DERIVATIVE
SECURITIES:
SUMMARY
@ECOsummaries
→ 20% discount
1
,Table of contents
Lecture 1_________________________________________________page 3-7
Lecture 2_________________________________________________page 8-13
Lecture 3_________________________________________________page 14-16
Lecture 4_________________________________________________page 17-22
Lecture 5_________________________________________________page 23-26
Lecture 6_________________________________________________page 27-29
Lecture 7_________________________________________________page 30-34
Lecture 8_________________________________________________page 35-36
2
,Lecture 1 – Forward contracts
Introduction:
Derivative: instrument whose value depends on the value of other, more basic, underlying
variables.
Options: the right to buy/sell an asset at a fixed price today (call/put)
Futures: agreement to buy or sell a specific commodity asset or security at a set future date
for a set price (traded publicly, standardized terms, prices settled daily until end of contract)
Forwards: same as futures but traded privately, customizable agreement, and is settled at
the end of the agreement.
Interest rate swaps: swap a variable for a fixed rate to protect against interest rate risk
Credit default swaps (CDS): insurance against default of a firm
Mortgage-backed securities (MBS): collection of mortgages divided in tranches based on
risk level with different payoff rates for each tranch.
Collateralized debt obligations (CDO): same tranch structure as MBS, but can be more debt
assets than mortgages, like bonds and loans.
Goals: reduce risk (hedge), speculate, arbitrage
Risks: asymmetric information (who are you trading with?), liquidity risks
Forward contract:
Forward contract: private (over the counter) agreement between two parties to buy/sell an
asset at a certain time in the future for a pre-determined price (K), determined at t=0.
- No money changes hands at t=0 (except with collateral fee)
- Settled at maturity
Spot contract: agreement to buy/sell immediately → different from forward contract.
Collateral fee: fee to mitigate credit risk as a % of the forward price (jar)
Replicating portfolio – forward contract:
Forward long:
X axis: share price
Y axis: payoff at T
P > K → profit
P < K → loss
Replicating intuition: you borrow ‘K’ that needs to be repaid at t=1, and use it to invest in the
long position. When P>K, you make a profit. When the price doesn’t move (P=K), you
breakeven as this is the amount you borrowed and can repay ‘K’ immediately. When P<K,
you make a loss of maximum ‘K’ as this is what you need to repay at t=1.
3
, Forward short:
Replicating intuition: you borrow a stock and immediately sell it, this money you lend out to
the other party. At t=1, you get back ‘K’ and have to pay ‘P’ to the other party. When P<K,
you make a profit. When P=K, you breakeven as you have to buy the stock for ‘K’ and use
your lend out money. When P>K, you make a loss as you need to pay more on top of ‘K’
which you bought the stock for originally.
Mirroring intuition: there are 2 parties in the contract, so each party should have the mirror
image of the other party.
Hedging: use forward contracts to hedge against price risk by locking in a price for the
future.
Example: airline uses oil forward to hedge fuel price risk for travel peaks (Christmas)
Idea: when oil price rises, you
make a loss, but with a forward
contract you gain when oil price
rises.
→ Net payoff equal
Net payoff: remains equal for the whole duration and protects for situation where the
liability would be going below the net payoff.
Pricing futures and forwards – investment assets:
Assumptions: no transactions costs, no taxes, borrowing/lending at Rf, risk averse investors.
Notation:
- St = spot price at t
- FtT = forward price at time t for delivery at time T
- T – t = time until delivery date
- r = risk-free rate for maturity T
Theory: forward price at t with maturity date T with an underlying asset that pays no
dividends is the following formula.
→ For t=0 we get
4
SECURITIES:
SUMMARY
@ECOsummaries
→ 20% discount
1
,Table of contents
Lecture 1_________________________________________________page 3-7
Lecture 2_________________________________________________page 8-13
Lecture 3_________________________________________________page 14-16
Lecture 4_________________________________________________page 17-22
Lecture 5_________________________________________________page 23-26
Lecture 6_________________________________________________page 27-29
Lecture 7_________________________________________________page 30-34
Lecture 8_________________________________________________page 35-36
2
,Lecture 1 – Forward contracts
Introduction:
Derivative: instrument whose value depends on the value of other, more basic, underlying
variables.
Options: the right to buy/sell an asset at a fixed price today (call/put)
Futures: agreement to buy or sell a specific commodity asset or security at a set future date
for a set price (traded publicly, standardized terms, prices settled daily until end of contract)
Forwards: same as futures but traded privately, customizable agreement, and is settled at
the end of the agreement.
Interest rate swaps: swap a variable for a fixed rate to protect against interest rate risk
Credit default swaps (CDS): insurance against default of a firm
Mortgage-backed securities (MBS): collection of mortgages divided in tranches based on
risk level with different payoff rates for each tranch.
Collateralized debt obligations (CDO): same tranch structure as MBS, but can be more debt
assets than mortgages, like bonds and loans.
Goals: reduce risk (hedge), speculate, arbitrage
Risks: asymmetric information (who are you trading with?), liquidity risks
Forward contract:
Forward contract: private (over the counter) agreement between two parties to buy/sell an
asset at a certain time in the future for a pre-determined price (K), determined at t=0.
- No money changes hands at t=0 (except with collateral fee)
- Settled at maturity
Spot contract: agreement to buy/sell immediately → different from forward contract.
Collateral fee: fee to mitigate credit risk as a % of the forward price (jar)
Replicating portfolio – forward contract:
Forward long:
X axis: share price
Y axis: payoff at T
P > K → profit
P < K → loss
Replicating intuition: you borrow ‘K’ that needs to be repaid at t=1, and use it to invest in the
long position. When P>K, you make a profit. When the price doesn’t move (P=K), you
breakeven as this is the amount you borrowed and can repay ‘K’ immediately. When P<K,
you make a loss of maximum ‘K’ as this is what you need to repay at t=1.
3
, Forward short:
Replicating intuition: you borrow a stock and immediately sell it, this money you lend out to
the other party. At t=1, you get back ‘K’ and have to pay ‘P’ to the other party. When P<K,
you make a profit. When P=K, you breakeven as you have to buy the stock for ‘K’ and use
your lend out money. When P>K, you make a loss as you need to pay more on top of ‘K’
which you bought the stock for originally.
Mirroring intuition: there are 2 parties in the contract, so each party should have the mirror
image of the other party.
Hedging: use forward contracts to hedge against price risk by locking in a price for the
future.
Example: airline uses oil forward to hedge fuel price risk for travel peaks (Christmas)
Idea: when oil price rises, you
make a loss, but with a forward
contract you gain when oil price
rises.
→ Net payoff equal
Net payoff: remains equal for the whole duration and protects for situation where the
liability would be going below the net payoff.
Pricing futures and forwards – investment assets:
Assumptions: no transactions costs, no taxes, borrowing/lending at Rf, risk averse investors.
Notation:
- St = spot price at t
- FtT = forward price at time t for delivery at time T
- T – t = time until delivery date
- r = risk-free rate for maturity T
Theory: forward price at t with maturity date T with an underlying asset that pays no
dividends is the following formula.
→ For t=0 we get
4
