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Advanced Options · ADV-15a · Advanced

Synthetic long stock

How does synthetic long stock express a linear bullish exposure view?

One concept per page · original written lesson · 554 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 long call plus a short put at the same strike and expiry produces a linear terminal exposure. The identity behind it is max(S−K,0)−max(K−S,0)=S−K. The two option names reduce to one directional slope at settlement.

Construction: read every leg

At equal illustrative premiums, entry cash is zero and terminal P/L is 100×(S−100). Same strike and expiry are essential. Real premium differences reflect financing, dividends and implementation, so zero premium is an example rather than a universal quote.

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

Matching European call and put Gamma/Vega cancel in BSM. Delta is e^(−qT) per unit, not always exactly one with continuous yield. Exercise, funding, dividends and borrowing can make the practical position differ from shares.

Manage the position deliberately

Treat it as leveraged ownership with a put obligation. Compare financing and costs with stock or futures. Expiry and any rollover require a plan; they are not automatic continuation of the exposure.

Fictional teaching ticket · no order submission

Synthetic long stock

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
BUY1Call1002026-11-204.2100
SELL1Put1002026-11-204.2100
Opening option cash (+received / −paid)0 USD
Entry option fees in cost variant1.3 USD
Shares included0
Joint-terminal results—not a guarantee of interim cash requirements
MeasureBefore costsAfter stated entry fees
Maximum terminal profitUnbounded in this terminal modelUnbounded in this terminal model
Maximum terminal loss magnitude10,00010,001.3
Breakeven settlement price(s)100100.013

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 call at 4.20; sell 1 100 put at 4.20. Option opening cash is $0.00 received as a credit. 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 $-1,000.00 before costs and $-1,001.30 after illustrative opening fees of $1.30. 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 unbounded in this model; maximum terminal loss magnitude is $10,000.00, before costs. Isolated zero-P/L settlement points in the model: 100. 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 × (0.00 − 4.20) = $-420.00: 100 call.
  2. -1 × 100 × (10.00 − 4.20) = $-580.00: 100 put.
  3. Opening fees: 1.30.
Before costs $-1,000.00; after entry fees only $-1,001.30.

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 unbounded in this model; maximum terminal loss magnitude is $10,000.00, before costs.
  2. Breakeven points: 100.
  3. Costs shift net P/L downward without moving the strikes.
Maximum terminal profit is unbounded in this model; maximum terminal loss magnitude is $10,000.00, 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.-1,771.42-1,063.11-354.803353.5031,061.811,770.12859197103109115
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.-1,771.42-1,063.11-354.803353.5031,061.811,770.12859197103109115
1. Combined terminal P/L before fees2. Combined terminal P/L after entry fees3. Leg 1: BUY 1 100 call4. Leg 2: SELL 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 callLeg 2: SELL 1 100 put
85-1,500-1,501.3-420-1,080
85.375-1,462.5-1,463.8-420-1,042.5
85.75-1,425-1,426.3-420-1,005
86.125-1,387.5-1,388.8-420-967.5
86.5-1,350-1,351.3-420-930
86.875-1,312.5-1,313.8-420-892.5
87.25-1,275-1,276.3-420-855
87.625-1,237.5-1,238.8-420-817.5
88-1,200-1,201.3-420-780
88.375-1,162.5-1,163.8-420-742.5
88.75-1,125-1,126.3-420-705
89.125-1,087.5-1,088.8-420-667.5
89.5-1,050-1,051.3-420-630
89.875-1,012.5-1,013.8-420-592.5
90.25-975-976.3-420-555
90.625-937.5-938.8-420-517.5
91-900-901.3-420-480
91.375-862.5-863.8-420-442.5
91.75-825-826.3-420-405
92.125-787.5-788.8-420-367.5
92.5-750-751.3-420-330
92.875-712.5-713.8-420-292.5
93.25-675-676.3-420-255
93.625-637.5-638.8-420-217.5
94-600-601.3-420-180
94.375-562.5-563.8-420-142.5
94.75-525-526.3-420-105
95.125-487.5-488.8-420-67.5
95.5-450-451.3-420-30
95.875-412.5-413.8-4207.5
96.25-375-376.3-42045
96.625-337.5-338.8-42082.5
97-300-301.3-420120
97.375-262.5-263.8-420157.5
97.75-225-226.3-420195
98.125-187.5-188.8-420232.5
98.5-150-151.3-420270
98.875-112.5-113.8-420307.5
99.25-75-76.3-420345
99.625-37.5-38.8-420382.5
1000-1.3-420420
100.37537.536.2-382.5420
100.757573.7-345420
101.125112.5111.2-307.5420
101.5150148.7-270420
101.875187.5186.2-232.5420
102.25225223.7-195420
102.625262.5261.2-157.5420
103300298.7-120420
103.375337.5336.2-82.5420
103.75375373.7-45420
104.125412.5411.2-7.5420
104.5450448.730420
104.875487.5486.267.5420
105.25525523.7105420
105.625562.5561.2142.5420
106600598.7180420
106.375637.5636.2217.5420
106.75675673.7255420
107.125712.5711.2292.5420
107.5750748.7330420
107.875787.5786.2367.5420
108.25825823.7405420
108.625862.5861.2442.5420
109900898.7480420
109.375937.5936.2517.5420
109.75975973.7555420
110.1251,012.51,011.2592.5420
110.51,0501,048.7630420
110.8751,087.51,086.2667.5420
111.251,1251,123.7705420
111.6251,162.51,161.2742.5420
1121,2001,198.7780420
112.3751,237.51,236.2817.5420
112.751,2751,273.7855420
113.1251,312.51,311.2892.5420
113.51,3501,348.7930420
113.8751,387.51,386.2967.5420
114.251,4251,423.71,005420
114.6251,462.51,461.21,042.5420
1151,5001,498.71,080420

The failure case

At stock zero, a no-debit entry loses 10,000. The short put removed the long call's limited-loss property.

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

$-1,000.00

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 linear bullish exposure 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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