CH 4: Principles of Exchange Traded Derivatives

Question 1

Futures pricing relationships - cost of carry

Answer 1

Priced based on the underlying asset value plus the cost of holding the position and financing costs

The price will not fully reflect the market’s perception of the price movement
All of the factors that affect this are called the cost of carry

Question 2

Cost of carry

Answer 2

Main components
1. Finance costs (interest expenses) over the period
2. Securitty costs (e.g. for precious metals)
3. Storage costs
4. Insurance
* All of these factors combined represent the fair value

Cost of carry can be significant for commodity futures contracts and therefore creates a disparity betwen current mkt price and futures price as storing the pphysical product can be expensive.

Financial futures have varying costs of carry based on dividend yield or shape of the yield curve for FI contracts.

Question 3

Fair value (Arbitrage free value) - explanation and when would investors buy the future

Answer 3

Fair value is the price that is fair to the buyer and the seller when considering market price and the costs of carry.

If the difference between cash and futures price is less than the cost of carry investors are better buying the future than the asset and visa versa (if higher, buy asset).

Question 4

Fair value of futures calculation

Answer 4

Fair value=Cash Price + cost of carry

Do the % costs for each cashflow and multiply by the date convetion to get the answer for each cashflow. Add them up and add to the cash price

Question 5

Fair value of equity index futures. Only considers what, calc

Answer 5

ONLY consider the financing costs as other costs are negligible.

Net fin.costs= Interest - present value of dividends

This is because the investor forgoes interest on the cash (as it is invested in funds) but recieves dividends

Question 6

Internation accoutning standards board (IASB) definition of fair value - requires daily what

Answer 6

Any deriv instrument can be transacted between 2 mkt participants at a given time at an arm’s length transaction

In english - fiar value = current mkt price. However IASB requires daily marking to market for futures contracts

Question 7

Contango - are futures prices above or below cash

Answer 7

In markets where there is a net cost of carry in holding the asset to delivery, futures prices are higher than cash prices. called contango

Question 8

Backwardation

Answer 8

In markets when there is a net benefit to holding the asset until delivery as futures prices are lower than cash prices.

Common in bond and short term interest rate markets as short term IRs are lower than longer term IRs.
Also seen in commodity markets when there is a high premium for immediate delivery of a UA, showing expectations of a short term storage in the UA.

Question 9

Convergence

Answer 9

Cost of carry assumes that teh contract is held from now until expiry.

However, as the contract moves closer to expiry, the costs of carry go down until they are virtually $0 at expiry because of this the price must go down due to the diminishing cost of carry value (converge) as the contract goes through it’s life

Question 10

Basis (aka crude basis) - backwardation and contango mkts

Answer 10

Basis = Cash price - futures price

Difference between the cash price and futures price and can be used to describe the difference between 2 futures prices (e.g. March and June futures).

• Contango markets = basis is NEGATIVE
• Backwardation markets = basis is POSITIVE
• Moves towards 0 over the life of the contract due to convergence.

Influenced by short term S+D pressures and the fact different mkt participants have different borrowing costs etc but in a perfect market it shoulld reflect the cost of carry.

Question 11

4 factors affecting the basis

Answer 11

1. Change in supply and demand
2. Changes to the cost of carry
3. Different costs for different market participants making fair value relative
4. Convergence (time until expiry)

Movements in basis can change hedging stratergies and create options for arbitrage

Question 12

Strengthening basis

Answer 12

=Basis moves in a positive direction (cash prices increase relative to futures prices). Expected in a contango market when future prices converge and a contract moves towards expiry. Basis becomes less negative

narrows price differentials in contango mkts.

In a backwardation market, strengthening sees a widening gap between 2 prices as they are positive.

Question 13

Weakening basis

Answer 13

Basis moves in a negative direction (cash prices decline relative to futures prices).

• Contango markets - widens the gap in prices (negative price differential decreases)
• backwardation market - gap narrows between prices as positive basis moves negatively (less positive).

Question 14

Relationship of convergence and basis in contango and backwardation

Answer 14

• contango mkt (e.g. equity index) - basis strengthens (becomes less negative) closer to expiry
• Backwardation (e.g. STIR and bond futures) - Basis weakens towards expiry

Question 15

Changes in basis (strengthen/weaken) - what will traders do to try and profit - basis strengthens/weakness, buy or sell near/far dates

Answer 15

Basis strengthens (regardles of contango or backwardation) the trader should BUY the near dated instrument and simultaneosuly sell teh long dated instrument.

If basis weakens - traders should sell the spread. Sell the near dated instrument and buy the far dated instrument.

Question 16

Basis risk

Answer 16

Basis risk = risk that a futures price will move differently to that of it’s underlying asset

The basis should broadly follow the UA price but different factors can make the change very large.

Risk is usually significantly lower than the market risk of the UA

Can only eliminate the risk by holding the contract until expiry when the prices converge to $0.

Question 17

Cash and carry arbitrage

Answer 17

If a future is trading above it’s fair value it is more expensive relative to the price of the UA.

Arbitrage trade = buy the relatively cheap UA and simultaneously sell the future.

Called cash and carry = as buying the cash asset carries the sale of the futures contract.

Question 18

Reverse cash and carry arbitrage

Answer 18

Future is trading below it’s fair value, therefore is cheap relative to the price of the UA.

Arbitrage trade = sell the relatively expensive cash UA and buy the futures contract

Question 19

The arbitrage channel

Answer 19

Arbitrage can sometimes not be profitable when considering additional costs associated with trading liek commisions, fees, tax etc.

this means a future price can move away from it’s fair value without creating arbitrage opportunities as long as the difference is less than the trading costs that would be incurred.

This creates the arbitrage channel = a range of prices that the cash/futures price can vary without creating arbitrage opportunities (due to trading costs cancelling profits/causing a loss). If futures prices move beyond the limits of the arbitrage channel then arbitrage becoomes possible and will move the price back in line with the channel.

Question 20

Basis risk impact on hedging with futures

Answer 20

Cash and futures prices are strongly correlated so basis risk can affect the performance of hedges.
* e.g. future might not have been trading at it’s fair value when teh hedge was made. Market movements will bring it back to it’s fair price but this will cause some profit of loss on the hedge.
* Basis might not change from the time the hedge was placed to the time it was offset = P/L on the hedge
* Hedge might over/underperform due to changes in basis
The risk of significant under performance is limited however due to arbitrage opportunites keeping the price in check.

Question 21

Options pricing - Options premium

Answer 21

Non refundable fee the holder pays to the seller of the option to buy it.

the fee is determined by buyers and sellers in the market and:
* distance from strike price to current UA price and the time until expiry.

Premium (PM) = Intrinsic value (IV) + Time value (TV)

Question 22

Intrinsic value

Answer 22

Intrinsic value= difference between strike price and UA price. Basically the minimum value an option can have.

• Call options have IV if the strike price is lower than the UA price
• Put options have IV is the strike is greater than the UA price.
• IV can never be negative - has be be 0 or more.
• 0 IV is not worth exercising
• All options with IV at expiry will be exercised and the premium is not considered in the choice whether to exercise as profits will be used to cover the premium
• If IV is greater than the premium the investor makes net profit
  *

Question 23

Intrinsic value descitpive phrases (in the money etc)

Answer 23

• Options with IV = In the money
• No IV = Out the money
• Exercise price equals or is close to UA price = at the money

Deep or far = describe if you are significantly in or out the money

Question 24

Time value (TV)

Question 25

Time Value

Answer 25

• Time value is the excess price above the option’s IV.

TV = Premium - intrinsic value

Time value refelccts the fact that probability that the price of the UA can move beyond or below the strike and is the price paid for the uncertainty

Question 26

Determinates of an option’s premium - 1/3 time to expiry

Answer 26

A longer dated option will have more Time Value than a short dated option as the UA price can move more in a longer time period, thus higher uncertainty.
* this leaves the option writer at risk for longer
* TV is eroded as options approach expiry as it is clear whether the option is worth exercising
* TV at expiry = 0
* TV works in the favour of the writer NOT the investor, as the TV erodes over time, reducing the option’s value for the investor.

Question 27

Determinates of an option’s premium - 2/3 distance from strike price to UA price

Answer 27

As TV reflects teh uncertainty that an option will be exercised or not we can look at if it is ITM or OTM when is is close to expiry, giving a good indication.
* ITM options - have less TV as they are likely to be exercised
* OTM options - have less TV as they are likely to abandonned
* ATM options - have the highest amount of TV as the UA price is close to the strike price so it can easily swing into ITM or OTM, creating uncertainty

Question 28

Determinates of an option’s premium - 3/3 volatility and 3 types of volatility

Answer 28

Higher volatility assets command a higher premium. TV is higher as volatility means the price is uncertain and moves irratically.

3 types of volatility
1. Historic (realised) - how volatile an asset has been in the past. Accurate as based on past info but history might not repeat itself
2. Future - Useful to know but very hard to predict
3. Implied - As it is impossible to exactly predict future volatility, implied volatility is the market’s collective view of what is likely to happen in the future

Question 29

Implied volatility pricing models - 4 data points

Answer 29

• Options pricing models are used to get a figure for implied volatility. They work by inputting volatilitty, strike price, UA price, cost of carry to get the premium. If the premium is known, you can use models to work backwards to find the volatility
  Models
• Black-Sholes - 1973 - algorithm - most famous - focusses on European style options
• Black-Sholes-Merton - as above with Merton, worked on continus time finance part of the model
• Binomial Pricing Model and Finite Difference - volatility for American style options
• Stochastic alpha, beta, rho (SABR) - uses different implied volatility to price options on the same UA. Works using volatility smile, V is greater for options deep ITM + OTM.

Adjustments willl need to be made to consider futures, options, the UA being used, dividends for equity dervis. Other models are better for certain UAs like STIR options as there are 2 inputs.

Question 30

Impacts of IRs, dividends and coupons on premium

Answer 30

• Prices of options can be affect by IRs and coupons as if IRs rise, the buyer of the call who keeps their money as cash earns more interest and the writer is disadvanged, so raises premium.
• If dividends rise, the writer can afford a lower premium as they are compensated from dividends
  *

Question 31

Impact of factors on CALL options premiums

Answer 31

• Price of UA rises = premium rises
• Time to expiry rises = rises
• Volatility rises = rises
• exercise price rises = falls
• IRs rise = rises
• options on physicals = rises
• Options on futures = generally no change

Question 32

Impact of factors on PUT options premiums

Answer 32

• Price of UA rises = premium falls
• Time to expiry rises = rises
• Volatility rises = rises
• exercise price rises = rises
• IRs rise = falls
• options on physicals = falls
• Options on futures = generally no change

Question 33

Put/call parity theorum and calc

Answer 33

Call and put options must have fair prices relative to one another or else arbitrage opportunites would appear.
Put/call parity defines the relationship between the put and call prices and UA prices.

Call premium - put premium = UA price^ - strike price
^(spot or cash price. futures price if a future)

Question 34

Put/call theorum for options with underlying income events (coupons, dividends) CALCULATION and more accurate for what exercise style

Answer 34

Call premium - put PM = UA price - strike/(1+annual risk free IR) ^time to expiry in years

Formula is used for individual equity options and equity index options.

This is more accurate for european style options as American style add the complication that they can be exercised whenever.

Question 35

Put/call theorum arbitrage opportunities - reversals and conversions

Answer 35

If call/put premiums are not consistent arbitrage opportunities exist.
* if the call is cheap, buy the call, sell the put and sell the future. This action creates a synthetic long futures position. by selling the future it then reverses the long future position, crystalising profits. Called reversal
* If the put is cheap - buy the put, sell the call and buy the future. creates a synthetic short future which is closed out by buying the future to crystalise profits. called conversion

Question 36

Delta - measures what, modelled by, calc, positive and negative when.

Answer 36

Delta measures the sensitivity of the option’s price to changes in the price of the UA Black-sholes model can calculate it.

delta= change in option premium / change in price of UA

• Delta of 0 = premium is tottally insensitive to small changes in the UA price. Applies to deep OTM puts and calls
• Delta of 1 (long positions) or -1 (shorts) means that the premium changes exactly in line with the UA price. Applies to deep ITM options, the UA itself and long futures
• Call deltas are positive as premiums rise when UA price rises
• Put deltas are negative as PMs fall when UA price rises

Question 37

Products and their typical delta value

Answer 37

• Deep ITM calls, long futures, physical UAs = delta of +1
• ATM calls = +0.5
• Far OTM calls and puts = 0
• ATM puts = -0.5
• Deep ITM puts, short futures = -1

Question 38

Delta value of cumulative positions - page 141 examples

Answer 38

Cumulative delta = delta of a whole portfolio of positions and gives an idea of the whole portfolio’s sensitivity to UA price mvmt (directional bias).

• Need to add the delta of each individual position’s delta together and it will give a final result to show the portfolio’s directional bias
• Used guage what hedges are appropriate
• When cum. delta is 0 = AKA delta hedged
• To achieve delta hedging you need to buy/sell contracts to cancel out the current delta to 0. e.g. cum delta = +3, need to sell 3X futures.
• Delta hedging only eliminates price risk, not time, volatility and basis risks
• Delta is time sensitive and changes over time.

Question 39

Greek measures - Gamma - measures what

Answer 39

• Gamma measures how delta changes with respect to the movement of the UA price.
• Gamma is small when options are deep ITM or OTM and at it’s highest when options are ATM and close to expiry
• Short dated ATM options Gamma can be traded for profit
• Represents the size of the adjustments to hedges in a portfolio as it measures delta
• When a portfolio is net positive = called positive gamma and visa versa

Question 40

Greek measures - Vega
Positive for what, when at its highest, useful because…,

Answer 40

• vega=a measure of how a 1% change in implied volatility affects and option’s price
• Always positive for long positions (whether put or call)
• Highest for ATM options and lowest for deep ITM/OTM options
• Vega is higher for long dated options and decreases as options approach expiry
• Useful = measures an option/portfolio of options sensitivity to expected volatility and current mkt conditions.
• Trader use it to indicate an option’s profitability as vega shows how well an option performs relative to the mkt conditions
  *

Question 41

Greek measures - Theta - longs have +/- theta?

Answer 41

• Theta=mesure of the rate of decline of an option’s value due to the passage of time
• Shows how much the price of an option will change as one day passes (and the UA price remains steady).
• Basically measures time risk - time decay in value of an option as if factors remain the same the price of the option will fall with time.
• Long calls and puts always have a negative theta
• Short calls and puts always have a positive theta
• Theta is highest foor ATM options and decreases as they move ITM/OTM.
• Theta increases sharply when options are close to expiry and can undermine long options positions if volatility decreases at the same time as theta is greater when volatility is high or there are fewer days to expiriation
• Used in trading stratergies alongside gamma and vega.
• If vega is falling, traders are likely to sell the option

Question 42

Greek measures - Rho - normal fluctuation value, impact on options

Answer 42

• measures how much an option’s value will change if interest rates change by 1%
• Options typically have a low Rho as relationships between otpions and IRs are fairly stable and unllikely to cause dramatic price swings
• Rho normally fluctuates between 0.04 and 0.02
• The impact of IRs on options pricing is due to costs of carry related to financing costs
• Increased IRs = increased value of calls, decreased value of puts and visa versa
• Rho is higher for options with longer until expiration
• ATM and ITM options have higher Rho and OTM options have lower

Question 43

Premium payments

Answer 43

• Typically, options buyers have to pay the premium immediately and the sller recieves teh money the next day. Typically has to post initial margin for this period whilst they are short the option.
• At the point of the trade, the writer’s clearing house becomes responsible for margin payments and will collect margin off the seller to pay the clearing house
• Bond and IR options on ICE futures and Euronext, premiums are paid futures style at some point during the life of the contract

Question 44

Margin requirements for equity indexes and single stock options

Answer 44

• Long positions = do not require initial margin OR varriation margin
• Short positions = require intial margin - do not require variation margin

Question 45

Margin requirements for Bond and STIR options

Answer 45

• Long positions = Do not require inital margin - require variation margin
• Short positions = require BOTH initial and variation margin

Question 46

DONE