# Put diagonal

**ADV-09b · Advanced Options · Advanced**

**Lesson question:** Why do different expirations require a different valuation question?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Read a complete two-expiry ticket.
- Reconstruct a near-expiry model mark.
- Explain nonparallel-IV and assignment risks.

**Prerequisites:** OPT-F04, BSM-10

A put diagonal owns longer-term downside exposure and sells a nearer lower put. It combines a directional view with a time-spread view and can dislike a decline that arrives too quickly.

## The construction

Buy the longer 105 put and sell the nearer 95 put. Both strike and time change. The remaining long value at short expiry cannot be replaced with a simple same-expiry width calculation.

## 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

Plan the assigned-short-put case. A near-term selloff can create a stock purchase while the long put remains open. Compare liquidation, exercise and any stock management using current economics.

## Priced fictional ticket

Read every leg before interpreting the combined payoff.

| Action | Quantity | Type | Strike | Expiry | Premium per unit | Multiplier |

|---|---:|---|---:|---|---:|---:|

| BUY | 1 | put | 105 | 2027-02-19 | 8.51 | 100 |

| SELL | 1 | put | 95 | 2026-11-20 | 1.99 | 100 |

Opening option cash: -652 USD (positive received, negative paid). Entry option fees: 1.3 USD.

$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 2027-02-19 105 put at 8.51; sell one 2026-11-20 95 put at 1.99. Both represent 100 units. Opening debit is $652.00 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 $109.76 before costs or $108.46 after entry fees only.

With stock unchanged but remaining IV at 18%, the result is $-20.58. At 35% it is $303.58. 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.

## Calculation popup: Calculate the near-expiry liquidation

```text
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=(8.51−1.99)×100=652.00.

2. Remaining long time=(136−45)/365=0.249315068 years.

3. At S=100 and back IV=25%, P/L before costs=109.762303290.

4. Opening fees only=1.30.

**Result:** Modeled P/L $109.76, before costs.

## Graph: Conditional value at the short expiry—not a final payoff

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

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.

Complete numerical data are embedded in `scripts/advanced-options/ADV-09b.js` and displayed as an accessible table in the HTML lesson.

## The failure case

Assuming the legs automatically cash settle together ignores the earlier contract's obligation. A correct bearish idea can still fail through timing, volatility or operational mismatch.

## Check your understanding

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

**Answer:** No.

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

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

**Answer:** No.

**Why:** The curve depends on an assumed future IV and liquidation date. **Critical risk check.**

## Takeaway

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

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [CME Option Calendar Spreads](https://www.cmegroup.com/education/courses/option-strategies/option-calendar-spreads)

- [OCC Options Disclosure Document](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)