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Advanced Options · ADV-08b · Advanced

Put calendar

Why do different expirations require a different valuation question?

One concept per page · original written lesson · 464 prose words · authored, not installed or production-approved

What you will learn and prerequisites

Read first: Read the whole multi-leg ticket, Vega

A put calendar owns longer-lived downside optionality and sells an earlier put at the same strike. A modest near-term range can fit it better than an immediate crash, despite the bearish sound of the word put.

The construction

Both are 100 puts. When the short reaches expiry, the long retains protection beyond that date. The price and volatility of this remaining protection are central to the result.

Two clocks and two volatility assumptions

The short expires 2026-11-20, 45 days after entry. The long expires 2027-02-19, 136 days after entry. Opening example prices use 30% front IV and 25% back IV, continuous rate 3% and yield 1%. Ticket premiums are rounded to cents and those rounded values define opening cash.

A front-event IV decline and a back-expiry IV decline affect different rights. A single aggregate Vega cannot describe every nonparallel term-structure change. The future long-option mark also depends on remaining time, spot and the assumed volatility surface.

Read the observation date before the curve

At the short expiry, the long option is still alive. Valuing both by intrinsic at that date deletes the very time value the calendar or diagonal purchased. The three curves therefore show alternative remaining-IV assumptions rather than one guaranteed payoff.

The demonstration uses European cash-settled valuation and assumes both legs are liquidated at the short-expiry observation. Real American equity options may be assigned earlier and create share obligations. A later option does not automatically settle an earlier assignment.

Management

Decide how short-put assignment would be funded or closed. Selling another short changes the future protection profile. Keeping the long alone requires its own current thesis.

Fictional teaching ticket · no order submission

Put calendar

QLT • reference spot $100 • independent illustrative prices • quote date 2026-10-06

Read action, quantity, type, strike, expiry, premium and multiplier before the payoff
ActionQtyTypeStrikeExpiryPremium/unitMultiplier
BUY1Put1002027-02-195.67100
SELL1Put1002026-11-204.07100
Opening option cash (+received / −paid)-160 USD
Entry option fees in cost variant1.3 USD
Shares included0
Different expiries: no single final-payoff claim.

The short leg reaches intrinsic at the first expiry; the long leg remains live and is revalued under each stated IV assumption. A plotted peak is not an unconditional maximum profit.

$0.65 per option contract on entry only; later liquidation/assignment/funding costs excluded.

Original rounded BSM teaching premiums, not quotes. Curves are conditional liquidation at the first expiry: short intrinsic plus the still-live long option valued with a stated remaining IV. They are not a same-expiry payoff, unconditional maximum profit or American-exercise simulation.

A priced two-expiry walkthrough

Buy one 2027-02-19 100 put at 5.67; sell one 2026-11-20 100 put at 4.07. Both represent 100 units. Opening debit is $160.00 before the illustrative 1.30 entry fees.

At the short-expiry observation, keep stock at 100 and assume 25% IV for the remaining long. Price the long with 91 days left and subtract the short's intrinsic liability. After subtracting the original debit, modeled liquidation P/L is $310.78 before costs or $309.48 after entry fees only.

With stock unchanged but remaining IV at 18%, the result is $172.39. At 35% it is $508.32. The comparison isolates uncertainty still owned after the nearer clock ends. It does not establish a unique maximum profit or an executable fill. Exit fees, bid–ask costs and assignment can change the outcome.

Open the calculation without leaving this lesson

Calculate the near-expiry liquidation

Same-page calculation. Closing restores the lesson position and originating control.

P/L = 100 × [BSM_long(S, remaining time, back IV) − short intrinsic(S)] − opening debit − costs

This is a chosen exit-horizon model, not both contracts' joint final payoff.

  1. Opening debit=(5.67−4.07)×100=160.00.
  2. Remaining long time=(136−45)/365=0.249315068 years.
  3. At S=100 and back IV=25%, P/L before costs=310.784281399.
  4. Opening fees only=1.30.
Modeled P/L $310.78, before costs.

Conditional value at the short expiry—not a final payoff

Vertical: Modeled liquidation P/L per ticket (USD)
Horizontal: Underlying at the first expiry (USD)

Conditional value at the short expiry—not a final payoffFront expiry 2026-11-20; far option still has 91 days. Each curve assumes a different surviving-leg IV. Entry fees of $1.30 are excluded from these curves; subtract them for that cost variant. No unconditional maximum is inferred from these plotted scenarios. The complete numerical data are available below.-280.823-109.96360.8967231.757402.617573.477758595105115125
1. Surviving-long IV 18% (before fees)2. Surviving-long IV 25% (before fees)3. Surviving-long IV 35% (before fees)
Front expiry 2026-11-20; far option still has 91 days. Each curve assumes a different surviving-leg IV. Entry fees of $1.30 are excluded from these curves; subtract them for that cost variant. No unconditional maximum is inferred from these plotted scenarios.
Read the graph as a data table
Complete graph data; original fictional observations or model calculations
Underlying at the first expiry (USD)Surviving-long IV 18% (before fees)Surviving-long IV 25% (before fees)Surviving-long IV 35% (before fees)
75-215.665-211.481-182.362
75.5-215.486-210.619-178.977
76-215.291-209.651-175.344
76.5-215.078-208.567-171.451
77-214.843-207.353-167.285
77.5-214.579-205.997-162.834
78-214.281-204.484-158.084
78.5-213.942-202.799-153.024
79-213.554-200.926-147.639
79.5-213.108-198.849-141.917
80-212.593-196.549-135.846
80.5-211.997-194.008-129.411
81-211.306-191.207-122.602
81.5-210.505-188.126-115.404
82-209.576-184.745-107.805
82.5-208.5-181.042-99.7943
83-207.257-176.996-91.3583
83.5-205.823-172.584-82.4857
84-204.173-167.785-73.1649
84.5-202.281-162.575-63.3847
85-200.116-156.932-53.1343
85.5-197.648-150.832-42.403
86-194.845-144.253-31.1807
86.5-191.67-137.17-19.4578
87-188.088-129.562-7.22478
87.5-184.06-121.4065.52711
88-179.548-112.67918.8063
88.5-174.511-103.3632.6207
89-168.907-93.427746.9777
89.5-162.695-82.861561.8843
90-155.833-71.641777.3468
90.5-148.279-59.749493.371
91-139.99-47.1666109.962
91.5-130.926-33.8762127.125
92-121.046-19.8626144.865
92.5-110.312-5.11072163.183
93-98.686110.3928182.085
93.5-86.133726.6603201.572
94-72.621443.7028221.646
94.5-58.118661.5299242.308
95-42.597880.15263.561
95.5-26.033999.5699285.403
96-8.40559119.795307.834
96.510.3056140.83330.855
9730.1144162.676354.463
97.551.0321185.336378.657
9873.0662208.809403.434
98.596.2209233.094428.792
99120.497258.188454.728
99.5145.89284.086481.238
100172.394310.784508.318
100.5150288.275485.964
101128.693266.55464.17
101.5108.458245.602442.931
10289.2758225.419422.242
102.571.1238205.992402.096
10353.9782187.308382.488
103.537.8125169.355363.41
10422.5984152.118344.856
104.58.30562135.584326.819
105-5.09726119.737309.291
105.5-17.643104.563292.264
106-29.365490.0446275.731
106.5-40.298876.1656259.683
107-50.478262.9091244.113
107.5-59.938650.2577229.011
108-68.715438.194214.369
108.5-76.843726.7002200.179
109-84.358115.7584186.432
109.5-91.2935.35068173.119
110-97.682-4.54106160.23
110.5-103.558-13.9348147.758
111-108.953-22.8484135.692
111.5-113.898-31.2997124.024
112-118.422-39.3063112.744
112.5-122.555-46.8857101.845
113-126.325-54.055291.3151
113.5-129.757-60.831581.147
114-132.877-67.231571.3312
114.5-135.708-73.271461.8587
115-138.274-78.967252.7205
115.5-140.594-84.334543.908
116-142.691-89.388535.4121
116.5-144.581-94.144127.2242
117-146.283-98.615519.3358
117.5-147.813-102.81711.7383
118-149.187-106.7614.42326
118.5-150.418-110.462-2.61756
119-151.52-113.932-9.39233
119.5-152.505-117.184-15.9091
120-153.384-120.228-22.1758
120.5-154.167-123.076-28.2001
121-154.864-125.739-33.9898
121.5-155.483-128.228-39.5523
122-156.032-130.551-44.895
122.5-156.519-132.72-50.025
123-156.95-134.742-54.9494
123.5-157.33-136.627-59.6751
124-157.666-138.383-64.2088
124.5-157.962-140.017-68.5572
125-158.223-141.537-72.7266

The failure case

A rapid decline can make both puts largely intrinsic and reduce the desired time-value difference. The short put can create shares before the later protection is deliberately used.

Check your understanding

Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.

Can the later option be valued only at intrinsic when the short expires?

Reveal the worked answer

No.

It still has time remaining; use an appropriate valuation or executable quote.

Critical risk question

May the highest plotted mark be called a guaranteed maximum profit?

Reveal the worked answer

No.

The curve depends on an assumed future IV and liquidation date.

Takeaway

Read every expiry, strike and volatility assumption. A calendar has matching strikes; a diagonal changes both strike and time.

Sources, assumptions and downloadable script

External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.

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