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Transcript of Liam Mescall Fin Engineering 2
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8/4/2019 Liam Mescall Fin Engineering 2
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Report on Option Trad-
ing Strategies and theirGreeks
FI6022
Financial Engineering
Dr. Mark Cummins
Liam Mescall (0144126)
4/15/2011
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Part A
Payoff Profile:
This position consists of a short share position and a short put position. Profits are made on
when the share price decreases but theseprofits are stopped once the strike price of the
put is reached as anything after that point must
be paid out to the holder of the put position.
The graph here shows the effect of an
increasing stock price where losses are
unlimited as share price rises. Losses are
slightly reduced in this case by the premium
earned for the sale of the put option. Profits
are limited with unlimited potential losses.
Rationale:
From the perspective of the investor this strategy is undertaken predicting a downward
movement in the underlying to the 45 mark or beyond and are happy to profit only to the
$45 mark and earn a premium from the sale of the put option. Earnings from the sale of the
premium will give profit if no movement noted, all things held equal, (share will have to be
bought back) or reduce losses if an increase in profit noted.
Type of Market:
The investor will be bearish on the market.
Income/Cost:
There will be a net income from the sale of the share and the sale of the premium on the
sale of the option. Revenues earned on the share will have to be used to buy back the share
in the future. If ITM and wish to close out option, revenues from sale will be used to
repurchase.
Risks:
Delta; at the 40 level in the below graph we see the short stock with a delta of -1 is much
greater than the positive delta of the short put position. Taking the 1m curve, the stockprice increase sees a net increase in the sensitivity of the delta as it moves from being ITM
40 42 44 46 48 50 52 54 56 58 60-10
-8
-6
-4
-2
0
2
4
6
8Strategy Payoff Profile at Put expiry
Stock Price at Put expiry
Payoff
6m
3m
1m
Expiry
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(position is short) to ATM at 45 arriving
at a delta of -.5. This tells us the delta
value of the share is still -1 and the put
has a positive delta value of +.5.
As the position moves further frombeing ITM to OTM (i.e. above 50) the
positive delta of the put has less impact
and the total delta value tends towards
-1 which is the delta value of the share
itself. All maturities will be subject to
conditions described for the 1m but to a
lesser extent as the length of time
grows. This effect causes different levels of Delta to be noted at different stock prices
causing peaks at three different times. When ATM the rate of change of the option value
steepens-as maturity approaches a minor decrease in share price will have a large decreasein option value affecting profitability.
Gamma; as the gamma of a stock is zero the position is influenced by the short put negative
gamma which begins negative for all maturities. Again, taking the most pronounced 1m
curve, as the put option moves from ITM towards being ATM the sensitivity of the gamma
increases as the rate of change of delta becomes more sensitive. Once OTM, the rate of
change is reduced and this trend continues as the option moves further and further OTM
until resting at -1 which means for
every change in the underlying there is
an opposite noted in the rate of change
of delta. All maturities will be subject to
conditions described for the 1m but to
a lesser extent as the length of time
grows as seen in pronouncement of
curves. This effect causes different
levels of Gamma to be noted at
different stock prices causing peaks at
three different times. The risk of a large
Gamma when ATM and approaching
maturity is losses as a result of a small
change in share price as noted above.
Vega; as a stock has a Vega of zero, the
position is again influenced by the short
put position which carries a negative
value. The impact of time is obvious
here with longer maturities more
sensitive to volatility than shorter dated
options.
40 42 44 46 48 50 52 54 56 58 60-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0Strategy Delta Profile at Initiation
Stock Price
Delta
6m
3m
1m
40 42 44 46 48 50 52 54 56 58 60-1.15
-1.1
-1.05
-1Strategy Gamma Profile at Initiation
Stock Price
Gamma
6m
3m
1m
40 42 44 46 48 50 52 54 56 58 60-14
-12
-10
-8
-6
-4
-2
0Strategy Vega Profile at Initiation
Stock Price
Vega
6m
3m
1m
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Clearly we can see the difference between the vega values which widen as the position
becomes more ITM telling us, the further the position is ITM then the greater the probability
of the option finishing ITM i.e. the longer there is the more scope there is for volatility to
bring the option back OTM which is reflected in the larger negative Vega value. From 40-60
we see that approaching the put strike the sensitivity increases drawing the Vega further
negative before tending back towards positive values as the option becomes further andfurther OTM.
Theta; again we see that the theta of a stock is zero leaving the curves at the mercy of the
put options theta value which is positive. We can
see that how positive that figure is becomes a
function of maturity with different curves for each.
Taking the 1m we can see that as the option
approaches being ATM, the sensitivity of the
positive theta increases until it peaks slightly
before the strike price. This positive theta adds
value to the option as we have sold it.
Once OTM the sensitivity rapidly approaches zero
theta value and continues this trend as it arrives
further and further away. All maturities will be
subject to conditions described for the 1m but to a lesser extent as the length of time grows.
This effect causes different levels of theta to be noted at different stock prices causing peaks
at three different times.
Time Horizon:
An appropriate time horizon for this strategy is the medium term. With relatively low
volatility of 25% it may take some time for the underlying to move. During this time, positive
theta will be earned as option was sold.
Name: The negative bear
40 42 44 46 48 50 52 54 56 58 600
1
2
3
4
5
6
7Strategy Theta Profile at Initiation
Stock Price
Theta
6m
3m
1m
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Part B:
Payoff Profile:
Observing the profile we see that the position is net long the underlying and makes a loss
when ATM (at 50). This is because of the cost of the three long positions and the fact thatyou are long two and short one i.e. exposed to
the down side unless a very large down
movement is noted in which case the put
option would be deeply ITM.
As the underlying increases we see the position
instantaneously move from loss making to
retracing losses through the upswing in the two
long positions. There are limited losses with
unlimited potential profits.
Rationale:
This is a volatility trade when the investor does not know where the market will go but has a
slight preference for the upside, hence the net long bias.
Type of Market:
The investor will want a highly volatile market for this trade.
Income/Cost:
There will be an initial cost for this position as it involves the purchase of three options.
Risks:
Delta; the position consists of two ATM
long calls (both positive delta) and one
long put (negative delta). As the call
options are far OTM at 40 they are greatly
reduced and the put delta approaches -1
(far ITM) leaving a negative total for the
position.
As the underlying increases, the -1 value
of the long put decreases with a
corresponding increase in the longpositions taking the net position to .5 at
40 42 44 46 48 50 52 54 56 58 60-1
-0.5
0
0.5
1
1.5
2Strategy Delta Profile at Initiation
Stock Price
Delta
6m
3m
1m
40 42 44 46 48 50 52 54 56 58 60
-15
-10
-5
0
5
10
15
20Strategy Payoff Profile
Stock Price
Payoff
6m
3m
1m
Expiry
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the 50 strike as you would expect for an ATM position with two calls and one put. All
maturities will be subject to conditions described for the 1m but to a lesser extent as the
length of time grows. This effect causes different levels of Delta to be noted at different
stock prices causing peaks at three different times. The main risk to this position is low
volatility. The high delta when ATM is beneficial to the position as long as movements in the
underlying are in one direction and to a point where cost of options are covered. Worst casescenario is where there is little movement in underlying and option cost not covered.
Gamma; both long put and long call positions both have positive gamma which is evident
from the positive values below. Positive gamma means the delta of long calls and long puts
will become more positive and move toward +1.00 when the stock prices rises, and less
positive and move toward 0.00 when the
stock price falls.
In the graph we see this clearly as there is aconstant growth in the positions gamma
consistent across all maturities. The shorter
maturities note steepness in the rate of
gamma increase as the options become
ATM. Shorter maturities bring with it a
greater sensitivity to delta movements
which is evident in the rate of change of
gamma. Positive Gamma positions carry
little risk.
Vega; similar to gamma, long put and long call positions both have positive Vega. This is
clear from the below graph where at all points, no negative Vega value is noted. Taking the
1m value we see an increase in the rate of change of the option for a 1% change in volatility.
This occurs as the options approach being ATM,
when the sensitivity of the Vega is at its
greatest.
Passing the strike and entering ITM we see thissensitivity reduced again as the rate of change
slows. All maturities will be subject to
conditions described for the 1m but to a lesser
extent as the length of time grows. This effect
causes different levels of Vega to be noted at
different stock prices causing peaks at three
different times.
40 42 44 46 48 50 52 54 56 58 600
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Strategy Gamma Profile at Initiation
Stock Price
Gamma
6m
3m
1m
40 42 44 46 48 50 52 54 56 58 600
5
10
15Strategy Vega Profile at Initiation
Stock Price
Vega
6m
3m
1m
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Theta;theta is highest for ATM options, and is progressively lower as options are ITM and
OTM. This makes sense because ATM options have the highest extrinsic value, so they have
more extrinsic value to lose over time than an
ITM or OTM option. The theta of options is
higher when either volatility is lower or there are
fewer days to expiration as illustrated per graph.
The 1m here moves steeply positive as the 50
strike comes closer but the sensitivity then
reduces again as position moves ITM. All
maturities will be subject to conditions described
for the 1m but to a lesser extent as the length of
time grows. This effect causes different levels of
theta to be noted at different stock prices
causing peaks at three different times.
Time Horizon:
I would take a medium term horizon as ATM options in the short term can be expensive.
The cheaper options will reduces costs but allow for a similar exposure to movement from
the expected volatility. That is my preference but more money could be made from a
shorter horizon as options would become further valuable with shorter maturity.
Name: The long V
40 42 44 46 48 50 52 54 56 58 60-7
-6
-5
-4
-3
-2
-1
0
1
2
Strategy Theta Profile at Initiation
Stock Price
Theta
6m
3m
1m
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Part C
Payoff Profile:
This diagram describes a position where an OTM put is bought along with a stock and an
OTM call is sold. This makes profits range bound and reduces potential losses from a suddendrop in price of the underlying. The position
starts as negative with the cost of the put
and the loss on the share held. Losses on the
put position are confined to losses to the
level noted per graph.
At the 45 mark the put is no longer ITM.
Steepness of the slope shows the losses that
would be made without the presence of the
put. The increasing value of the share brings
the slope steeply to the 55 mark after whichpoint the call becomes ITM and we must pay
out any increases we benefit from on the
further rise of the share price to the option holder. Profits and losses are limited.
Rationale:
In this strategy the shareholder wishes to earn a premium from the sale of a call option,growth in the underlying and protect himself from a sudden decline in the market. Upside
growth is expected.
Type of Market:
The investor in this strategy is bullish and will maximize profits at the 55 and above as he
will profit from the rise in value of his share from 50 to 55.
Income/Cost:
There will be a cost to this transaction when taking the price of the share into account
assuming it is around the $50 mark. The price of the OTM options will be a fraction of this
and will largely offset each other.
Risk:
Delta; the position is long a put (negative delta),
short a call (negative delta) and long a stock
(positive delta of +1). The sum of these positions
differs depending on each maturity as illustrated
below. Taking the most pronounced i.e. the 1m, we
see the delta starts increasing as the 45 markapproaches and the put position is ATM. Following
35 40 45 50 55 60 65-6
-4
-2
0
2
4
6Strategy Payoff Profile
Stock Price
Payoff
6m
3m
1m
Expiry
35 40 45 50 55 60 650
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Strategy Delta Profile at Initiation
Stock Price
Delta
6m
3m
1m
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on from this the share held approaches 1 (as it will have a delta of 1 with itself) but does not
reach one as it is combined with the put option delta value.
As the price continues to rise, the call option at strike of 55 brings further negative delta to
the position which continues at a slower pace until zero is reached. All maturities will be
subject to conditions described for the 1m but to a lesser extent as the length of time grows.This effect causes different levels of delta to be noted at different stock prices causing peaks
at three different times.
Gamma; considering the initial position is long a
put with a positive gamma, short a call with a
negative gamma and long a stock with a zero
gamma we can see at 35 that the positive gamma
on the put is larger than the negative gamma of
the call as the stock price is so low. As the stockprice increases the gamma becomes more
sensitive approaching the 45 strike.
Following this point, as the put becomes more and
more OTM, the influence of the negative gamma
in the call becomes more evident as it approaches being ATM. Once ITM, the sensitivity
decreases and gamma approaches +1 levels again. All maturities will be subject to
conditions described for the 1m but to a lesser extent as the length of time grows. This
effect causes different levels of Gamma to be noted at different stock prices causing peaks
at three different times.
Vega; the position is long a put with positive
Vega and short a call with negative vega. The
stock has zero Vega. Taking the 1m, at 35 we
see the positive Vega equals the negative and
position starts to grow as the put strike of 45
is approached I.E. as stock price increases, so
does Vega. Following this the negative Vega of
the short call position becomes larger with theOTM put Vega becoming smaller which is
clearly seen in the declining slope.
This peaks at the 55 strike when it becomes ITM and sensitivity reduces again towards zero
when the put is deeply OTM and call is deeply ITM (from investors perspective). All
maturities will be subject to conditions described for the 1m but to a lesser extent as the
length of time grows. This effect causes different levels of Vega to be noted at different
stock prices causing peaks at three different times.
35 40 45 50 55 60 650.9
0.95
1
1.05
1.1
1.15Strategy Gamma P rofile at Initiation
Stock Price
Gamma
6m
3m
1m
35 40 45 50 55 60 65-12
-10
-8
-6
-4
-2
0
2
4
6
8Strategy Vega Profile at Initiation
Stock Price
Vega
6m
3m
1m
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Theta; the long put position has a negative theta while the short call has a positive theta.
Positive theta/time decay works in our favour. The stock position has zero theta. At the 35
mark we can see that the positive theta is
greater than the negative leaving all three
maturities positive.
Taking the 1m maturity we see that the
increase of the underlying towards the strike
of 45 makes the negative put more sensitive
and accordingly notes a rise in negative
theta. Once the position becomes ITM the
sensitivity reduces and continues to do so.
With the strike of the positive short call
position approaching it becomes larger still
until peaking ATM and decreasing once ITM
towards the initial levels noted. All maturities will be subject to conditions described for the1m but to a lesser extent as the length of time grows. This effect causes different levels of
theta to be noted at different stock prices causing peaks at three different times.
Time Horizon:
As a positive theta has been established, I would hold this position into the medium term
hoping for gradual growth in the underlying towards the 55 level.
Name: The snake
35 40 45 50 55 60 65-8
-6
-4
-2
0
2
4
6
8
10
12Strategy Theta Profile at Initiation
Stock Price
Theta
6m
3m
1m
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Part D
Price Profile:
Initial cost of the ATM position is more than revenues earned from the sale of the two OTM
short positions as ATM options tend tobe expensive. As the price of the
underlying increases as the long position
becomes more and more in the money.
Upon reaching the 55 level, the first of
the two sold call options becomes ITM
generating expenses (from being liable to
pay out when exercised) that equal
revenues, straightening the line per
graph.
As the underlying price continues toincrease, the larger position sold short
compared to long (i.e. 2:1 ratio, short:
long) cause a profit neutral position to change to a loss making position the further the price
increases. The initial cost changes with time to maturity as the proximity affects the option
price as seen in graph. Profits are limited with unlimited potential losses.
Rationale:
From an investors perspective this transaction would be undertaken with the viewpoint that
the price of the underlying will increase past 50 but not past 60. In this instance the investor
will have bought a long position and offset much of the cost of it through the sale of call
options. Should the price not breach 50 then none of the sold options will be exercised and
a profit made by extent long position ITM minus opening cost of position. Profits are
maximised between 55 and 60 at which point they become neutral before decreased
profitability at any point past 60.
Type of Market:
The market sought by the investor is moderately bullish i.e. a 10% increase in the value of
the underlying or to anywhere between 55 and 60. At this level profits will be maximised.
Income/Cost:
There will be a net cost to the transaction as ATM options are far more expensive than OTM
options. Revenues from the sale of OTM options will offset some of the cost.
45 50 55 60 65-2
-1
0
1
2
3
4
5
Strategy Payoff Profile
Stock Price
Payoff
6m
3m
1m
Expiry
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Risk:
Delta; with the underlying price rising, deltas react differently for each maturity. The delta
has an initial positive position as we are long an ATM call (positive delta) which will have a
higher delta value than the sum of two
OTM call deltas which I am short (negativedelta). As the share price increases the
delta peaks between 50 and 55 reflecting
the sensitivity of ATM long call.
As the underlying approaches the 55 mark
the first of the short positions delta begins
to increase as it becomes ATM reducing
overall position net delta. This continues to
increase to the second short position and
as the first and second become further
ITM, the larger their deltas become,
making the overall position increasingly negative. All maturities will be subject to conditions
described for the 1m but to a lesser extent as the length of time grows. This effect causes
different levels of Delta to be noted at different stock prices causing peaks at three different
times.
Gamma; similarly, we see a corresponding level of pronouncement differences in the
gamma greek. Taking the 1m mark we see to the 50 level, gamma is rising as delta
sensitivity increases as the long position becomes ATM. The points of most sensitivity are
when the underlying approaches the
strike price. This is when the delta is
most sensitive i.e. ATM. Between 50 and
55 the position takes on negative gamma
as the long position moves away from
ATM becoming less sensitive to delta. As
the 55 mark approaches, the Gamma for
the short positions (negative) increase
continuously until the 60 level is
approached. After this point the position
will remain gamma negative but at a
lower level which is seen as the curve
retraces towards zero.
The shorter the maturity the greater the sensitivity of gamma to changes in the underlying.
All maturities will be subject to conditions described for the 1m but to a lesser extent as the
length of time grows. This effect causes different levels of Gamma to be noted at different
stock prices causing peaks at three different times. The risk of a large, negative gamma
means it will generate deltas that are unfavourable for up/down movements in the stock.
45 50 55 60 65-1
-0.5
0
0.5Strategy Delta Profile at Initiation
Stock Price
Delta
6m
3m
1m
45 50 55 60 65-0.15
-0.1
-0.05
0
0.05
0.1Strategy Gamma Profile at Initiation
Stock Price
Gamma
6m
3m
1m
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Vega; taking the 1m maturity, we see the Vega is initially positive Vega as the long ATM
position Vega is greater than the sum of the two short positions Vegas. As the long position
moves from being ATM to ITM the Vega
becomes less sensitive to change, with the
increasing closeness of the negative Vega short
call at 55 the overall negative position continuesto increase.
This pattern repeats itself getting closer to 60
before all positions become ITM and the
sensitivity to change reduces. Again the effect of
a shorter maturity on this position is to
pronounce the shape of the curve as it becomes
more sensitive to changes in the underlying at
maturity. As time to maturity increases, there is a
reduction in these effects noted for the 1m.
Theta; at 45 there is a variety of starting points for theta depending on the maturity horizon
of the position. Long positions have a negative theta while short are positive theta. We can
see that the 1m starting point has net negative
theta as the ATM long negative theta position is
greater than the sum of the OTM short positive
theta positions. This negative sensitivity
increases as the long position approaches the
strike before fading away when it becomes ITM.
As the OTM short positions with positive theta
approach there is a sharp movement towards
positive theta which reaches its peak before the
60 strike and falls away then as all become ITM
as the rate of change of all the positions reduces.
All maturities will be subject to conditions
described for the 1m but to a lesser extent as the length of time grows. This effect causes
different levels of theta to be noted at different stock prices causing peaks at three different
times.
Time Horizon:
I would choose a medium term horizon to give the position time to grow to the 55-60 range
described given the modest volatility of 25%. There would be less volatile theta in the
interim for this time horizon.
Name: The Table
45 50 55 60 65-25
-20
-15
-10
-5
0
5Strategy Vega Profile at Initiation
Stock Price
Vega
6m
3m
1m
45 50 55 60 65-10
-5
0
5
10
15
20Strategy Theta Profile at Initiation
Stock Price
Theta
6m
3m
1m
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Part E
Price Profile: The initial cost of the low-strike is seen in the dip in payoff as the option sold
continues to cost the seller more as price increases. After the 55 mark the two long
positions become ITM and generate
revenues greater than those to be paid onthe short position, described by the
continuous increasing payoff as the stock
price increases.
This strategy will profit in times of large
volatility in either direction but will suffer
losses should the underlying stay within a
tight range i.e. between 50 and 55 per
graph. There are limited losses for this
position and unlimited potential profits.
Rationale:
This option strategy is utilized when you believe there will be a lot of volatility in the stock
but are not 100% sure whether it will move up or down. If the stock spikes up, as shown in
graph, you will earn a profit. If the stock moves a lot, but in the opposite direction, you will
earn a small profit. However, if the stock doesn't move much and is stuck in a trading range,
you will make a loss.
Type of Market:
The market sought by the investor is volatile in either direction but preferable upwards
stock growth.
Income/Cost:
As you are selling a call option that is ATM and buying 2 call options that are OTM, this posi-
tion should be a credit position i.e. earns a premium from opening position. However, be-cause you are selling an option, you are not able to allow this position to expire. You will
need to buy back the option before expiration date, which is one of the risks of the position.
Risks:
If the stock price stays below the strike price of the sold call option (the ITM price), you can
allow the position to expire since none will be exercised. Profit in this case is the initial pre-
mium made when position was opened. If the stock moves above that ATM strike price but
is still below the strike of the 2 calls you are facing losses. The 2 calls with the OTM strike
price would still be worthless, but the call you sold at the ATM strike price would be worthsomething and will need to be bought back before expiration. This will maximise losses.
45 50 55 60 65 70-6
-4
-2
0
2
4
6
8
10
12Strategy Payoff Profile
Stock Price
Payoff
6m
3m
1m
Expiry
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Delta; at 45 as the position is net negative delta i.e. long positions have a positive delta but
the sum of their two deltas are less than the ATM call being sold which is negative. As the
negative delta position hits the approaches 50
it becomes more sensitive as ATM, after 50 areduction in delta is noted as the pace of
change when ATM is far greater than ITM. As
55 approaches, the two long positions with
see their positive delta values increase making
the whole position delta positive. This increas-
es at a decreasing rate past the 60 mark as all
positions become ITM and tend towards one.
All maturities will be subject to conditions de-
scribed for the 1m but to a lesser extent as the
length of time grows. This effect causes different levels of delta to be noted at different
stock prices causing peaks at three different times.
Gamma; the Gamma position at 45 is negative meaning the Gamma values are smaller for
the two long OTM calls (positive) than the one ATM short call (negative) for the 1m maturi-
ty. This is not the case as maturity lengthens,
as we can see the larger Gamma in the OTM
options give the initial Gamma position a net
positive value on the 6m maturity. Taking the
1m, the position becomes further sensitive to
change as the short position approaches its
strike. This then retreats towards zero before
the strike at 55 approaches.
The two long positions have larger positive
Gamma at this point giving a steep inclination
to the peak at 55. When all positions are ITM
the Gamma retreats again towards zero re-
maining marginally positive as a reflection of the extent the long positions have greater
gamma than the short. All maturities will be subject to conditions described for the 1m but
to a lesser extent as the length of time grows. This effect causes different levels of gamma
to be noted at different stock prices causing peaks at three different times.
Vega; as with the Gamma position, the starting points for maturities vary i.e. 6m maturity
gives the initial Vega a positive position as the long positions with positive Vega have larger
Vega than the negative Vega in the short position. The 1m position starts with net negativeVega i.e. the sum of the two long positions Vega is smaller than the ATM short position. We
45 50 55 60 65 70-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25Strategy Gamma Profile at Initiation
Stock Price
Gamma
6m
3m
1m
45 50 55 60 65 70-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Strategy Delta Profile at Initiation
Stock Price
Delta
6m
3m
1m
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see an increase in negative Vega as the 50 strike
approaches. This negative Vega means the value of
an option decreases when volatility increases and
increases when volatility decreases. These options
are most sensitive when ATM, and accordingly
when entering ITM, the levels of Vega reduces. Asthe two positive Vega long positions at 55 become
closer there is a sharp increase in the positive Vega.
This is briefly constant at 55 until all positions move
ITM and the sensitivity reduces leaving Vega mod-
erately above zero reflecting the marginally positive net value. All maturities will be subject
to conditions described for the 1m but to a lesser extent as the length of time grows. This
effect causes different levels of Vega noted at different stock prices causing peaks at three
different times.
Theta; at 45 there is a variety of starting points for theta depending on the maturity horizon
of the position. The 1m position is positive as the short ATM call option (positive theta) is
greater than the sum of the two long
positions. This is not the case for the 6m
where the opposite is true. Taking the 1m
which is the most pronounced, there is an
increase in sensitivity as the short position
becomes more sensitive to the loomingstrike.
Once it becomes ITM, the sensitivity
declines and continues to decline as the
negative theta long call positions approach.
Once the 55 mark is hit and all positions
are ITM, the theta values decline and approach zero. Again the level of pronouncement
depends on the time to maturity. All maturities will be subject to conditions described for
the 1m but to a lesser extent as the length of time grows. This effect causes different levels
of theta noted at different stock prices causing peaks at three different times.
Time Horizon:
A short term horizon will ensure you are not losing money as time passes by as you will
generate positive theta. The strategy is also depending on large volatility or event driven
occurrences in the marketplace. As such a short investment horizon is best.
Name: The tick
45 50 55 60 65 70-5
0
5
10
15
20Strategy Vega Profile at Initiation
Stock Price
Vega
6m
3m
1m
45 50 55 60 65 70-20
-15
-10
-5
0
5Strategy Theta Profile at Initiation
Stock Price
The
ta
6m
3m
1m