MONASH
BUSINESS
SCHOOL
BFF5340 – Applied Derivatives
Topic 4 – Payoff diagrams and introduction to structuring
Combining options
2
- It’s common to combine long and short options of differing types, with
different strike rates or maturity dates or other features
- The premium received from granting options fund the premium paid
from purchasing options
- This strategy decreases the cost (i.e. premium paid) and therefore can
improve returns for a given risk scenario – especially when outlier rises
(falls) in asset prices are infrequent
- Structuring is examined later in the unit
Asset Price
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Intrinsic Value
Option value, with no time left until maturity (i.e. “at maturity”)
Long call option – various payoffs
Asset Price
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Time
Value
Intrinsic Value
Option value, with no time left until maturity (i.e. “at maturity”)
Option value, with a small amount of time left until maturity
Long call option – various payoffs
Asset Price
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Time
Value
Intrinsic Value
Option value, with a lot of time left until maturity
Option value, with no time left until maturity (i.e. “at maturity”)
Option value, with a small amount of time left until maturity
Long call option – various payoffs
Asset Price
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Time
Value
Option value, with a lot of time left until maturity
Option value, with no time left until maturity (i.e. “at maturity”)
Option value, with a small amount of time left until maturity
Long call option – various payoffs – including premium
An investor has a long asset position
… and is nervous about a market selloff
They also buy a PUT option (i.e. the
right to sell).
An investor has a long asset position
… and is nervous about a market selloff
They also buy a PUT option (i.e. the
right to sell).
Combined result:
This provides protection without limiting
gains from future topside moves
=
An investor has a long asset position
… and is nervous about a market selloff
They also buy a PUT option (i.e. the
right to sell).
Combined result:
This provides protection without limiting
gains from future topside moves
=
An speculator believes that a quiet
period in the market is about to come to
an end.… but is uncertain in which
direction the price will move.
They combine a bought CALL and a
bought PUT
Combined result:
If the market breaks out in either
direction, the speculator profits. The
maximum loss is the combined
premiums paid.
=
Asset Price
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Synthetic long underlying
Long call
Asset Price
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a
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K
Synthetic long underlying
Long call
Short put
Asset Price
O
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n
V
a
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K
Synthetic long underlying
Long call
Short put
Long underlying
Asset Price
O
p
ti
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n
V
a
lu
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K
Synthetic long underlying
Long call
Short put
Long underlying
Asset Price
O
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V
a
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K
Synthetic long underlying
Long call
Short put
Long underlying
Asset Price
O
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ti
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V
a
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K
Synthetic long underlying
Long call
Short put
Long underlying
Asset Price
O
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a
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K
Synthetic long underlying
Long call
Short put
Long underlying
Asset PriceO
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V
a
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K
Long straddle
Long call
Asset PriceO
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a
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K
Long straddle
Long callLong put
Asset PriceO
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K
Long straddle
Long callLong put
Long straddle
Asset PriceO
p
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n
V
a
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K
Long straddle
Long straddle
Asset PriceO
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V
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Long strangle
Long call (Kc)
Long put (Kp)
KcKp
Asset PriceO
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V
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Long strangle
Long call (Kc)
Long put (Kp)
KcKp
Long strangle
Asset Price
O
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K
How is this useful?
Long call
Short put
Long underlying
Asset Price
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K
= Synthetic asset
Long call
Short put
Long underlying
Asset PriceO
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V
a
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K
How is this useful?
Long straddle
Asset PriceO
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How is this useful?
KcKp
Long strangle
Asset PriceO
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n
V
a
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How is this useful?
KcKp
Asset PriceO
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V
a
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How is this useful?
Long call (Kc)
Short put (Kp)
KcKp
AUD/USDO
p
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a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
AUD/USD FEC
used as a hedge
AUD/USDO
p
ti
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V
a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
AUD/USD FEC
used as a hedge
Hedged exposure
AUD/USDO
p
ti
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V
a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
AUD/USDO
p
ti
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V
a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
Exporter buys
OTM AUD CALL
AUD/USDO
p
ti
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V
a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
Exporter buys
OTM AUD CALL
Hedged position
Potential cost
of hedge
AUD/USDO
p
ti
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V
a
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0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
AUD/USDO
p
ti
o
n
V
a
lu
e
0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
Exporter buys
OTM AUD
CALL
Exporter sells
OTM AUD
PUT
AUD/USDO
p
ti
o
n
V
a
lu
e
0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
Exporter buys
OTM AUD
CALL
Exporter sells
OTM AUD
PUT
Hedged
position
AUD/USDO
p
ti
o
n
V
a
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0.7200
0.6800
What if the exporter was mildly
bearish on AUD/USD, but was
mandated to hedge?
Hedged
position
AUD/USDO
p
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V
a
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0.7200
0.6800
From another perspective
AUD/USDO
p
ti
o
n
V
a
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e
0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(unhedged)
From another perspective
AUD/USDO
p
ti
o
n
V
a
lu
e
0.7200
0.6800
AUD/USD
exposure of an
Australian exporter
(hedged)
From another perspective
Asset PriceO
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How is this useful?
S0
Asset PriceO
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How is this useful?
K2K1
S0
Long Call (K1).
ITM
Short Call (K2).
OTM
Asset PriceO
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Bull spread
K2K1
S0
Asset PriceO
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Bear spread (aka short bull spread)
– how is this constructed?
K2K1
S0
More than one way ….
46
- Put/call parity allows identically performing structured products to be
created using a range of components
- For example:
- Long $49.00 CALL, short $50.00 CALL (long BULL spread)
- Long $49.00 PUT, short $50.00 PUT (short BEAR spread)
Asset PriceO
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K2
Long Bull Spread
Long Call, K1
K1
Asset PriceO
p
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V
a
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K2
Long Bull Spread
Long Call, K1
Short Call, K2
K1
Asset PriceO
p
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V
a
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K2
Long Bull Spread
Long Call, K1
Short Call, K2
Long Bull Spread
K1
Asset PriceO
p
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n
V
a
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K2
Long Bull Spread
Long Bull Spread
K1
Asset PriceO
p
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n
V
a
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K2
Short Bear Spread
Long Put, K1
K1
Asset PriceO
p
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V
a
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K2
Short Bear Spread
Short Put, K2
Long Put, K1
K1
Asset PriceO
p
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V
a
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K2
Short Bear Spread
Short Put, K2
Long Put, K1
Short Bear Spread
K1
Asset PriceO
p
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V
a
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Short strangle
K2K1
Bitcoin (USD)
O
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Short BITCOIN strangle
$1,200$800
Short put (K$800).
OTM
Short call (K$1,200).
OTM
$60,000
($lots!!)
Ouch!
Activity - Synthetic structures
56
Construct a payoff profile that has a payoff identical to a long ATM straddle
payoff profile without using puts
Activity - Synthetic structures
57
Construct a payoff profile that has a payoff identical to a long ATM straddle payoff
profile without using puts
A straddle is normally constructed of long 1 ATM Call, long 1 ATM Put
Long 1 Call required delta hedge to SELL 0.5 underlying
Long 1 Put requires delta hedge to BUY 0.5 underlying
Delta’s offset leaving just long 1 ATM Call and long 1 ATM Put
Activity - Synthetic structures
58
Construct a payoff profile that has a payoff identical to a long ATM straddle payoff
profile without using puts
Activity - Synthetic structures
59
Construct a payoff profile that has a payoff identical to a long ATM straddle payoff
profile without using puts
A straddle is normally constructed of long 1 ATM Call, long 1 ATM Put
Long 1 Call required delta hedge to SELL 0.5 underlying
Long 1 Put requires delta hedge to BUY 0.5 underlying
Delta’s offset leaving just long 1 ATM Call and long 1 ATM Put
Activity - Synthetic structures
60
Construct a payoff profile that has a payoff identical to a long ATM straddle payoff
profile without using puts
A straddle is normally constructed of long 1 ATM Call, long 1 ATM Put
Long 1 Call required delta hedge to SELL 0.5 underlying
Long 1 Put requires delta hedge to BUY 0.5 underlying
Delta’s offset leaving just long 1 ATM Call and long 1 ATM Put
Long 1 ATM Put = long 1 ATM Call, SELL 1 underlying,
plus delta of BUY 0.5 underlying
Net result: Long 2 ATM Calls, SELL 1 (i.e. -0.5-1.0+0.5) underlying
Activity - Synthetic structures
61
Construct a payoff profile that has a payoff identical to a long ATM straddle payoff
profile without using puts
Activity - Synthetic structures
62
Long 1 ATM Call, Long1 ATM Put Long 2 ATM Calls, Short 1 underlying
Reverse engineering
63
Identify the components of the following structure.
When would this structure be useful?
Asset Price
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S0
Reverse engineering
64
Identify the components of the following structure
When would this structure be useful?
Asset Price
O
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a
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S0
Activity:
65
Construct a payoff profile that mimics a long straddle, where
Δc = 0.25, without using puts
Activity:
66
Construct a payoff profile that mimics a long straddle, where
Δc = 0.25, without using puts
- For the call…
- Buy 1 * 25Δ call
- Sell 0.25 underlying (as delta)
- To replicate the put…
- Buy 1 * 25Δ call
- Sell 1 underlying
- Buy 0.25 underlying (as delta)
Activity:
67
Construct a payoff profile that mimics a long straddle, where
Δc = 0.25, without using puts
- For the call…
- Buy 1 * 25Δ call
- Sell 0.25 underlying (as delta)
- To replicate the put…
- Buy 1 * 25Δ call
- Sell 1 underlying
- Buy 0.25 underlying (as delta)
Activity:
68
Construct a payoff profile that approximates a short strangle,
where Δp and Δc = 0.25, without using calls
Activity:
69
Construct a payoff profile that approximates a short strangle,
where Δp and Δc = 0.25, without using calls
- For the call…
- Buy 1 * 25Δ call
- Sell 0.25 underlying (as delta)
- To replicate the put…
- Buy 1 * 75Δ call
- Sell 1 underlying
- Buy 0.75 underlying (as delta)
Activity:
70
Construct a payoff profile that approximates a short strangle,
where Δp and Δc = 0.25, without using calls
- For the call…
- Buy 1 * 25Δ call
- Sell 0.25 underlying (as delta)
- To replicate the put…
- Buy 1 * 75Δ call
- Sell 1 underlying
- Buy 0.75 underlying (as delta)
Final thought:
71
What is a covered call?
When is this used?
Differentiate between a covered call and its equivalent raw structure?
Why use THIS structure over the raw structure?