S1. Futures & Forwards Flashcards
Absolute Approach
= Equilibrium approach
- pricing asset by reference to its exposure to fundamental sources of macroeconomic risk
- price endogenously determined by characterising the optimal decisions of agents &market clearing
- asset pricing theory to give economic explanation for why prices are how they are & predict prices
- CAPM, FAMA
- pricing based on exposure to fundamental source, macroeco factors
- pricing theory: eco. explanation of why prices are how they are (descriptive view, explanation of market based on models)
Relative Approach
=non-arbitrage approach
- what we can learn about asset´s value given price of some other assets
- not interested in sources - take prices given (exog.) for granted
- little information about fundamental risk factors are used
- prices given exogenously by markets - agents sach th conditions that those prices must satisfy so as to avoid arbitrage opportunities
- Black Scholes, Cox Rubenstein etc
Derivatives
= financial assets whose price derives from the evolution of another asset, called underlying
- makes it easier to price derivatives (based on stock)
- simply characterise the price of underlying (statistically) so as to capture the future evolution of the underlying
- price of derivative =function of price of underlying
In Economic context - price of underlying is already given (exog.) hence take relative approach for derivatives ( maybe bonds) & absolute for stocks
Pricing derivatives
Relative approach
conditions:
a) Absence of arbitrage opportunity
- make money without risk
- in practice harder to find than in theory
- but on LT arbitrage opportunity dissapears
b) Existence of Replicating Portfolios
A) option = B) stock + bond
- whole PF = sum of value of its components otherwise market moves to cheaper side
- go to option market = go to bond+stock
- same payoff
- cost of creating pf (B) should be 0
hence using B on is bale to drive option value
How are derivatives priced?
- understand payoffs
- characterised its replicating PF (combination of assets with same payoff)
Derivative pricing - looks for combo in asset (replicating PF) providing same payoff - where prices of RP are already given
- compute value of replicating PF
as value of RP = value of option because RP payoff is identical, otherwise employ arbitrage opp.
Future/Fwd Markets
agreement to BUY/SELL an asset at certain time in future at certain price
OBLIGATION: LONG OR SHORT
Delivery:
- if contract not closed out before maturity - usually settled by delivering the assets underlying the contract
- alternatives about when, what, where - then SHORT side chooses
- few contract settled in cash (stock indices or Eurodollars)
Consumption vs Investment
- C = assets held primarily for consumption - copper
- I = assets held significant nr of people purely for investment purposes (gold, silver)
Futures vs forwards
traded on exchange vs OTC
Echange provides mechanism (insurance) hat gives 2 parties the guarantee that contract will be honored
stadardised vs customised contract
usually specify by Exchange
range of delivery dates vs one specific fate
settled daily - settled an end
contract closed out prior to maturity (usually) - delivery or final cash settlement takes place
virtually no credit risk - some credit risk (base risk)
Advantages of settling every day?
Futures
reduce risk (defaulting)
each party has to have some deposit
account reviewed every day
extra amount saved as credit margin - as clearing house deposit - to cover up in case counterparity fails
- maintenance margin = like cussion (capital buff to avoid credit risk problems) if counterparty fails
-insurance
Clearing House
Clearing House –> margin –> Clearing Members
CM –> margin –> Broker
CM & Broker –> margin with clients selling/buying derivatives
CH serves as intermediary/middle man in transactions
guarantees the performance of the parties for each transaction performance of parties to each transaction
Market to market
Margins
margins make MTM an effective daily settlement process
- need to on MA with broker
- make an initial margin deposit (credit letter, shares, debt instruments allowed)
- MA debited (credited) daily as function of gain/losses in future position
- margin calls to top up to MA to initial margin level, whenever MA balance falls > MM
- withdraw money from MA whenever MA balance is above initial level
hedging strategies with future
idea = take position that neutralises risk as far as possible
Long hedge
= need to buy “apples”, lock prices in case they increase
- long position in futures market (buy future)
- seeks protection against future increase of commodity
- either short on sport market or has to buy commodity on future date at futures spot price (purchasing price)
Short hedge
= already own commodity e.g. “apple producer”
- user assumes SHORT on futures market (sells futures)
- seeks protection against future decrease in price of commodity
- long on spot (owns asset) or has to sell commodity on future date (selling price)
Basis risk
- asset whos priced should be hedge might not be exactly the same as asset underlying the futures contract
hedger might be uncertain as to exact date when asset will be bought/sold
hedger might require the future contract to be closed out preiour to delivery month
basis = spot price of asset (hedge) - future price (contract)
as time passes - spot and future prices don´t necessarily change by same amount (volatility, sensitivity)
as result - basis changes
problems with standardised futures
not traded in an infinite number of underlying assets and maturities
most times no perfect matching of underlying assets, dates and quantities
very important to determine which contract to trade in terms of:
- underlying asset: hedge, analysis of available contracts
- quantity: optimal hedge ratio, tailing hdge
- interest rates
problems with standardised futures
Underlying Asset
most hedges are cross hedges
= cash asset &asset underlying future no identical
correlation between movements of asset
- check beta (how they move together), correlation, coeff. of determination
- liquidity of contract
- degree of misspricing
problems with standardised futures
delivery month
hedging period is longer than futures maturities
a) strip hedge (diff. mat) vs b) rolling hedge (close and rolls over)
- check : liquidity; transaction cost; relative mispricing
hedging periods shorter than futures
- chose fut. contract that expires before cash position - expose to price risk
- choose fut. contract that expires after the cash position - expose to basis risk
problems with standardised futures
Quantity
how many futures constracts are needed for specific hedge
nr of contracts to be bought/sold =determine by hedge ratio (h)
optimal hedge ratio = min.variance portfolio
- nr. of futures contracts to sell/buy knowing its long/short on 1 unit of cash asset (ratio)
- represents the slope coefficient (DS / DF)
risk-minimising hedge = (NF) - convert ratio into actual number
NF = h* (PS/PF)
problems with standardised futures
Quantity
market to market
impact of MTM (settled daily)
it creates a divergence between
a) moment when profit (loss) of futures occurs
b) moment when loss(profit) on cash asset occurs
opportunity cost to daily resettlement CF
danger that accum. losses on futures contracts can deplete the assets of hedger &forcehim o liquidate hedge prematurely
by tailing hedge (trading smaller amount than h*)
- -> the MTM effect can be neutralised
- -> future contract becomes very similar to fwd contract
problems:
- futures aren´t infinitely divisible
- cont. monitoring &trading of futures increases the costs of hedging strategy (transact. costs)
trading&hedging part. important when:
- IR are very high (high r)
- hedging horizon is very long (long t)
replicating Portfolio
no arbitrage oppornity
assumption
no transaction costs market participants: - are subject to the same tax rate - can borrow money at same rf ate as lend money - take adv. of arbitrage opportunity
Options vs futures
option have asymmetrical payoffs at expiry vs futures have symmetrical (linear payoffs)
options allow buyer to preserve its upside potential vs futures user exchanges the upside potential for the elimination of the downside danger
rights awarded with the opinion have a price (=premium) vs future is for free
seller of option is conditioned by the decision of the buyer, therefore it requires a premium (insurance)
options are quatoed in terms of value of the option, not the value of the underlying
Rights& Obligation
Buyer:
a) call = buy asset + pay K if exercised + pay premium
b) put = sell asset + receiveK + pay premium
Writer/seller:
a) call = receive premium + exercise price; sell asset
b) put = receive premium; buy asset
Margin Accounts with Options
LONG:
call & put
initial = option premium no maintenance
SHORT
call & put
initial = option premium + % of undrl. asset value
Option Style- depending on maturity
European
- only excercise at expiry
American:
- exercise at any moment until expiry
Mid-Atlantic/Bermuda
- exercise at specific dates until expiry
determinants of option value
- underlying asset spot price S
- exercise price of the option K
- Tim to expiry T
- risk free rate r
- volatility of rate of return on S (most important, as chances increases)
- dividend component D (refinement of model)
determinants of option value
European Option
CALL:
higher S –> +
Exercise price –> -
time to expiry –> + (price has time to increase without you risking - difference is bigger)
r –> +
volatility –> + ( as it can deviate a lot, but since one is covered in dowside this is beneficial)
dividend –> -
PUT: S --> - (as might sell it for cheaper price) K --> + (more money you receive) T --> uncertain (not clear) r --> - (higher rate, cheaper price) volatility --> + dividends --> +
Why do people hold positions without exercising?
because one needs a lot of cash to exercise
it is easier not to go through settlement process
you cannot forget to exercise, hence in this case you prefer doing it earlier than never
Trading Strategies
non linear hedging strategies
- risk exposure can sometimes be NONLINEAR (=progessive/asymmetrical corporate taxes)
borrowing/shortselling constraints
diff. risk tolerances of agents
knowledge of market (forecasting ability)
low market volatility
Nonlinear hedging strategis
increase in price
- buy call (convex)
- sell puts (concave)
- buy call&sell puts (collar)
decrease in price
- buy puts (convex)
- sell calls (concave)
- buy puts&sell calls(collar)
Derivative market payoff
CALL:
long: -C C*ert + payoff (max (St-K),0)
short: +C (cert) - payoff (max (St-K),0)
PUT:
long: -P + payoff (max (K-St),0)
shot: +P - payoff(max (K-St),0)
Risk faced by option holder
- run the risk of losing the full value of premium they paid for the option
- the closer an OTM option is to expiry - th greater the LH that it will be impossible o close out or exercise profitably
- if one exercises option which is not hedge in stock market - one must be prepared to pay for the full value of stock (call option) o deliver it (put option)
Risk faced by option writer
- call: required to deliver the stock being assigned if exercised
- put: required to take the delivery of and paid fo stock on being assigned
- call and put writers might be assigned at any time
- all short positions are subject to sudden increases in margin requirements
- covered call writers lose the right to any upside in stock pice but remain exposed in event that the stock price falls
A perfect hedge
completely eliminates the hedger’s risk.
does not always lead to a better outcome than an imperfect hedge.
It just leads to a more certain outcome.
Consider a company that hedges its exposure to the price of an asset. Suppose the asset’s price movements prove to be favorable to the company. A perfect hedge totally neutralizes the company’s gain from these favorable price movements. An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.
time value
difference between option value - intrinsic value
reflect possibility that until expiry - the underlying asset moves in an adv. direcion for HOLDER
comprehends of
- TVM on exercise price
- Insurance value of option
- present value of any dividend payments
TV call = TV + Insurance - Dividends (PV)
TV put= -TV+Insurance+PV Dividends
Time value and exercise Style
America options:
- TV is always >0 or 0 at expiry or exercise - there exists always a good time to exercise
European call:
- TV always >0 o 0 (expire) - hence American should be always equal (at least) to value of a Eu. call
European Put:
- TV is negative <0 for DEEP in the money - thus value of American put should b higher than value of Eu. option (equivalently)
- as time passes the prob. of prieces increasing is HIGH - hence high chance of person willing to exercise against you
- higher prob. that option moves from ITM to ATM
- easier for a put than for a call
Why?
- in puts the limits you gain is bounded (only a certain extent to which price can go down) - extent to by how much “deep in the money” you can go
- whereas for call “gains are unbounded” - no limits for “in the money” - pries can rise indefinitely
Graphical representation
TV decays as expiry date comes nearer - as there is no time left to expiry - hence the probability of fitting added value due to time passing diminishes
maximum for at the money options - when prices are surrounding strike prices
- because if option is ATM you never know if option will actually be exercised or not - hence value of waiting fo the uncertainty makes TV very high
