing house.

• Price converges to spot at expiration.

• Limits on daily price moves.

Swaps (Detailed)

• Commitment to exchange cash flows in the future.

• Typically floating for fixed or vice versa.

• Most common: Interest rate swaps.

• Floating rate payer (fixed-rate receiver) vs. Fixed rate payer (floating-rate receiver).

• Equivalent to a series of forward contracts.

Simple Interest Rate Swap

• One party pays a fixed rate of interest.

• One party pays a variable (floating) rate of interest.

• Payments can be based on interest rates or stock/portfolio/index returns.

• Can involve two different currencies.

• The market reference rate (MRR) paid by the floating-rate payer resets each period, while the fixed rate (referred to as the swap rate) is constant.

Swap Types

• Plain vanilla interest rate swap.

• Currency swap.

• Equity swap.

• Example

  • A gives to B LIBOR + 5%

  • B pay UBOR

  • Net cash flow (LIBOR + 5% - UBOR )

• Plain vanilla IR Swap
  Bond bought from CompXYZ
  LIBOR on Bond - LIBOR on swap + 5

Swap Contracts - Knowledge check

• Similarity: Both forwards and swaps represent firm commitments with an initial value of zero where cash flows are exchanged in the future at a pre-agreed price.

• Difference: Forwards usually involve one future exchange of cash flows, while a swap contract involves more than one exchange of future cash flows.
  *Under a swap contract, we refer to the counterparty paying the variable cash flows as the floating-rate payer (or fixed-rate receiver) and the counterparty paying fixed cash flows as the fixed-rate payer (or floating-rate receiver).

• Interest Rate Swap Paricipants

  • A. Fixed-rate payer

  • B. Floating-rate payer

  • C. Both a fixed-rate payer and a floating-rate payer

    • Makes a payment each interest period based on a market reference rate : Correct anser B. A floating-rate payer on a swap makes a payment
      each period based on a market reference rate.

    • May face a positive or a negative mark to market over the life of an interest rate swap contract: The correct answer is C. Both a fixed-rate payer and a floating-rate payer
      may face a positive MTM or negative MTM on a swap contract.

    • Receives a net payment on the swap for any interest period for which the market reference rate exceeds the fixed rate: correct answer is A. A fixed-rate payer (also known as the
      floating-rate receiver) receives a net payment if the market reference rate
      exceeds the fixed rate for a given period

1. Receive a net payment on the swap
   for any interest period for which the
   market reference rate exceeds the fixed
   rate

Options

• Contingent claims where one party has the right to determine whether a trade will settle.

• Option contracts are the most common contingent claim.

• Buyer has the right but not the obligation to transact.

• Seller has the obligation to fulfill the transaction.

• Payoff to buyer is always zero or positive.

• One-sided counterparty credit risk. Seller has credit exposure to the buyer.

Option Payoff Profiles

• Long Call: Profit above strike price plus premium.

• Short Call: Profit capped at premium, loss unlimited.

• Long Put: Profit if price falls below strike, capped at strike price minus premium.

• Short Put: Profit capped at premium, loss if price falls below strike.

Call and Put Options

• Buyer's right to buy (Call) or sell (Put) at a predetermined price (X).

• Scenarios:

  • S_T > X: In the money.

  • S_T = X: At the money.

  • S_T < X: Out of the money.

• Value for Buyer: max(0, S_T - X)

• Maximum Loss: Premium. Maximum Gain: Unlimited (for call buyer).

• Seller (Writer): Option can never be negative for the buyer.

• Buyer: Maximum loss = Premium

• the Option can never be negative to the buyer

• payoff Graph for Option

  • payoff Graph for call

    • Short call +x = +premium profit limited

    • Long call - Maximum loss = puemium , Maximum Profit is unlimited

  • payoff Graph for PUT

    • short put maximum is puemium , losses are below zero, if price above x

Put Options

Right of holder
to sell
underlying at x = 100
value (Buyor)
Scenarios
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Option Contracts - Exampls and Knowledge Check

• Call Option at Expiration with Exercise price 100

  • S=98, selling at 7

    • A The price of the underlying at expiration is $102 (S_I)

    • Value C0,S-X) = (0, 102-100 = $2

    • GIL = prem=2-7=-5

    • The price of the underlying at expiration is $94.

    • V= (0,5-x)=(0, 94-100) = 0

    • GIL= v-p=0-7=17

• Put option with exercise price of 60 with rate of 4

  • Option sellfor $4 & S(0) =62

    • (A) The price of the underlying at expiration is $62. (SI)

      • V = (0, x-s) = (0,60-62 )

      • GIL=V-P=0=-4
        (B) The price of the underlying at expiration is $55.

      • V- 0, x-5 = (0,60-55) - 5

      • GIL - V - P = 5-4=+1

• Hightest Capital will reach a breakeven point and earn zero profit six exercise is 1,240 & premium = 24.85

  • breakeven point 1,240 + $24.85, or $1,264.85.

• what is the option sellers maximum loss and profit

  • maximum profit is $5 , loss under $25

• Option contract participants

  • B. Call option seller - Has no counterparty credit risk to the
    option buyer once the upfront premium
    has been paid

Credit Derivatives (Detailed)

• Based on credit underlying or default risk.

• Credit Default Swap (CDS): Lender pays cash flows to protection seller, receives payment if credit event occurs.

• Underlying may be corporate, sovereign, or special purpose entity.

• Credit protection buyer seeks to gain from higher credit spreads, short credit risk.

• Contract similar to insurance.

• CDS buyer makes MTM gain when credit spread widens.

• If default occurs, CDS seller pays the CDS buyer Loss Given Default (LGD) × Notional.
  Cedit Events

• CDS MTM change = Credit Spread x Notiona x EffDuration
  Contingent payment loss given default
  what us CDS proterction seller , position similar
  A credit protection seller receives a periodic CDS spread payment in ex-change for the contingent risk of payment to the buyer under an issuer cred-it event. A cash bond investor receives a periodic coupon that incorporatesan issuer's credit spread in exchange for a potential loss if the issuer defaults.

• Credit protection seller versus credit protection buyer

  • CDS contract transfers the risk of loss
    Seeks to gain from higher issuer credit spreads

Firm Commitment vs. Contingent Claims

• Firm commitment requires both counterparties to perform.

• Option buyer can decide whether to perform.

• Similar exposures can be created using different instruments.
  Long Forward Position and Long Call Option both gain from the increase in price

• Comparing the profit
  * Forward Contract Profit: [ST – F0(T)],
  * Option Contract Profit: \Pi = max[0, ST – F0(T)] – c0
  Payoff and profit Profile of Forward vs Option

• When we are settings forward profit [ST – F0(T)] to the option profit

• when the results are as follows:
  ST – F0(T) > –c0 Forward profit exceeds option profit
  ST – F0(T) = –c0 Forward profit equals call option profit
  ST – F0(T) < –c0 Option profit exceeds forward profit

Derivatives Benefits, Risks, and Issuer and Investor Uses

• Benefits

  • Risk Allocation, Transfer, and Management

    • Derivatives allow market participants to allocate, manage, or trade exposure without exchanging an underlying in the cash market.
      *Information Discovery

    • Derivative instrument prices serve a price discovery function beyond the underlying cash or spot market. For example, futures prices are often seen as revealing information about the direction of cash markets in the future.

    • Option prices imply implied volatility
      Operational Advantages

    • Lower Transaction Costs: Commodity derivatives eliminate the need to transport, insure, and store a physical asset in order to take a position in its underlying price.

    • Increased Liquidity: Derivative markets typically have greater liquidity as a result of the reduced capital required to trade derivatives versus an equivalent cash position in an underlying.

    • Upfront Cash Requirements: Initial futures margin requirements and option premiums are low relative to the cost of a cash market purchase.

    • Short Positions
      Market Efficiency
      When prices deviate from fundamental values, derivative markets offer less costly ways to exploit the mispricing hence improving market efficiency

  • Derivatives risks:

    • Speculative Use :Magnifies losses

    • Lack of Transparency:

    • Basis Risk: Basis risk may arise if a derivative instrument references a price or index that is similar to, but
      does not exactly match, an underlying exposure such as a different market reference rate or anissuer CDS spread versus that of an actual bond

    • Liquidity Risk: A divergence in the cash flow timing of a derivative versus that of an underlying transaction.
      Counterparty Credit Risk
      Destabilization and Systemic Risk:Leveraged Positions taken by speculators Market reforms such as the central clearing mandate for swaps between financialintermediaries and a central counterparty (CCP) include margin provisions similar tof utures in order to standardize and reduce counterparty credit risk

  Issues Use of Derivatives
  * Hedge Risk
  Hedge Accounting:Any derivative purchased or soli must be marked to makret through the income statement to earnings
  Allows offset with derivative and the hedged asset/liabilites and hence reduce
  financial statement volatility OTC vs ETD
  Investor Use of DerivativesInvestor use Derivatives

  Derivatives can be use to

  • Replicate a cash market strategy

  • Hedge a fund’s value against adverse movements in underlyings

  • Modify ( Covered call)

Arbitrage, Replication and Cost of Carry

Arbitrage
Arbitrage opportunity arises if law of one price is violated According to the ‘law of one price’ two identical assets should trade at the same price arbitrage opportunities arises in derivatives whenEither if two assets with identical future cash flows trade at different prices
If an asset with a known future price does not trade at the present value of its futureprice determined using an appropriate discount rate

Example: Assume two zero-coupon bonds with identical features, the sameissuer, the same maturity date with a payoff of par and the same default riskBond A has a price of EUR99 at time t = 0
Both bonds have an expected future price of EUR100Bonds A and B at time 0.
Since the law of one price is violated and arbitrage opportunity exists as both assetstrade at different prices today