Summary derivatives and risk management
Derivative, financial instrument that has value determined by price underlying asset
Uses of Derivatives
- Hedging, use of derivatives to offset price risk from exposure to underlying (reduce risk)
- Speculation, bet on direction of price, derivatives as investment (make leveraged bet)
o Investors without exposure to underlying
- Arbitrage, riskless profit from relative mispricing financial instrument or assets (price differ)
Over-the-counter (OTC) derivatives, derivatives traded directly between two parties bilaterally
- Forwards, Swaps OTC contracts, options can be both
- Futures exchange trade, options can be both
Lecture 1 – introduction (Ch. 1)
Derivative security is a financial security whose value depends on other, more fundamental underlying
financial variable (such as stock price, interest rate, index level, commodity price or exchange rate)
three classes of derivative securities: Futures & forwards, Swaps, Options
- Derivatives are a large market (trillions of USD)
Forward contract, two parties agree to specific trade at a specified point in the future
- Both parties commit to taking part in the trade or exchange specified in contract
- Common motivation is the elimination of cash-flow uncertainty from future transaction
- Contracts may be used as instrument of hedging
Future contract, are forward contracts where buyers and sellers trade through an exchange rather than
bilaterally.
Swaps are akin to forward contracts in which the parties commit to a series of exchanges at several
dates in the future.
Options: Characterized by optionality concerning the specified trade.
- One party, the option holder, retains the right to enforce or opt out of the trade. The other
party, the option writer, has a contingent obligation to take part in the trade.
- Call option: Option holder has the right, but not the obligation, to buy the underlying asset at
the price specified in the contract.
Option writer has a contingent obligation to participate in the specified trade as the seller.
- Put option: Holder has the right, but not the obligation, to sell the underlying asset at the price
specified in the contract.
Option writer has a contingent obligation to participate in the specified trade as the buyer.
3 popular ways to classify derivatives are:
- By underlying; equity, interest rate, credit etc.
- By nature of instrument, forward, future, options
- By nature of market, over-the-counter, exchange-traded
Risk management Roles
- Futures, forwards and swaps enable investors to lock in cash flows from future transactions.
(instruments for hedging – offsetting existing cash-flow risk)
- Options provide one-sided protection. Offers a right without obligation
o Call, protection against price increase: Put, protection against price decrease
Interest rate conventions: (appendix) – any convention can be used (choice of convenience)
- Different interest-rate conventions are simply different mechanisms for converting sums of
money due in the future into present values today, or investments made today into future
values due at maturity. (conventions doesn’t matter as long as we obtain correct PV and FV)
- Interest rates expressed
, - Interest rates expressed under different conventions aren’t the same but always possible to
convert. Convention is simply mechanisms telling how to compute present values of future
amounts
Continuous-compounding
- Commonly used un theoretical work in modern finance and has several technical advantages
which is why it is popular. (If the T-year continuously-compounded interest rate is r)
o $1 invested for T years grows to $e rT by time T.
o The present value of $1 receivable at time T is PV (A) = $1e—rT .
Money-market convention
- In the US money-market, an interest rate of ℓ over a horizon [0,T ] means that the interest
𝑑
payable per dollar of principal is ℓ = 360. Where d is the actual number of days in horizon [0,T]
- Example: if the 3-month interest rate is 5% and there are 91 calendar days in the 3-month
horizon, then the interest received per dollar of investment is
- Under Actual/360 convention, amount A invested over [0,T ] at rate ℓ grows by time T to
𝑑 𝐴
𝐴 (1 + ℓ 360) PV of A received at T: 𝑑
(1+ℓ )
360
Note on short selling
Short selling, securities are sold by someone who does not own them
1. Borrow securities from someone
o This is done via broker
o Term of short-sell almost always one day; loans are typically renewed many times
o The lender can require you to return the shares whenever he wants (short-squeeze)
2. Sell securities at the current price (shares are sold in the stock market)
o Proceeds put in collateral account; do not have access to funds until you return the
borrowed shares
o Money earns interest (risk-free)
o Assets = collateral account (cash), Liability = value of stock owed
3. Eventually; buy back securities and return them to owner (plus cash flows generated by
securities: dividends or coupons) close out position
o Buy amount shares borrowed and return them to broker (+cash flows)
o Collect all money in collateral account
- Profit = Initial price – Ending price
- Suppose short MSFT at price $50: two months later price is $40 so profit is $10 (per share)
Lecture 2 – Pricing Forwards and Futures I (Ch. 3)
Forward/Future, agreement to buy/sell asset at a certain time in the future for a price fixed today
Forward, agreement between two parties to trade in specified quantity of specified good at specified
price on specified date in the future
- Contract is bilateral (over-the-counter) contract between two parties
- Buyer in the contract has long position, Seller in contract has short position
Characteristics
- Bilateral contract Negotiated directly by seller and buyer.
- Customizable Terms of the contract can be "tailored."
- Credit Risk There is possible default risk for both parties.
- Unilateral Reversal Neither party can unilaterally transfer its obligations in the contract to a
third party
Hedging, forwards enable buyers/sellers to lock in a price for a future market consumption - Hedge
- Forwards used for elimination of cash flow uncertainty.
Derivative, financial instrument that has value determined by price underlying asset
Uses of Derivatives
- Hedging, use of derivatives to offset price risk from exposure to underlying (reduce risk)
- Speculation, bet on direction of price, derivatives as investment (make leveraged bet)
o Investors without exposure to underlying
- Arbitrage, riskless profit from relative mispricing financial instrument or assets (price differ)
Over-the-counter (OTC) derivatives, derivatives traded directly between two parties bilaterally
- Forwards, Swaps OTC contracts, options can be both
- Futures exchange trade, options can be both
Lecture 1 – introduction (Ch. 1)
Derivative security is a financial security whose value depends on other, more fundamental underlying
financial variable (such as stock price, interest rate, index level, commodity price or exchange rate)
three classes of derivative securities: Futures & forwards, Swaps, Options
- Derivatives are a large market (trillions of USD)
Forward contract, two parties agree to specific trade at a specified point in the future
- Both parties commit to taking part in the trade or exchange specified in contract
- Common motivation is the elimination of cash-flow uncertainty from future transaction
- Contracts may be used as instrument of hedging
Future contract, are forward contracts where buyers and sellers trade through an exchange rather than
bilaterally.
Swaps are akin to forward contracts in which the parties commit to a series of exchanges at several
dates in the future.
Options: Characterized by optionality concerning the specified trade.
- One party, the option holder, retains the right to enforce or opt out of the trade. The other
party, the option writer, has a contingent obligation to take part in the trade.
- Call option: Option holder has the right, but not the obligation, to buy the underlying asset at
the price specified in the contract.
Option writer has a contingent obligation to participate in the specified trade as the seller.
- Put option: Holder has the right, but not the obligation, to sell the underlying asset at the price
specified in the contract.
Option writer has a contingent obligation to participate in the specified trade as the buyer.
3 popular ways to classify derivatives are:
- By underlying; equity, interest rate, credit etc.
- By nature of instrument, forward, future, options
- By nature of market, over-the-counter, exchange-traded
Risk management Roles
- Futures, forwards and swaps enable investors to lock in cash flows from future transactions.
(instruments for hedging – offsetting existing cash-flow risk)
- Options provide one-sided protection. Offers a right without obligation
o Call, protection against price increase: Put, protection against price decrease
Interest rate conventions: (appendix) – any convention can be used (choice of convenience)
- Different interest-rate conventions are simply different mechanisms for converting sums of
money due in the future into present values today, or investments made today into future
values due at maturity. (conventions doesn’t matter as long as we obtain correct PV and FV)
- Interest rates expressed
, - Interest rates expressed under different conventions aren’t the same but always possible to
convert. Convention is simply mechanisms telling how to compute present values of future
amounts
Continuous-compounding
- Commonly used un theoretical work in modern finance and has several technical advantages
which is why it is popular. (If the T-year continuously-compounded interest rate is r)
o $1 invested for T years grows to $e rT by time T.
o The present value of $1 receivable at time T is PV (A) = $1e—rT .
Money-market convention
- In the US money-market, an interest rate of ℓ over a horizon [0,T ] means that the interest
𝑑
payable per dollar of principal is ℓ = 360. Where d is the actual number of days in horizon [0,T]
- Example: if the 3-month interest rate is 5% and there are 91 calendar days in the 3-month
horizon, then the interest received per dollar of investment is
- Under Actual/360 convention, amount A invested over [0,T ] at rate ℓ grows by time T to
𝑑 𝐴
𝐴 (1 + ℓ 360) PV of A received at T: 𝑑
(1+ℓ )
360
Note on short selling
Short selling, securities are sold by someone who does not own them
1. Borrow securities from someone
o This is done via broker
o Term of short-sell almost always one day; loans are typically renewed many times
o The lender can require you to return the shares whenever he wants (short-squeeze)
2. Sell securities at the current price (shares are sold in the stock market)
o Proceeds put in collateral account; do not have access to funds until you return the
borrowed shares
o Money earns interest (risk-free)
o Assets = collateral account (cash), Liability = value of stock owed
3. Eventually; buy back securities and return them to owner (plus cash flows generated by
securities: dividends or coupons) close out position
o Buy amount shares borrowed and return them to broker (+cash flows)
o Collect all money in collateral account
- Profit = Initial price – Ending price
- Suppose short MSFT at price $50: two months later price is $40 so profit is $10 (per share)
Lecture 2 – Pricing Forwards and Futures I (Ch. 3)
Forward/Future, agreement to buy/sell asset at a certain time in the future for a price fixed today
Forward, agreement between two parties to trade in specified quantity of specified good at specified
price on specified date in the future
- Contract is bilateral (over-the-counter) contract between two parties
- Buyer in the contract has long position, Seller in contract has short position
Characteristics
- Bilateral contract Negotiated directly by seller and buyer.
- Customizable Terms of the contract can be "tailored."
- Credit Risk There is possible default risk for both parties.
- Unilateral Reversal Neither party can unilaterally transfer its obligations in the contract to a
third party
Hedging, forwards enable buyers/sellers to lock in a price for a future market consumption - Hedge
- Forwards used for elimination of cash flow uncertainty.
