PowerPoint Presentation
IC301
Derivative Securities
IC301– Topic 3
Options and Trading Strategies
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Options
Right but not the obligation to buy or sell
OTC or exchange listed
Black Scholes
Greeks – delta, gamma, theta, vega, rho
Vanilla options
Delta neutral hedging.
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Option terminology
Holder/buyer/long
Writer/seller/short
Underlying
Expiry
Exercise or strike price
Premium = intrinsic value + time value
5 factors drive premium: underlying, strike, remaining life, volatility of underlying, IR.
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Exchange traded options
Stock options
Commodity options
Bond & other interest rate options
Index (equity) options
Options on futures contracts.
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OTC options
Interest rate options
Currency cross rate options
Options on swaps
Also employee stock options (no secondary market).
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Option Contracts – definitions
A CALL option is the right to buy an underlying asset at a specified price
A PUT option is the right to sell an underlying asset at a specified price
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Futures price at expiry
profit
loss
$50
$60
$40
Bullish oil option on futures trade
Buy $ 50 call option
-$2
Maximum loss is premium paid
limited losses, unlimited gains.
A call option gives the owner the right (but not the obligation) to own the underlying stock on the expiry date at the exercise or strike price.
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Call and Put options – payouts at expiry
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Spot (ST)
Profit or Loss (+/-)
Contract Rate (K)
Spot (ST)
Profit or Loss (+/-)
K
Call option
Put option
NOTE – the payout charts exclude the option premium
Call and Put options – the full set!
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ST
K
K
Long Call
Long Put
ST
ST
K
K
Short Call
Short Put
ST
NOTE – the payout charts exclude the option premium
Formally, for a call:
Call = Max {ST -K,0}
Put = Max{K-ST,0}
More definitions
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Call/Put sellers are also known as option ‘writers’
Expiry terms
European Option – can only be exercised on the maturity date at a specific time
American Option – can be exercised at any time up to and including the expiry date and time
Why would anyone sell an option?
Basics of Option Valuation
Premium = Intrinsic value + Time value
Intrinsic value is the value if the option is exercised now. Positive when in the money but can’t be negative.
Time Value – Theta
If there is time left to expiry, then an option is said to have time value
There is a probability that the underlying may trade through the strike before expiry, giving the option value
The probability is greater:
– The longer the remaining time to expiry
– The greater the volatility of the underlying
Time Decay
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Time Value
Time value is greatest ATM
If the option is deep OTM, there is a lower probability of the underlying trading through the strike: Lower time value
If the option is deep ITM, the main component of its value is intrinsic value
IC Trader – no time decay, but Delta (direction) and Vega (volatility) positions
So option premiums won’t decay over time in IC Trader
In the real world they do, so to counteract time decay, we need underlying market direction (delta) and volatility (vega)
If volatility increases, call and put premiums will increase, so positive vega makes money, opposite if volatility decreases
If Delta is positive, we make money with underlying rising in price
If Delta is negative, opposite is true
Option deltas
Net deltas.
IC Trader
Option Vega
Option Delta
Underlying shares
Net delta
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How to delta hedge to be delta neutral
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position delta Exposure (shares)
Long 39,997 shares 1 39,997
Short 50,000 puts 0.4 20,000
Long 50,000 puts 0.6 (30,000)
Long 25,000 puts 0.5195 (12987)
Total net 17,010
Can you think of the quickest hedge? Any other ways?
Sell shares or sell calls or buy more puts
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Vanilla Call Value
X
ST
Long Call
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Call Payoff Functions
IN THE MONEY (ITM): ST> X.
AT THE MONEY (ATM): ST= X .
OUT OF THE MONEY (OTM): ST< X.
Moneyness of options
Put Payoff Functions:
ITM: X > ST
ATM: X = ST
OTM: X < ST 20 Moneyness of options 20 Vanilla Call Delta X ST Long Call 21 Delta – different times to expiry 22 The probability of ending up in the money is at the heart of option pricing Underlying Mar'20 future price £/$ 1.2300 Calls Strike Puts 0.0772 1.18 0.0191 0.0697 1.19 0.0216 0.0626 1.20 0.0244 0.0559 1.21 0.0275 0.0495 1.22 0.0311 0.0436 1.23 0.0350 0.0381 1.24 0.0395 0.0331 1.25 0.0444 0.0286 1.26 0.0499 0.0247 1.27 0.0558 0.0212 1.28 0.0622 23 Call premiums rise Put premiums rise Topic 4 Trading Strategies Involving Options IC301 24 24 Option Strategies 25 Option strategies are a way of expressing market views Direction (“Bullish/Bearish“ ++,+-,-+,--) Volatility – large moves or ranges? Fixed maximum payouts or unlimited upside? Flexibility in expressing view ++ = long call = bullish -- = short put = bullish Bullish Trades (market price is 1.00) ST 1.00 Buy call at 1.00 Sell call at 1.10 Moderately bullish Max payout 0.10 1.10 Call Spread ST 1.00 Buy call at 1.00 Sell 2 calls at 1.10 Less strongly bullish Max payout 0.10 Can make a loss 1.10 Ratio Call Spread 1.20 26 Neutral Trades (market price is 1.00) Buy 1call at 0.95 Sell 2 calls at 1.00 Buy 1 call at 1.05 Butterfly Spread ST OR !! Buy 1 puts at 1.05 Sell 2 puts at 1.00 Buy 1 put at 0.95 0.95 1.00 1.05 27 Leverage Call Spread (compare) 1.00 ST Buy 1 call at 1.00 Sell 1 call at 1.10 Max payout 0.10 1.10 Call Spread ST 1.09 Buy 10 calls at 1.09 Sell 10 calls at 1.10 Max payout 0.10 1.10 10 x Leveraged 28 Call Spread Positions in an Option & the Underlying (Figure 12.1, page 279) IC301 29 Profit ST K Profit ST K Profit ST K Profit ST K (a) (b) (c) (d) 29 a) Covered call c) protective put – Red line shows combined payoff expiry profile Two popular equity strategies Covered calls [see a) – previous slide] Protective puts [see c) – previous slide] 30 Break it down, slowly 30 Protective put 31 See option practice word document 31 Create a pay-off table 32 underlying 10 20 30 40 50 Long stock -20 -10 0 10 20 Long 30 put +20 +10 0 0 0 Premium -2 -2 -2 -2 -2 Total -2 -2 -2 +8 +18 /docProps/thumbnail.jpeg