Chapter 4: Principles of Exchange-Traded Derivatives Flashcards
How is the price of a future derived?
Price of asset plus the cost of holding the position, e.g. financing
What is the Cost of Carry and what makes it up (4)?
Cost of holding the physical asset until expiry date
finance costs
security costs
storage costs
insurance
What is the fair value of a future?
cash price + cost of carry
If a future cost more than this, it would make more sense to purchase and hold the physical asset
How is the fair value of an equity index future calculated?
As other costs are negligible, only the net finance costs need to be considered
What is the formula for net finance costs for equity index futures?
interest - present value of dividends
How does the IASB define the fair value of a future?
The price at which it can be traded between two market participants at any given time
What is a contago?
A market where the net cost of carry to hold the asset to delivery are higher than cash prices
What is backwardation?
Markets where there is a net benefit to holding the asset to delivery, where futures prices are lower then cash prices
When is backwardation most common?
When long term interest rates are higher than short term rates
In commodity markets when there is high demand for immediate delivery
What is convergence in futures?
Cost of carry tends to zero as expiry approaches
This means that cash and futures prices eventually meet
What is basis & its formula?
Measure of the difference between cash and futures prices
Basis = cash price - futures price
What is the basis in contango markets?
Contango is where futures > cash
Thus negative
What is the basis in backwardation markets?
Cash > futures
Thus positive
How does basis differ towards expiry in contango vs backwardation markets?
In contango markets (eg, equity index), the basis strengthens towards
expiry.
In backwardation markets (eg, STIR and bond futures), the basis weakens towards expiry.
What should a trader do if they expect the basis to strengthen?
Buy near dated instrument
Sell far dated instrument
What should a trader do if they expect the basis to weaken?
Sell near dated instrument
Buy far dated instrument
How does the gap differ between contango and backwardation markets for a strengthening basis?
Contago - narrowing gap
Backwardation - widening gap
What is basis risk?
That a future will move differently to that of its underlying asset
What is the only way to eliminate basis risk?
Hold future till expiry, futures and cash prices will converge
What is a cash and carry arbitrage?
Where a future is trading above its fair value
Buy the underlying asset, sell the future
What is a reverse cash and carry arbitrage?
Where a future is trading below fair value
Buy future, sell underlying asset
What is the premium made up of? (2)
Intrinsic Value (IV) + Time Value (TV)
What is intrinsic value?
The difference between the strike price and the assets underlying price
What is the definition of in-the-money and out-the-money options?
ITM - Has IV
OTM - No IV
What is the rate at which time value decays?
Exponential, increases as it approaches expiry
At what strike price does TV increase?
ATM
More uncertainty about whether will expire ITM or OTM
How would TV differ for
ITM
OTM
ATM
TV reflects uncertainty about likelihood of exercise
ITM - High probability of exercise, low TV
OTM - High probability of being abandoned, low TV
ATM - Highest uncertainty of exercise, high TV
How does volatility impact TV?
Higher volatility, higher TV
What are the three types of volatility to be considered?
Historic - past
Future - no one can predict
Implied - market view on future volatility based on options pricing
How is the Implied Volatility figure derived?
Options pricing models
Black-Scholes
What is limitation of Black-Scholes?
Only good for European options as cannot factor in early exercise
What is the Stochastic Alpha, Beta, Rho (SABR) pricing model?
Uses different levels of implied volatility to price options on the same underlying asset
It uses the volatility smile, states that IV is greater for options that are deep ITM or OTM
Why would options pricing change based on interest rates?
Options are basically financing
Buyer of a call gets to keep money in bank
Seller has to own the shares
So premium would go up for example
What is Put/Call Parity?
Call and put premium must be fair in relation to one another, otherwise arbitrage opportunities present themselves
What is the put/call parity formula?
C - P = S - K
C = call premium
P = put premium
S = spot price
K = strike price
When does the put/call parity formula apply?
All options at expiry and futures at all times
When does the put/call parity formula need to be adjusted?
To take account for the cost of carry for options when the underlying asset when it is not a future or a forward, and has a possible income flow that is paid before option expires
E.g. option on a share with upcoming dividend
What is the adjusted put/call parity formula?
Strike changes
K/(1+r)^t
Where
r = the annual risk-free rate
t = time to expiry in years
What is the delta of an option?
Sensitivity of the options price to changes in the price of underlying
What are the two ways to arbitrage options mispricings? (on futures)
If call is cheap (create synthetic long)
Buy call, sell put, sell future - called reversal
If put is cheap (create synthetic short)
Buy put, sell call, buy future - called conversion
Basically create a synthetic version of whatever asset you want, and take the opposite side on the spot - locked in profit
What is the calculation for delta?
change in premium / change in price of underlying
What is the cumulative delta?
Delta of a combined portfolio
Gives sensitivity and direction bias of a portfolio
What does delta hedging hedge against? And what risks remain?
Price risk
Time decay, volatility and basis still remain
What is Vega?
Measure of how a 1% change in implied volatility affects an options price
Greatest for ATM options
Greatest for long dated
What is Gamma?
Gamma is the rate of change of delta
Small when deep ITM or OTM
What is Theta?
Theta is the measure of the rate of decline of an options value due to the passage of time
Long options have negative theta, it’s working against you
Short options have positive theta
What is Rho?
Measures how much an options value will change from a 1% change in interest rates
least used - this relationship is fairly stable
has minimal impact to pricing
usually around 0.02 to 0.04
How will an increase in rates impact calls and puts?
Call premium goes up
Put premium goes down
How long does it usually take for premium to be paid?
T+1
Which is the only position that requires margin for equity index and stock options? And what kind of margin?
Short requires initial margin
Which is the only position that does not require margin for Bond and STIR options? And what kind of margin?
Long, does not require initial margin
