Derivatives Chapter 4 Flashcards
(arbitrage free) fair value of a future is
Fair Value = ….
Fair Value = Cash price + Cost of carry
Cost of carry main components
storage
insurance
interest
the cash price of an asset is £1,250.
interest rates are 6%pa
storage is 1% pa
Calculate the fair value of a 90 day future
fair value = cash price + cost of carry
cash price = 1250 given
cost of carry? : 1+6, 7% for 90 days. 7/365*90= 1.7%
1250*0.017= cost of carry £21.25
fair value = 1250+21.25 = £1272.25
S&P 500 index is currently 1,265.
one year US interest rates are 4.55%.
index’s dividend yield is 2.25%.
Calculate the fair value of the 182 day future.
fair value = cash price + cost of carry
cash price = 1265 given
cost of carry? :
- 55% - 2.5% = 2.3% (we had to MINUS, because that is money EARNED by holding the asset)
- 3/265*182 = 1.15%
1265*0.0115 = cost of carry £14.5
1265 + 14.5 = fair value £1,280
Explain Convergence
futures price converges on the cash price as time to delivery is closer.
Basis = ….
normally, basis is …
but it can also be ..
Changes in basis can be as a result of:
Terminology
Basis = Cash price - Futures price
(the futures price should be the fair value, so then, basis = - carry)
- basis is usually NEGATIVE (contango markets)
- can also be POSITIVE (backwardation markets)
Changes:
- supply & demand
- cost of carry
- changes in time to delivery (convergence)
Terminology:
- strengthening of basis (bigger gap)
- weakening of basis (smaller gap)
Arbitrage Trades
?
Hedging and Basis Risk
You CANNOT hedge against change in basis. The hedge will still be exposed to some risk (basis change)
unhedged positions are at risk of changes in the price of the underlying asset. If you do hedge, however, you will still be exposed to risk in basis changing.
options premium
Premium = ….
explain the other two parts!
Premium = Intrinsic Value (IV) + Time Value (TV)
intrinsic value is the difference between strike and value of the underlying. IV can be positive, or ZERO (for puts and calls)
- call options: value of underlying - strike (you will pay!
- put options: strike - value of underlying
Time value: difference between premium and intrinsic value
Status of an options (in the money etc) table
Determinants fo an Option’s Premium
1) Price of Underlying Asset
- intrinsic value
- price ^ –> call prem ^ put prem v
- price v –> call prem v put prem ^
2) Time to Expiry
- time valuye decays as an option approaches expiry
- the eriosion SPEEDS UP as expiry approachs (see curve)
- erosion works in favour of the writer (why?)
- time v –> call prem v put prem v
3) Volatility
- vol ^ –> prems ^ vol v –> prems v (dierct relationship)
- historic volatility (what)
- implied volatility (check)
4) Interest Rate
- thing that we are interested in here: CASH
- interest rates ^ –> call prem ^ (because buying calls becomes more popular)
- interest v –> call prem v (because buying calls less popular, buying the share straight awayis done too)
5) Dividend Yield
- thing that we are interested in here: SHARE
- yields ^ –> call prem v (less popular to buy call)
- yields v –> call prem ^ (less popular to buy share)
Put/Call Parity Theorum (zero arbitrage) formula
share price is 600p
premium for 500 put is 7p
the option expires in 3 months
interest rates are currently 6%
What is the premium for the 500 call?
C-P=S-(K/(1+rt))
C = 600p-(500p/(1+0.06*0.25))+7p
= call premium £114
Delta
definition
equation
delta table & graphs with values
delta value of cumulative positions
is a measure of the sensitivity of an option’s price premium to changes in the price of the underlying.
Delta = change in option premium change in price of underlying
table & graphs showing values in image
cumulative position: deltas can be used to measure the sensitivity of portfolios (futures, calls, puts, but on same underlying (i think)! if the delta is null, it is delta neutral or delta hedged:)
investor has the following portfolio on the same underlying asset:
long 5 futures
long 4 puts (deltas 0.65)
long 8 far OTM calls
Gamma
measures rate of change of an options Delta
- is the largest in the ATM part of the curve (most curved!)
- signal as to how often a position needs to be delta hedged
Theta
measures rate of decay of time value for an option
Vega
measures sensitivity of an option premiums to changes in volatility
Rho
measures sensitivity of an option premium to changes in interest rate
When are options premiums payable?
Generally, option premiums are payable T+1 (one day after transaction of agreement)
- so, option sellers receive premium on the morning of the day following a trade
- option sellers are subject to a margin
Market Order
go at best available price (quite quick)
Limit Order
set maximum or minimum price (have more time)
