When it makes sense to Early-Exercise a position

Quanto · Jan 29, 2024

taowave said:
I dont think,I know

You are just sure that you know it, definetely, but you can't explain it, right?

Do you understand synthetics.i.e put and call???

You resort to talking unrelated/off-topic/distracting BS, as is usual with your ilk here when asked something concrete.

If you want to participate in my discussion topics then you have to answer the question you get asked first before continuing with your own questions. And you have to be on-topic.
Otherwise it's an attempt to disturb a fruitful discussion.

El OchoCinco · Jan 29, 2024

Quanto said:
I just made-up the following example for demonstrating an Early Exercise of a LongCall position.
Let me know if you spot an error in the calcs.

I spotted your error: "I just made-up the following example..."

Quanto · Jan 29, 2024

El OchoCinco said:
I spotted your error: "I just made-up the following example..."

Yeah, true, very normal when modelling a situation.
FYI: the error has been fixed in later postings.

Quanto · Jan 29, 2024

Quanto said:
Sometime later I'll do also a brute-force search to find the optimum as I suspect there must be an optimum point in time.

Early-Close always gives the highest profit, but it's not always possible to apply it in practice (due to wide Bid/Ask spreads, no liquidity (ie. no volume) etc.
Early-Exercise is the next best and does not have any of the above listed problems of Early-Close.
The least favorable is waiting till expiry and let it Auto-Exercise.
Here are daily results of simulation runs: ie. "what-if scenarios" if Premium on day x is $1.10, ie. in this case the Bid.

Code:

PgmArgs(6): ./yfapi.exe compare_early_exercise 1 5 S0=5,DTE=60,Pr=0.50 Sx=6,DTE=50,Pr=1.10

CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=50  Pr=1.1000  (IV=52.64   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 10 days --> 1000.36% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 10 days --> 723.44% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)



---------- simulation: --------------


------------------- DTE=59 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=59  Pr=1.1000  (IV=48.45   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 1 days --> 2602295086161.03% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 1 days --> 143327337876.44% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=58 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=58  Pr=1.1000  (IV=48.87   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 2 days --> 16131530.69% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 2 days --> 3785759.72% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=57 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=57  Pr=1.1000  (IV=49.30   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 3 days --> 296236.75% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 3 days --> 112648.22% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=56 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=56  Pr=1.1000  (IV=49.74   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 4 days --> 40064.20% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 4 days --> 19357.29% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=55 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=55  Pr=1.1000  (IV=50.19   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 5 days --> 12007.97% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 5 days --> 6680.56% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=54 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=54  Pr=1.1000  (IV=50.65   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 6 days --> 5343.68% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 6 days --> 3257.80% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=53 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=53  Pr=1.1000  (IV=51.12   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 7 days --> 2975.45% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 7 days --> 1932.58% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=52 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=52  Pr=1.1000  (IV=51.61   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 8 days --> 1904.10% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 8 days --> 1294.89% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=51 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=51  Pr=1.1000  (IV=52.12   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 9 days --> 1336.36% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 9 days --> 940.81% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=50 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=50  Pr=1.1000  (IV=52.64   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 10 days --> 1000.36% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 10 days --> 723.44% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=49 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=49  Pr=1.1000  (IV=53.17   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 11 days --> 784.81% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 11 days --> 579.82% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=48 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=48  Pr=1.1000  (IV=53.72   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 12 days --> 637.81% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 12 days --> 479.47% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=47 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=47  Pr=1.1000  (IV=54.29   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 13 days --> 532.68% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 13 days --> 406.21% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=46 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=46  Pr=1.1000  (IV=54.88   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 14 days --> 454.57% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 14 days --> 350.84% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=45 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=45  Pr=1.1000  (IV=55.48   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 15 days --> 394.72% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 15 days --> 307.78% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=44 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=44  Pr=1.1000  (IV=56.11   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 16 days --> 347.67% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 16 days --> 273.48% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=43 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=43  Pr=1.1000  (IV=56.76   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 17 days --> 309.89% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 17 days --> 245.63% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=42 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=42  Pr=1.1000  (IV=57.43   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 18 days --> 278.99% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 18 days --> 222.62% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=41 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=41  Pr=1.1000  (IV=58.13   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 19 days --> 253.33% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 19 days --> 203.33% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=40 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=40  Pr=1.1000  (IV=58.85   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 20 days --> 231.72% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 20 days --> 186.96% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=39 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=39  Pr=1.1000  (IV=59.60   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 21 days --> 213.31% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 21 days --> 172.91% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=38 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=38  Pr=1.1000  (IV=60.38   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 22 days --> 197.46% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 22 days --> 160.73% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=37 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=37  Pr=1.1000  (IV=61.19   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 23 days --> 183.69% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 23 days --> 150.09% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=36 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=36  Pr=1.1000  (IV=62.03   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 24 days --> 171.63% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 24 days --> 140.72% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=35 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=35  Pr=1.1000  (IV=62.91   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 25 days --> 160.98% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 25 days --> 132.41% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=34 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=34  Pr=1.1000  (IV=63.83   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 26 days --> 151.53% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 26 days --> 124.99% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=33 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=33  Pr=1.1000  (IV=64.79   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 27 days --> 143.08% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 27 days --> 118.33% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=32 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=32  Pr=1.1000  (IV=65.79   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 28 days --> 135.49% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 28 days --> 112.33% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=31 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=31  Pr=1.1000  (IV=66.85   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 29 days --> 128.64% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 29 days --> 106.89% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=30 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=30  Pr=1.1000  (IV=67.95   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 30 days --> 122.42% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 30 days --> 101.93% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=29 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=29  Pr=1.1000  (IV=69.11   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 31 days --> 116.76% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 31 days --> 97.41% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=28 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=28  Pr=1.1000  (IV=70.34   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 32 days --> 111.58% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 32 days --> 93.26% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=27 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=27  Pr=1.1000  (IV=71.63   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 33 days --> 106.83% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 33 days --> 89.44% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=26 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=26  Pr=1.1000  (IV=72.99   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 34 days --> 102.46% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 34 days --> 85.91% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=25 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=25  Pr=1.1000  (IV=74.44   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 35 days --> 98.42% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 35 days --> 82.65% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=24 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=24  Pr=1.1000  (IV=75.97   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 36 days --> 94.68% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 36 days --> 79.61% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=23 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=23  Pr=1.1000  (IV=77.61   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 37 days --> 91.20% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 37 days --> 76.79% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=22 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=22  Pr=1.1000  (IV=79.35   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 38 days --> 87.97% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 38 days --> 74.16% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=21 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=21  Pr=1.1000  (IV=81.22   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 39 days --> 84.95% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 39 days --> 71.70% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=20 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=20  Pr=1.1000  (IV=83.22   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 40 days --> 82.13% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 40 days --> 69.40% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=19 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=19  Pr=1.1000  (IV=85.39   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 41 days --> 79.49% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 41 days --> 67.23% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=18 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=18  Pr=1.1000  (IV=87.72   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 42 days --> 77.00% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 42 days --> 65.20% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=17 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=17  Pr=1.1000  (IV=90.27   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 43 days --> 74.67% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 43 days --> 63.28% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=16 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=16  Pr=1.1000  (IV=93.05   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 44 days --> 72.47% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 44 days --> 61.47% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=15 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=15  Pr=1.1000  (IV=96.10   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 45 days --> 70.39% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 45 days --> 59.76% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=14 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=14  Pr=1.1000  (IV=99.47   ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 46 days --> 68.43% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 46 days --> 58.14% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=13 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=13  Pr=1.1000  (IV=103.23  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 47 days --> 66.57% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 47 days --> 56.61% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=12 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=12  Pr=1.1000  (IV=107.44  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 48 days --> 64.81% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 48 days --> 55.15% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=11 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=11  Pr=1.1000  (IV=112.22  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 49 days --> 63.14% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 49 days --> 53.77% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=10 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=10  Pr=1.1000  (IV=117.70  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 50 days --> 61.55% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 50 days --> 52.45% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=9 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=9   Pr=1.1000  (IV=124.06  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 51 days --> 60.04% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 51 days --> 51.19% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=8 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=8   Pr=1.1000  (IV=131.59  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 52 days --> 58.60% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 52 days --> 50.00% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=7 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=7   Pr=1.1000  (IV=140.67  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 53 days --> 57.22% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 53 days --> 48.85% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=6 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=6   Pr=1.1000  (IV=151.94  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 54 days --> 55.91% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 54 days --> 47.76% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=5 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=5   Pr=1.1000  (IV=166.45  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 55 days --> 54.66% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 55 days --> 46.72% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=4 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=4   Pr=1.1000  (IV=186.09  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 56 days --> 53.46% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 56 days --> 45.72% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=3 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=3   Pr=1.1000  (IV=214.88  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 57 days --> 52.31% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 57 days --> 44.76% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=2 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=2   Pr=1.1000  (IV=263.18  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 58 days --> 51.21% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 58 days --> 43.84% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=1 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=1   Pr=1.1000  (IV=372.19  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 59 days --> 50.15% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 59 days --> 42.95% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

------------------- DTE=0 ----------------------
CALL K=5.00
S0=5.0000   DTE=60  Pr=0.5000  (IV=61.99   ) rPct=0.00  qPct=0.00 
Sx=6.0000   DTE=0   Pr=1.1000  (IV=526.35  ) rPct=0.00  qPct=0.00 
Se=6.0000   DTE=0   Pr=1.0000  (IV=78.12   ) rPct=0.00  qPct=0.00 

Calculations (w/o commissions):
Early-Close:                 Pr=1.1000   PL=0.6000  (120.00% in 60 days --> 49.14% p.m.)
Early-Exercise:              Pr=1.1000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)
Auto-Exercise-at-Expiration: Pr=1.0000   PL=0.5000  (100.00% in 60 days --> 42.10% p.m.)

p.m. : per month (30.416667 days)

El OchoCinco · Jan 29, 2024

Quanto said:
Yeah, true, very normal when modelling a situation.
FYI: the error has been fixed in later postings.

You cannot model real time pricing.... your model is making the erroneouos assumption that the option will be extremely mispriced, that the B/A spread will allow you to make the trade at the price you want, and that no one else has systems monitoring to ensure no arbitrage...

Quanto · Jan 29, 2024

El OchoCinco said:
You cannot model real time pricing.... your model is making the erroneouos assumption that the option will be extremely mispriced, that the B/A spread will allow you to make the trade at the price you want, and that no one else has systems monitoring to ensure no arbitrage...

We are playing just a possible scenario. Here the fixed wording:
"
Bought 1 Call DTE=60 Strike=5 when underlying stock S=5.00 (ie. ATM) and Call Bid=0.40 Ask=0.50
(ie. PremiumPaid=0.50 plus Commission=0.65)
After 10 days the underlying stock has risen to S=6.00, and Call ~~Bid=0.30 Ask=0.40~~ Bid=1.10 Ask=1.20.
You think the stock won't rise any more.
Should you do an Early-Exercise or just let it Auto-Exercise at expiration?
"
Just let us know how you would model it.

El OchoCinco · Jan 29, 2024

Quanto said:
We are playing just a possible scenario. Here the fixed wording:
"
Bought 1 Call DTE=60 Strike=5 when underlying stock S=5.00 (ie. ATM) and Call Bid=0.40 Ask=0.50
(ie. PremiumPaid=0.50 plus Commission=0.65)
After 10 days the underlying stock has risen to S=6.00, and Call ~~Bid=0.30 Ask=0.40~~ Bid=1.10 Ask=1.20.
You think the stock won't rise any more.
Should you do an Early-Exercise or just let it Auto-Exercise at expiration?
"
Just let us know how you would model it.

I dont model...I use real prices and real bid ask spreads. Models are for college professors wokring in theory, not making real money..

Quanto · Jan 29, 2024

El OchoCinco said:
I dont model...I use real prices and real bid ask spreads. Models are for college professors wokring in theory, not making real money..

Then what are you doing in this discussion? Just disturbing it.
I hate such off-topic hollow-talkers! Bye bye!