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Core Options · OPT-03a · Core

Long put

How does long put express a bearish view?

One concept per page · original written lesson · 566 prose words · authored, not installed or production-approved

What you will learn and prerequisites

Read first: Read a contract and its premium, Rights, obligations and expiration, Defined payoff risk is not margin, Read the whole multi-leg ticket

A purchased put buys downside participation or protection. It can express a bearish view without initially shorting shares, but the premium can still be lost in full. The purpose differs when the put is held alone versus alongside a stock portfolio.

Construction: read every leg

The 100 put costs 420. Its expiry intrinsic is max(100−S,0) per unit; breakeven is 95.80. Maximum gain is finite because an equity price cannot fall below zero. At zero, intrinsic is 10,000 and net profit is 9,580 before costs.

Read the ticket before the graph

BUY means you own an option right; SELL means you accept a short-option obligation. Positive quantities are long and negative quantities are short in the calculation. Check quantity, call/put, strike, multiplier and expiry before netting premium.

All legs in this example share November 20, 2026 expiration. The entry observation is October 6, 2026, with fictional QLT at 100. These are independent illustrative premiums, not a current option chain or executable quotes. The terminal diagram assumes every leg and any shares are resolved at one common settlement price.

Before expiry: time and volatility

A long put has negative Delta and positive Gamma and Vega in standard BSM. Downside volatility may already be expensive. A modest decline combined with IV contraction can still produce a loss. Theta is often negative, with state-dependent exceptions for some European inputs.

Manage the position deliberately

Match the expiry to the thesis and compare an outright put with a bear-put spread. For protection, evaluate the combined shares and put instead of celebrating the hedge's gain while ignoring the larger portfolio loss.

Fictional teaching ticket · no order submission

Long put

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
BUY1Put1002026-11-204.2100
Opening option cash (+received / −paid)-420 USD
Entry option fees in cost variant0.65 USD
Shares included0
Joint-terminal results—not a guarantee of interim cash requirements
MeasureBefore costsAfter stated entry fees
Maximum terminal profit9,5809,579.35
Maximum terminal loss magnitude420420.65
Breakeven settlement price(s)95.895.7935

This is a mathematical expiry experiment using the displayed legs, not an executable quote. The slider range is not a risk limit.

$0.65 per option contract on entry only. No exit, assignment, financing or tax costs modeled.

Independent fictional premiums, not one simultaneous arbitrage-consistent chain. All legs realized simultaneously at intrinsic at the same expiry; terminal calculations do not model American early exercise, temporary unhedged positions, forced liquidation or live liquidity. Displayed chart domain is not a tail-risk cap.

From opening cash to a settlement result

Read the opening instructions: buy 1 100 put at 4.20. Option opening cash is $420.00 paid as a debit. A received credit is not earned profit while the obligation remains open.

Set the common settlement price to 90.00. Calls have intrinsic value max(S−K,0); puts have max(K−S,0). Subtract the opening premium from each intrinsic value, then multiply by signed quantity and the 100-unit multiplier. Shares contribute their price change from their own cost. The calculation popup shows every leg.

The combined result is $580.00 before costs and $579.35 after illustrative opening fees of $0.65. Exit fees, slippage, funding, dividends and taxes are not included. Opening fees are 0.65 per option contract, not a statement of any broker's pricing.

Maximum terminal profit is $9,580.00; maximum terminal loss magnitude is $420.00, before costs. Isolated zero-P/L settlement points in the model: 95.8. Move the scenario slider across each strike and explain why the slope changes there. A strike is a contract threshold, not a prediction.

This terminal model is useful for comparing risk shapes, but actual American-style assignment, share delivery, forced liquidation or a failed multi-leg exit can produce a different path. A long protective leg is not an automatic instruction that a broker must exercise it when another leg is assigned.

Open the calculation without leaving this lesson

Calculate this exact ticket

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

P/L = Σ[q × multiplier × (intrinsic − opening premium)] + shares × (S−share entry) − costs

Intrinsic is nonnegative before the signed quantity is applied. This is a fictional terminal calculation.

  1. +1 × 100 × (10.00 − 4.20) = $580.00: 100 put.
  2. Opening fees: 0.65.
Before costs $580.00; after entry fees only $579.35.

Maximum risk and breakevens

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

Evaluate S=0, all strikes and the final tail slope; solve P/L=0 on each linear segment.

Same-expiry payoffs are piecewise linear. A finite chart range cannot prove a tail is bounded.

  1. Maximum terminal profit is $9,580.00; maximum terminal loss magnitude is $420.00, before costs.
  2. Breakeven points: 95.8.
  3. Costs shift net P/L downward without moving the strikes.
Maximum terminal profit is $9,580.00; maximum terminal loss magnitude is $420.00, before costs.

The whole ticket at common expiry

Vertical: P/L per complete ticket (USD)
Horizontal: Underlying settlement price (USD)

The whole ticket at common expirySolid combined curve is before fees; the second includes only the stated entry fees. Individual-leg lines explain construction. This is terminal intrinsic P/L, not current option value. Price can move outside the displayed range. The complete numerical data are available below.-555.708-201.555152.598506.752860.9051,215.06859197103109115
1. Combined terminal P/L before fees2. Combined terminal P/L after entry fees
Solid combined curve is before fees; the second includes only the stated entry fees. Individual-leg lines explain construction. This is terminal intrinsic P/L, not current option value. Price can move outside the displayed range.
See the individual legs behind the combined curveThe whole ticket at common expirySolid combined curve is before fees; the second includes only the stated entry fees. Individual-leg lines explain construction. This is terminal intrinsic P/L, not current option value. Price can move outside the displayed range. The complete numerical data are available below.-555.708-201.555152.598506.752860.9051,215.06859197103109115
1. Combined terminal P/L before fees2. Combined terminal P/L after entry fees3. Leg 1: BUY 1 100 put
Read the graph as a data table
Complete graph data; original fictional observations or model calculations
Underlying settlement price (USD)Combined terminal P/L before feesCombined terminal P/L after entry feesLeg 1: BUY 1 100 put
851,0801,079.351,080
85.3751,042.51,041.851,042.5
85.751,0051,004.351,005
86.125967.5966.85967.5
86.5930929.35930
86.875892.5891.85892.5
87.25855854.35855
87.625817.5816.85817.5
88780779.35780
88.375742.5741.85742.5
88.75705704.35705
89.125667.5666.85667.5
89.5630629.35630
89.875592.5591.85592.5
90.25555554.35555
90.625517.5516.85517.5
91480479.35480
91.375442.5441.85442.5
91.75405404.35405
92.125367.5366.85367.5
92.5330329.35330
92.875292.5291.85292.5
93.25255254.35255
93.625217.5216.85217.5
94180179.35180
94.375142.5141.85142.5
94.75105104.35105
95.12567.566.8567.5
95.53029.3530
95.82.66454e-13-0.652.66454e-13
95.875-7.5-8.15-7.5
96.25-45-45.65-45
96.625-82.5-83.15-82.5
97-120-120.65-120
97.375-157.5-158.15-157.5
97.75-195-195.65-195
98.125-232.5-233.15-232.5
98.5-270-270.65-270
98.875-307.5-308.15-307.5
99.25-345-345.65-345
99.625-382.5-383.15-382.5
100-420-420.65-420
100.375-420-420.65-420
100.75-420-420.65-420
101.125-420-420.65-420
101.5-420-420.65-420
101.875-420-420.65-420
102.25-420-420.65-420
102.625-420-420.65-420
103-420-420.65-420
103.375-420-420.65-420
103.75-420-420.65-420
104.125-420-420.65-420
104.5-420-420.65-420
104.875-420-420.65-420
105.25-420-420.65-420
105.625-420-420.65-420
106-420-420.65-420
106.375-420-420.65-420
106.75-420-420.65-420
107.125-420-420.65-420
107.5-420-420.65-420
107.875-420-420.65-420
108.25-420-420.65-420
108.625-420-420.65-420
109-420-420.65-420
109.375-420-420.65-420
109.75-420-420.65-420
110.125-420-420.65-420
110.5-420-420.65-420
110.875-420-420.65-420
111.25-420-420.65-420
111.625-420-420.65-420
112-420-420.65-420
112.375-420-420.65-420
112.75-420-420.65-420
113.125-420-420.65-420
113.5-420-420.65-420
113.875-420-420.65-420
114.25-420-420.65-420
114.625-420-420.65-420
115-420-420.65-420

The failure case

At settlement 98, intrinsic is only 200 against 420 paid. Correct bearish direction did not satisfy the premium hurdle. An oversized hedge can also make the entire book net bearish.

Check your understanding

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

What is whole-position terminal P/L at QLT 90.00, before costs?

Reveal the worked answer

$580.00

Use all signed legs, not just the winning leg. The popup and graph use the same ticket.

Critical risk question

Does a terminal loss bound guarantee every early-assignment or liquidation outcome?

Reveal the worked answer

No.

It describes the specified common-settlement payoff. Product rules, stock delivery, capital and execution still matter.

Takeaway

Explain the intended bearish exposure, each leg's obligation and the adverse price region before using the strategy name.

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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