This document was carefully drafted to include notes on the course's reading material, commentary on the lecture slides, and includes the summary of each chapter on the bottom panel on each of the subsections. This is a very efficient yet in-depth document for students who want to omptimize their s...
• 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
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