Principles of Exchange Traded Derivatives Flashcards
Fair value of future:
Cash price of underlying + Costs of carry
Fair value for equity index futures
- Cash index
- Foregone interest (cost of carry)
- Dividend yield (benefit of carry)
FTSE 100 index future
• Contract for difference
- Quotation: Index points
- Valuation: GBP5 per 0.5 index points
IASB definition of fair value:
A future’s fair value is equal to its current market price
Arbitrage channel:
Definition: The range of values through which a future can trade away from its fair value where arbitrage is not profitable
Basis:
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
Convergence:
As the future approaches delivery, the fair value converges with the cash price.
Universal stock futures
• 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
Long gilt future
GBP100,000NV 4% gilt
• Quotation: GBP100NV
• Valuation: GBP10 per GBP0.01 per GBP100NV
Hedging with bond futures
Number of contracts required = Nominal value of CTD holding / Nominal value of contract X CTD price factor
Short-term interest rate future (STIR)
• 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
Option pricing (OP):
Premium = Intrinsic Value + Time Value
Intrinsic value OP
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.
Time value OP
• 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.
Volatility OP:
• Historic vs. implied
- Black-Scholes
- Binomial
- SABR
Other factors OP:
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
Delta:
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.
Gamma:
- 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
Vega:
- 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
Theta:
- 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
Rho:
- 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
Put-call parity: Arbitrage
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
Premium payment
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
