Principles of Exchange Traded Derivatives

Question 1

Fair value of future:

Answer 1

Cash price of underlying + Costs of carry

Question 2

Fair value for equity index futures

Answer 2

• Cash index
• Foregone interest (cost of carry)
• Dividend yield (benefit of carry)

Question 3

FTSE 100 index future

Answer 3

• Contract for difference

• Quotation: Index points
• Valuation: GBP5 per 0.5 index points

Question 4

IASB definition of fair value:

Answer 4

A future’s fair value is equal to its current market price

Question 5

Arbitrage channel:

Answer 5

Definition: The range of values through which a future can trade away from its fair value where arbitrage is not profitable

Question 6

Basis:

Answer 6

Cash price - futures price
Contango -> negative basis
Backwardation -> positive basis
Basis movement is non-linear and tends to be less volatile than the cash market

Question 7

Convergence:

Answer 7

As the future approaches delivery, the fair value converges with the cash price.

Question 8

Universal stock futures

Answer 8

• A form of single stock futures (contract to buy/sell particular shares)
• Global product
• Contract specifications
- Physically delivered or cash settled depending on the share
- Contract size
• Typically 100 shares
• Italian and UK stock 1,000 shares
- Valuation: price per share
- Tick size: ¤0.01

Question 9

Long gilt future

Answer 9

GBP100,000NV 4% gilt
• Quotation: GBP100NV
• Valuation: GBP10 per GBP0.01 per GBP100NV

Question 10

Hedging with bond futures

Answer 10

Number of contracts required = Nominal value of CTD holding / Nominal value of contract X CTD price factor

Question 11

Short-term interest rate future (STIR)

Answer 11

• Contract for difference
• GBP500,000 deposit at 3 month LIBOR
- Quotation: 100 minus implied interest rate
- Valuation: GBP12.50 per basis point
• Speculating
• Hedging
- Deposits
- Loans

Question 12

Option pricing (OP):

Answer 12

Premium = Intrinsic Value + Time Value

Question 13

Intrinsic value OP

Answer 13

Intrinsic value cannot be less than zero. An option is most likely to be exercised when it is in the money, i.e. it has intrinsic value.
The premium of an option will include the intrinsic value of that option.

Question 14

Time value OP

Answer 14

• The erosion of time value acts against the holder and in favour of the writer.
• For the holder, if everything else remains the same, their option is losing value each day.
Time value is highest when the option is at the money.

Question 15

Volatility OP:

Answer 15

• Historic vs. implied

• Black-Scholes
• Binomial
• SABR

Question 16

Other factors OP:

Answer 16

When dividends rise, call option time value falls and put option time value rises
When interest rates rise, call option time value rises and put option time value falls

Question 17

Delta:

Answer 17

Definition 1: The sensitivity of an option premium to a change in the price of the underlying.
Change in value of option premium / change in value of underlying
Definition 2: Likelihood of option expiring in the underlying.
Definition 3: Options as a relative number of futures positions.

Question 18

Gamma:

Answer 18

• The sensitivity of an option’s Delta to a change in the price of the underlying
• For an ATM option, Gamma increases as the remaining life decreases
• Gamma is negative for short options and positive for long options

Question 19

Vega:

Answer 19

• Sensitivity of an option premium to a 1% change in implied volatility
• Positive for long positions
• Greatest for at-the-money options
• Higher for longer-dated options

Question 20

Theta:

Answer 20

• Sensitivity of an option premium to a change in a unit of time
• Negative for long options
• Greatest for at-the-money options
• Increases as options approach expiry

Question 21

Rho:

Answer 21

• Sensitivity of an option premium to a 1% change in interest rates
• Positive for calls
• At-the-money and in-the-money options have relatively higher Rho
• Higher for longer-dated options

Question 22

Put-call parity: Arbitrage

Answer 22

Synthetic < future/underlying
• Trade: Reversal
• Actions:
- Synthetic long (buy call and sell put)
- Sell future/underlying

Synthetic > future/underlying
• Trade: Conversion
• Actions:
- Synthetic short (sell call and buy put)
- Buy future/underlying

Question 23

Premium payment

Answer 23

Upfront
• Pay premium immediately (T+1)
• Equity and equity index options
On close
• Pay premium on exercise or expiry
• Options on futures
- E.g. options on bonds and STIRs