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Advanced Options · ADV-09a · Advanced

Call diagonal

Why do different expirations require a different valuation question?

One concept per page · original written lesson · 463 prose words · authored, not installed or production-approved

What you will learn and prerequisites

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

A call diagonal changes strike and expiry together. The longer lower-strike call supplies bullish exposure; the nearer higher-strike short finances part of it while limiting a fast near-term advance.

The construction

Buy a longer 95 call and sell a nearer 105 call. A ten-point strike gap does not establish a fixed ten-point maximum payoff because the two contracts do not expire together.

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

If spot rallies beyond the short strike, compare closing values before exercising. Exercising a still-live long can sacrifice extrinsic value. Each new short-call sale needs a fresh risk and thesis check.

Fictional teaching ticket · no order submission

Call diagonal

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
BUY1Call952027-02-199.16100
SELL1Call1052026-11-202.34100
Opening option cash (+received / −paid)-682 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 95 call at 9.16; sell one 2026-11-20 105 call at 2.34. Both represent 100 units. Opening debit is $682.00 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 $121.97 before costs or $120.67 after entry fees only.

With stock unchanged but remaining IV at 18%, the result is $4.67. At 35% it is $301.14. 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=(9.16−2.34)×100=682.00.
  2. Remaining long time=(136−45)/365=0.249315068 years.
  3. At S=100 and back IV=25%, P/L before costs=121.973983622.
  4. Opening fees only=1.30.
Modeled P/L $121.97, 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.-800.972-485.864-170.755144.353459.461774.57758595105115125
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)
75-680.803-668.962-618.696
75.5-680.487-667.026-613.126
76-680.098-664.856-607.188
76.5-679.624-662.433-600.868
77-679.049-659.735-594.153
77.5-678.357-656.74-587.028
78-677.527-653.426-579.479
78.5-676.538-649.768-571.492
79-675.366-645.743-563.056
79.5-673.986-641.326-554.155
80-672.368-636.491-544.779
80.5-670.482-631.215-534.914
81-668.294-625.471-524.549
81.5-665.769-619.233-513.672
82-662.869-612.476-502.272
82.5-659.555-605.175-490.339
83-655.785-597.304-477.863
83.5-651.516-588.839-464.834
84-646.702-579.755-451.243
84.5-641.3-570.029-437.082
85-635.262-559.638-422.344
85.5-628.542-548.56-407.021
86-621.093-536.774-391.106
86.5-612.868-524.26-374.594
87-603.823-511-357.48
87.5-593.914-496.976-339.759
88-583.096-482.172-321.427
88.5-571.33-466.573-302.481
89-558.577-450.166-282.918
89.5-544.802-432.939-262.736
90-529.971-414.883-241.934
90.5-514.056-395.988-220.512
91-497.031-376.248-198.468
91.5-478.873-355.658-175.805
92-459.566-334.214-152.522
92.5-439.095-311.914-128.622
93-417.45-288.758-104.107
93.5-394.626-264.747-78.9798
94-370.623-239.884-53.2441
94.5-345.442-214.173-26.9038
95-319.091-187.6210.0367163
95.5-291.581-160.23427.5724
96-262.927-132.02155.6978
96.5-233.147-102.99384.4071
97-202.263-73.1599113.694
97.5-170.299-42.5346143.552
98-137.282-11.1304173.973
98.5-103.24421.0383204.951
99-68.215453.9561236.477
99.5-32.230787.607268.544
1004.67451121.974301.143
100.542.4633157.04334.266
10181.098192.786367.903
101.5120.54229.193402.045
102160.75266.244436.684
102.5201.69303.918471.81
103243.32342.196507.413
103.5285.603381.058543.483
104328.498420.484580.012
104.5371.971460.455616.988
105415.983500.949654.401
105.5410.501491.948642.243
106405.488483.432630.502
106.5400.913475.381619.168
107396.744467.775608.232
107.5392.95460.597597.684
108389.503453.827587.513
108.5386.375447.446577.709
109383.541441.437568.263
109.5380.976435.783559.164
110378.657430.466550.403
110.5376.563425.47541.97
111374.673420.779533.856
111.5372.97416.376526.05
112371.436412.247518.544
112.5370.055408.378511.329
113368.813404.754504.395
113.5367.694401.361497.734
114366.688398.187491.336
114.5365.783395.219485.194
115364.968392.446479.298
115.5364.234389.855473.64
116363.572387.436468.212
116.5362.975385.178463.007
117362.435383.072458.017
117.5361.946381.108453.233
118361.501379.276448.648
118.5361.097377.57444.256
119360.729375.979440.049
119.5360.391374.498436.021
120360.081373.118432.164
120.5359.795371.833428.473
121359.53370.636424.94
121.5359.284369.521421.56
122359.054368.483418.326
122.5358.838367.516415.234
123358.635366.615412.277
123.5358.442365.775409.45
124358.259364.992406.748
124.5358.084364.262404.165
125357.916363.58401.697

The failure case

Early assignment can leave short stock alongside a long call. The long right is not the same as already-owned delivery shares; funding, borrow and dividends can matter.

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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