Principles of Exchange-Traded Derivatives Flashcards
how is the price of a future derived?
From the underlying price of the asset in the cash market, plus the net cost of holding the position over the term of the contract.
what is the cost of carry?
the costs involved in holding the physical assets to the expiry dates
what are the main components of costs of carry?
- finance costs
- security costs
- storage costs
- insurance
what is the fair value?
storage and insurance costs along with any financing costs
how is the fair value of a future calculated?
cash price + cost of carry
how does the calculation of the the fair value of an equity index future differ?
only net finance costs need to be considered as all other costs are negligible. Investor forgoes interest on funds invested in shares but still receives dividend
net finance costs= interest - present value of dividends
what does it mean when a market is in contango?
there is a net cost of carry in holding the asset to delivery so future prices will be higher than cash prices
what is backwardation?
there is a net benefit in holding the asset to delivery, so future prices are lower than cash prices
where is backwardation most common (markets)?
in both the bond and short term interest rate markets when long-term interest rates are higher than short term rates
how does convergence work in relation to the cash and future prices?
at expiry the cost of carry is zero so the cash and future prices must converge over the life of the future until they meet at expiry
what is basis and how is it calculated?
measure of the differences between cash and futures prices. can also be used to describe the difference between two futures prices
basis = cash price - futures price
what will the basis be in a contango/backwardation market?
in a contango market, basis will be negative as the futures price is greater than the cash price
In a backwardation market the basis will be positive as the cash price is greater than the futures price
what can cause the basis to change?
- supply and demand
- cost of carry
- market participants having different cost bases
- time remaining to expiry
what does it mean when the basis is strengthening in a contango market?
when the cash price increases relative to futures prices, the basis is moving in a positive direction so is strengthening. expected in a contango market as the future moves to expiry and the cash/futures prices converge
what does it mean the basis is strengthening in a backwardation market?
widening gap between the cash and futures price
what is weakening of the basis in the contango/backwardation market?
weakening in contango: widening the gap between the cash and futures market, negative price differential increasing
weakening in backwardation market: narrowing of the gap, positive basis moves in a negative direction to become less positive
what should a trader to when a basis is expected to strengthen?
buy the spread: buy near dated instruments and sell far dated instruments
what should a trader do when a basis is expected to weaken?
they should sell the spread by selling the near-dated instruments and buying the far-dated instruments
what is basis risk?
risk that a futures price will move differently to that of its underlying asset
how can one eliminate basis risk?
by holding a futures contract to its expiration, until the prices converge
what is arbitrage?
traders attempt to profit by exploiting price differentials between identical, or similar financial instruments that are trading on different markets or in different forms
where is there a potential for arbitrage in futures?
when there is a mispricing between the underlying instrument and the futures available on that instrument- this exists when the future is not trading at its fair value
what is a reverse cash and carry arbitrage?
when a future is currently trading below its fair value, it means its cheap relative to the price of the underlying so to exploit the mispricing they should sell the relatively expensive underlying cash asset and buy the relatively cheap future
what is a cash and carry trade?
when a future is trading above its fair value, its expensive relative to the price of the underlying asset so the appropriate trade is to buy the relatively cheap underlying and sell a future
what is the arbitrage channel?
when the futures price moves away from its fair value without there being any arbitrage activity from the movement, as the transaction costs outweigh any benefits
what happens once the futures price moves out of the arbitrage channel?
arbitrage becomes profitable, the activity then forces the futures price back into the channel and back towards the fair value
what is the relationship between hedging and basis risk?
the future might not have been trading at its fair value at the time the hedge was undertaken so there may be profits/losses on the hedge
what are the two main factors that influence the level of the premium for an option?
the distance of the strike price from the current price of the underlying and the time to run until the option expires
what two broad elements is the premium made up of?
the intrinsic value and the time value
premium = intrinsic value + time value
what is the intrinsic value of an option?
the difference between the strike price and the underlying assets price
- call option will have it if the strike is lower than the underlying
- put will have it if the strike is greater than the underlying
what values can the intrinsic value be?
can never be negative, it can only be positive or zero
what happens when an option has intrinsic value at expiry?
it will be exercised , premium won’t play a factor in this. if the IV is higher than the premium holder will make a net profit and the writer will make a loss
what does it mean when an option is in/out/at the money in relation to the intrinsic value?
- An option with IV is described as being in-the-money (ITM).
- An option with no IV is described as being out-of-the-money (OTM).
- An option with an exercise price that equals, or is close to, the underlying asset price is described as
being at-the-money (ATM).
what is the time value of an option?
the excess above the options intrinsic value i.e., the difference between the premium and the intrinsic value.
TV = PM - IV
what does the Time Value reflect?
the possibility that the price can move beyond any given strike which would make it worth exercising- its the price paid for the uncertainty of the underlying’s movements
what is the relationship between time value and time to expiry in options?
longer-dated options will have a greater time value as there is more uncertainty- as expiry approaches there is less uncertainty about whether an option will be worth exercising. erosion of time value increases over the life of an option
what is the relationship between the difference between the strike and the underlying and the Time value in options?
in the money: high chance of being exercised. less uncertainty, less time value
out of the money: high chance of being abandoned. less uncertainty, less time value
at the money: highest amount of time value, most uncertainty exists
what is the nature of the relationship between time value, premium and volatility?
higher the volatility, higher the time value and therefore the premium as holders have a higher chance of making a large profit if the price movement sways massively in their favour- writers at a greater risk
what are the three types of volatility to consider when looking at the premium and pricing of an option?
- historic
- future
- implied, market takes collective view by buying and selling
what is the black-Scholes model and what does it show?
helps to calculate an actual figure for volatility. by using inputs such as volatility, strike price, underlying price, time to expiry and cost of carry, it works backwards to calculate the volatility implied by the premium
what sort of options can the Black-Scholes model only be used for?
to price european exercise options as it doesn’t account for varying exercise dates
what models can be appropriate for pricing American style options?
Binomial pricing model and finite difference as they aren’t constrained by a specific exercise date
what is the SABR model?
stochastic alpha, beta, rho pricing model- uses different levels of implied volatility to price options on the same underlying asset
what is the pricing basis for the SABR model?
the volatility smile which states that the implied volatility is greater for options with strike prices that are deep in the money and deep out of the money i.e., when the strike price is very different from the underlying assets price
how does the interest rate/ dividend yield affect the price of an option?
buyers and sellers will have to include the effects of a rise or fall in interest rates/dividends in the cost and price of the option. e.g., if the dividend rises relative to interest rates the writer can afford to charge a lower premium as they are benefitting from the dividend
why must call and put options be fair in relation?
otherwise arbitrage opportunities would present themselves
what is the put/call parity theorem?
defines the relationship between put and call prices and the price of the underlying asset
what is the put/call parity formula?
C-P = S-K
where;
C: call premium
P: put premium
S: underlying price
K: strike price
used for individual equity options and equity index options
what are the trade options if a call or put option is mispriced according to the put/call parity formula?
- if the call is relatively cheap as per the formula, buy the call, sell the put and sell the future
- if the put is relatively cheap as per the pricing formula, buy the put, sell the call and buy the future
what is a delta of an option?
measure of the sensitivity of the options price in relation to changes in the price of the underlying asset
what is the formula to calculate the delta of an option?
change in option premium/change in price of the underlying
what do the different deltas mean?
0 means the premium is totally insensitive to an underlying price change
+1 or -1 means the premium will change by exactly the same amount as the underlying
what is the difference between call option deltas versus put option deltas?
call deltas will be positive as the premium will rise when the price of the underlying rises
put deltas are negative as the premium will fall when the price of the underlying rises
how does the time to expiration affect the delta?
as an option gets closer to expiry the delta will increase as a change in price of the underlying will have a greater impact on the premium
what is the cumulative delta?
measure of sensitivity of a portfolio containing futures/underlying, calls and puts. calculated by adding the deltas of the individual positions together
How is directional bias accounted for in the cumulative delta?
by taking into account the number of long/short positions. to work it out you assign a + or - to the number of positions being considered, (long is +, short is -), then multiplying this by the delta of the option to get a net delta position
what can cumulative deltas be useful for?
to gauge what is required to hedge a portfolio, managers will be able to hedge by entering into positions with an opposite cumulative delta of the portfolio
what is the Gamma?
measure of how the delta changes in relation to movements in the price of the underlying
How does the Gamma change depending on whether the option in ITM or OTM.
small when the option is ITM or deep OTM, greatest when its ATM
how do traders and asset managers use the Gamma?
- traders will monitor the impact of gamma on the premiums of options
- asset managers will use the Gamma in hedging strategies
what does the Gamma represent in relation to hedges?
represents the required adjustments to any hedges associated with a single options position or a portfolio of options
what is Vega?
a measure of how a 1% change in implied volatility affects an option’s price- always positive for long options positions
what causes the vega to be smaller?
the further ITM or OTM the option goes, the smaller the Vega
how does time affect the changes in volatility on an option and how does this relate to the Vega?
Vega is higher for long-dated options than short-dated options, Vega will fall as the option reaches its expiry date
How can the Vega be useful in analysis?
measures an options/ options portfolio’s sensitivity to both market sentiment and current market conditions in relation to volatility
What is Theta?
measure of the rate of decline of an option’s value due to the passage of time, represents how much an options value will change as one day passes and the underlying asset price remains steady
what does the Theta quantify?
the risk that time imposes on options due to the eventual expiry/ exercise date
what are the different Thetas in different options positions?
Long calls/puts always have negative Theta
Short calls/puts always have positive theta
what happens to Theta as an option approaches expiry?
it increases sharply which can undermine a long option holder’s position, Theta will be greater when there are fewer days till expiration
what is Rho?
measure of changes in an option’s value due to a change in interest rates- how much an option’s value will change from a 1% change in market interest rates
what is the impact of interest rates on an option’s price based on?
the cost of carry associated with holding the underlying asset relative to the option
how will an increase in interest rates affect the value of puts and calls?
will lead to an increase in the value of calls and decrease in the value of puts
what is the main convention for the payment of premiums?
the buyer of the option is requested to pay the premium immediately
who is liable for any margin required by the clearing house at the point of trading?
the writer’s broker, collected by marking to market
why is the margining of some option’s positions made more complex?
as they are payable futures style, meaning they aren’t payable immediately but are paid during the life of the contract through margining
