L1 - Intro
maandag 13 november 2023 09:06
Title: Lecture 1 - Intro
• Assessment:
• final examination (85%)
• group assignment (15%)
• Derivative instrument's characteristics:
• Payoff structure comes from the cash flows of an underlying asset.
○ Payoffs of every possible scenarios must be specified.
○ Measurability:
▪ There must be highly detailed (even if 'relative').
□ e.g.: elections / weather
• Their underlying asset has an uncertain value.
○ They are typically used to hedge risks (exposure to underlying asset).
• Optionality: pay-offs may depend on choice
○ e.g.: when to exercise such options. A call option gives you the right to buy the
underlying asset at the strike price. The choice of exercising an option is when
the value of the option matters.
• Idealized notions / Perfect markets have the following features:
• Transactions:
○ No transaction costs: there are no frictions in trading
○ Short-selling is allowed freely.
○ No information costs.
○ There are no restrictions to buy a fraction of shares.
• Competition:
○ No market power: prices are taken as given, so no individual player can alter
the price by themselves.
○ Complete 'spanning': if you introduce a new share in the market, the risk-
return profile of it has already been captured by the rest of the shares in the
market.
▪ Then you can derive the price of new products because alternatives are
already available and embody the risk-return profile.
• Investors:
▪ Unbounded rational: investors can forecast all future possibilities/scenarios
and is able to process all available information, so she can calculate the
probability of each scenario happening.
▪ Steady preferences: risk preferences are constant.
▪ Rational expectations: if theres a market price that closes demand and supply,
but is not based on perfect market it cannot be the equilibrium.
• Perfect markets: there is no 'riskless' arbitrage.
▪ Same pay-offs -> identical values ("equilibrium").
▪ Markets are efficient: prices in the market capture all available information.
▪ Weak market efficiency: we cannot predict anything based on historical
prices.
• Derivative markets:
• Trading: it may happen either…
▪ Over-the-counter (OTC): may be very tailored.
▪ Danger: you may enter into large exposures with small positions.
▪ Exchange: standardized ('marking-to-market')
▪ Motives:
▪ Hedging: reducing the overall net exposure (downside risks).
▪ Speculation: taking on (additional) risks
▪ Risk of derivatives is that the investor may enter a risk that they do not
DI Page 1
, ▪ Risk of derivatives is that the investor may enter a risk that they do not
understand. Because the positions are fractional, the exposure is much
larger than what the cost of the investment is.
▪ Only rational if you have superior information that is not available to
everyone else (educated beliefs).
▪ Arbitrage: trading on price differentials.
▪ If there are arbitrage opportunities, you can use derivatives to exploit
these.
▪ Recently:
▪ OTC markets have increasingly gained more central clearing / collateralization.
▪ Exchange trading had already this implemented.
▪ Temporary restrictions on short-selling.
▪ e.g.: business snapshot 4.1
• Forwards:
▪ Contractual specifications:
▪ Underlying asset
▪ Quantity / quality
▪ Price (formula)
▪ Date / location
▪ Other specifics
▪ Pay-off structure:
▪ Long position (buy asset)
▪ If the price of the security at delivery date is below (above) the strike
price, the long position has a loss (profit).
▪ Leads to a problem: counterparty default risk.
□ Implication: you want to trade with banks that have at least an A
rating.
□ Collaterals/covenants are demanded from
Covenants may also be used if the derivative is part of a
credit facility.
▪ Short position (sell asset)
▪ If the price of the security at delivery date is below (above) the strike
price, the short position has a profit (loss).
▪ The gains of one party are the losses of the other.
▪ Replicating pay-offs.
▪ Buy asset today by borrowing the money. At delivery time you have the
asset and pay for it + interests.
▪ This position has mostly zero value at
• Futures contracts:
▪ Contractual specifications:
▪ Asset are frequently traded.
▪ Size / kind set by the exchange.
DI Page 2
, ▪ Size / kind set by the exchange.
▪ Fixed price (standardized)
▪ Two modes of settlement (cash delivery vs physical delivery)
▪ If physical: what date or location?
▪ Cornering the market: it is the supply side that has the option of where
the delivery takes place.
□ Trading places (movie): talks about this.
▪ Payoff structure:
▪ Very similar to forwards
▪ Difference: marking to market.
▪ Margin maintenance is contingent on this marking to market.
• Options:
▪ Different types:
▪ Call option: right to sell asset
▪ Like a long forward contract with insurance against losses.
□ You do not have to exercise the option if you would make a loss.
▪ Put option: right to sell asset
▪ Like a short forward contract with insurance against losses.
▪ Possible exercise:
▪ Just on expiration date: European
▪ Throughout option life: American
▪ Pay-off structure:
▪ Long position
▪ Short position
Summary:
DI Page 3
, Ch. 6 - Interest rate futures
November 26, 2023 10:59 AM
Title: Ch. 6 - Interest rate futures
Ch. 6: Interest rate futures
6.1 DAY COUNT AND QUOTATION CONVENTIONS
• Day count: the way in which interest accrues over time.
• Usually expressed as X>Y.
○ X: the way in which the number of days between the two dates is calculated
○ Y: the way in which the total number of days in the reference period is
measured.
• Conventions commonly used in the United States:
a. Actual/actual (in period)
▪ Used for Treasury bonds in the United States.
▪ The interest earned between two dates is based on the ratio of the
actual days elapsed to the actual number of days in the period between
coupon payments.
b. 30/360
▪ Used for corporate and municipal bonds in the United States.
▪ We assume 30 days per month and 360 days per year when carrying
out calculations.
▪ Sometimes the 30>360 day count convention has surprising
consequences.
□ 30/360 assumes that there are 3 days between 28/02 and 01/03,
but actual/actual assumes there's only one day.
c. Actual/360
▪ Used for money market instruments in the United States.
▪ The interest earned during part of a year is calculated by dividing the
actual number of elapsed days by 360 and multiplying by the rate.
• Price quotations of treasury bills:
• Discount rate: the interest earned as a percentage of the final face value rather
than as a percentage of the initial price paid for the instrument.
○ The prices of money market instruments (e.g.: Treasury bills) are sometimes
quoted using it.
• In general, the relationship between the cash price per $100 of face value and the
quoted price of a Treasury bill in the United States is:
○ P is the quoted price, Y is the cash price, and n is the remaining life of the
Treasury bill measured in calendar days.
• Price Quotations of U.S. Treasury Bonds:
• Treasury bond prices in the United States are quoted in dollars and thirty-seconds
of a dollar.
○ The quoted price is for a bond with a face value of $100.
• Clean price: price quoted.
○ Not the same as the cash price paid by the purchaser of the bond (= dirty
price).
• What does the x/32 mean? (p. 154)
DI Page 4
maandag 13 november 2023 09:06
Title: Lecture 1 - Intro
• Assessment:
• final examination (85%)
• group assignment (15%)
• Derivative instrument's characteristics:
• Payoff structure comes from the cash flows of an underlying asset.
○ Payoffs of every possible scenarios must be specified.
○ Measurability:
▪ There must be highly detailed (even if 'relative').
□ e.g.: elections / weather
• Their underlying asset has an uncertain value.
○ They are typically used to hedge risks (exposure to underlying asset).
• Optionality: pay-offs may depend on choice
○ e.g.: when to exercise such options. A call option gives you the right to buy the
underlying asset at the strike price. The choice of exercising an option is when
the value of the option matters.
• Idealized notions / Perfect markets have the following features:
• Transactions:
○ No transaction costs: there are no frictions in trading
○ Short-selling is allowed freely.
○ No information costs.
○ There are no restrictions to buy a fraction of shares.
• Competition:
○ No market power: prices are taken as given, so no individual player can alter
the price by themselves.
○ Complete 'spanning': if you introduce a new share in the market, the risk-
return profile of it has already been captured by the rest of the shares in the
market.
▪ Then you can derive the price of new products because alternatives are
already available and embody the risk-return profile.
• Investors:
▪ Unbounded rational: investors can forecast all future possibilities/scenarios
and is able to process all available information, so she can calculate the
probability of each scenario happening.
▪ Steady preferences: risk preferences are constant.
▪ Rational expectations: if theres a market price that closes demand and supply,
but is not based on perfect market it cannot be the equilibrium.
• Perfect markets: there is no 'riskless' arbitrage.
▪ Same pay-offs -> identical values ("equilibrium").
▪ Markets are efficient: prices in the market capture all available information.
▪ Weak market efficiency: we cannot predict anything based on historical
prices.
• Derivative markets:
• Trading: it may happen either…
▪ Over-the-counter (OTC): may be very tailored.
▪ Danger: you may enter into large exposures with small positions.
▪ Exchange: standardized ('marking-to-market')
▪ Motives:
▪ Hedging: reducing the overall net exposure (downside risks).
▪ Speculation: taking on (additional) risks
▪ Risk of derivatives is that the investor may enter a risk that they do not
DI Page 1
, ▪ Risk of derivatives is that the investor may enter a risk that they do not
understand. Because the positions are fractional, the exposure is much
larger than what the cost of the investment is.
▪ Only rational if you have superior information that is not available to
everyone else (educated beliefs).
▪ Arbitrage: trading on price differentials.
▪ If there are arbitrage opportunities, you can use derivatives to exploit
these.
▪ Recently:
▪ OTC markets have increasingly gained more central clearing / collateralization.
▪ Exchange trading had already this implemented.
▪ Temporary restrictions on short-selling.
▪ e.g.: business snapshot 4.1
• Forwards:
▪ Contractual specifications:
▪ Underlying asset
▪ Quantity / quality
▪ Price (formula)
▪ Date / location
▪ Other specifics
▪ Pay-off structure:
▪ Long position (buy asset)
▪ If the price of the security at delivery date is below (above) the strike
price, the long position has a loss (profit).
▪ Leads to a problem: counterparty default risk.
□ Implication: you want to trade with banks that have at least an A
rating.
□ Collaterals/covenants are demanded from
Covenants may also be used if the derivative is part of a
credit facility.
▪ Short position (sell asset)
▪ If the price of the security at delivery date is below (above) the strike
price, the short position has a profit (loss).
▪ The gains of one party are the losses of the other.
▪ Replicating pay-offs.
▪ Buy asset today by borrowing the money. At delivery time you have the
asset and pay for it + interests.
▪ This position has mostly zero value at
• Futures contracts:
▪ Contractual specifications:
▪ Asset are frequently traded.
▪ Size / kind set by the exchange.
DI Page 2
, ▪ Size / kind set by the exchange.
▪ Fixed price (standardized)
▪ Two modes of settlement (cash delivery vs physical delivery)
▪ If physical: what date or location?
▪ Cornering the market: it is the supply side that has the option of where
the delivery takes place.
□ Trading places (movie): talks about this.
▪ Payoff structure:
▪ Very similar to forwards
▪ Difference: marking to market.
▪ Margin maintenance is contingent on this marking to market.
• Options:
▪ Different types:
▪ Call option: right to sell asset
▪ Like a long forward contract with insurance against losses.
□ You do not have to exercise the option if you would make a loss.
▪ Put option: right to sell asset
▪ Like a short forward contract with insurance against losses.
▪ Possible exercise:
▪ Just on expiration date: European
▪ Throughout option life: American
▪ Pay-off structure:
▪ Long position
▪ Short position
Summary:
DI Page 3
, Ch. 6 - Interest rate futures
November 26, 2023 10:59 AM
Title: Ch. 6 - Interest rate futures
Ch. 6: Interest rate futures
6.1 DAY COUNT AND QUOTATION CONVENTIONS
• Day count: the way in which interest accrues over time.
• Usually expressed as X>Y.
○ X: the way in which the number of days between the two dates is calculated
○ Y: the way in which the total number of days in the reference period is
measured.
• Conventions commonly used in the United States:
a. Actual/actual (in period)
▪ Used for Treasury bonds in the United States.
▪ The interest earned between two dates is based on the ratio of the
actual days elapsed to the actual number of days in the period between
coupon payments.
b. 30/360
▪ Used for corporate and municipal bonds in the United States.
▪ We assume 30 days per month and 360 days per year when carrying
out calculations.
▪ Sometimes the 30>360 day count convention has surprising
consequences.
□ 30/360 assumes that there are 3 days between 28/02 and 01/03,
but actual/actual assumes there's only one day.
c. Actual/360
▪ Used for money market instruments in the United States.
▪ The interest earned during part of a year is calculated by dividing the
actual number of elapsed days by 360 and multiplying by the rate.
• Price quotations of treasury bills:
• Discount rate: the interest earned as a percentage of the final face value rather
than as a percentage of the initial price paid for the instrument.
○ The prices of money market instruments (e.g.: Treasury bills) are sometimes
quoted using it.
• In general, the relationship between the cash price per $100 of face value and the
quoted price of a Treasury bill in the United States is:
○ P is the quoted price, Y is the cash price, and n is the remaining life of the
Treasury bill measured in calendar days.
• Price Quotations of U.S. Treasury Bonds:
• Treasury bond prices in the United States are quoted in dollars and thirty-seconds
of a dollar.
○ The quoted price is for a bond with a face value of $100.
• Clean price: price quoted.
○ Not the same as the cash price paid by the purchaser of the bond (= dirty
price).
• What does the x/32 mean? (p. 154)
DI Page 4
