Separate a trade from a volatility quote
CME describes the 25-delta measure using two points on an implied-volatility curve. Under the call-minus-put convention, RR25 = IV(call, delta +0.25) - IV(put, delta -0.25), for one underlying and maturity. A negative value means the selected put has higher IV. It does not show that either option is mispriced or predict the next price move.
- Equal absolute deltas do not require equal distances from spot, equal premiums or identical strikes. The hypothetical 95/105 strikes below are not asserted to be 25-delta contracts.
- With ordinary share deltas of +0.25 for the call and -0.25 for the put, buying the call and selling the put gives +0.50 delta per share of exposure. The trade is not delta-neutral merely because the absolute deltas match.
- A same-strike long call and short put has expiry payoff ST - K before premiums, like a synthetic forward. Different strikes create the flat middle region shown below.
| Meaning | Inputs | Output |
|---|
| Directional strategy | Long/short legs, strikes, sizes, paid/received premiums | Cash P&L for a specified price and time |
| 25-delta skew quote | Matched-expiry call and put IV at equal absolute delta | Difference in volatility percentage points |
| Example quote | 22% call IV minus 27% put IV | -5 volatility points, or -0.05 in decimal volatility |
FX quotes require a currency and delta convention
Reiswich and Wystup document FX spot versus forward delta and premium-adjusted versus unadjusted delta. Record the currency pair direction, maturity, delta convention, premium currency and call-minus-put sign before comparing RR quotes. A call on EUR in EUR/USD is also a put on USD; changing the named currency changes what call and put mean.
- A 25-delta label identifies model sensitivity under a convention, not a fixed strike or a promised 25% real-world exercise probability. Recovering strikes requires the relevant spot/forward, rates, volatility and delta definition.
- When reversing a currency pair, rebuild the quote under the new conventions. Do not carry over the original sign, strikes and notional unchanged.
- An FX volatility quote alone does not specify a tradable two-leg premium. Confirm settlement currencies, notionals and actual bid/ask terms; the USD-per-share equity example below does not supply those FX terms.
Specify both legs in the same units
Assume a hypothetical stock at $100 and two unadjusted equity options expiring together in 30 days. Each contract represents 100 shares; prices are USD per share. Buy one 105 call for $2.40 and sell one 95 put for $2.00. The bullish trade pays a $40 net premium. Assume $4 total lifecycle fees, fixed across scenarios, with no financing, dividends, taxes or earlier assignment. These are invented calculation inputs, not quotes.
- The reverse example uses the same hypothetical premiums for comparison. Real purchases and sales face different bid/ask prices; reversing a trade does not guarantee the same credit.
- Match underlying, expiry, settlement reference, exercise style, deliverable and exposure. Verify actual multipliers for adjusted equity, index, futures and FX options instead of applying 100 universally.
- For q matched contracts with multiplier M, use N = q × M. A quantity mismatch leaves additional option exposure and requires a fresh leg-by-leg calculation.
| Position | Call at Kc = $105 | Put at Kp = $95 | Opening premium cash flow |
|---|
| Bullish | Buy 1 at $2.40: pay $240 | Sell 1 at $2.00: receive $200 | -$40 before fees |
| Bearish reverse | Sell 1 at $2.40: receive $240 | Buy 1 at $2.00: pay $200 | +$40 before fees |
Calculate expiry P&L and locate the breakeven
Let ST be the nonnegative stock price at expiration, c and p the entry call and put premiums per share, and F total fees in dollars. Define g(ST) = max(ST - Kc, 0) - max(Kp - ST, 0), with Kp < Kc. Bullish net P&L = N × [g(ST) - (c - p)] - F. Bearish net P&L = N × [-g(ST) - (p - c)] - F. Evaluate both intrinsic values, subtract the net debit and then subtract fees once.
- Bullish breakeven is $105.44: the call must recover the $0.40 net debit and $0.04 fees per share. Bearish breakeven is $105.36: the $0.36 credit remaining after fees absorbs that much call intrinsic loss.
- For a general bullish trade, set A = c - p + F / N. If A > 0, breakeven is Kc + A. If A < 0, it is Kp + A. If A = 0, every ST between Kp and Kc breaks even.
- For a bearish trade, set B = p - c + F / N. If B > 0, breakeven is Kp - B. If B < 0, it is Kc - B. If B = 0, the whole middle interval breaks even. Discard roots below zero for this equity model; there may be no feasible crossing.
- At ST = 0, the bullish example loses $9,544 and the bearish example gains $9,536. Bullish gains have no upper bound as ST rises; bearish losses have no upper bound. Those bounds assume the stated equity price domain and exclude added carrying costs.
| Price region | g(ST) | Bullish example | Bearish example |
|---|
| ST < $95 | ST - 95 | 100 × (ST - 95) - 44 | 100 × (95 - ST) + 36 |
| $95 ≤ ST ≤ $105 | 0 | -$44 | +$36 |
| ST > $105 | ST - 105 | 100 × (ST - 105) - 44 | 100 × (105 - ST) + 36 |
Reproduce the payoff at the strikes and in the tails
The call and put columns below are the bullish leg profits including their entry premiums. Deduct $4 once to get bullish net P&L. For the bearish version, reverse the two gross leg profits and deduct its own $4. Therefore the two net results add to -$8, not zero. Values represent expiration economics, not a promise of cash liquidation at that price.
- Zero premium check: change both premiums to $2.00, keeping the strikes and $4 fees. Bullish middle-region P&L is -$4, breakeven is $105.04 and the loss at zero is $9,504. Matching premiums leaves the short put obligation intact.
- Credit check: pay $1.50 for the call and receive $2.00 for the put. After $4 fees, the bullish middle region earns $46 and its lower-region breakeven is $94.54. A credit moves the crossing; it does not cap downside loss.
- Two matched pairs double the leg amounts. If total fees also double to $8, the original bullish net result at $120 becomes $2,912. Scaling only the premium but not the short obligation understates risk.
| ST | Long-call P&L | Short-put P&L | Bullish net | Bearish net |
|---|
| $0 | -$240 | -$9,300 | -$9,544 | +$9,536 |
| $80 | -$240 | -$1,300 | -$1,544 | +$1,536 |
| $95 | -$240 | +$200 | -$44 | +$36 |
| $100 | -$240 | +$200 | -$44 | +$36 |
| $105 | -$240 | +$200 | -$44 | +$36 |
| $105.36 | -$204 | +$200 | -$8 | $0 |
| $105.44 | -$196 | +$200 | $0 | -$8 |
| $120 | +$1,260 | +$200 | +$1,456 | -$1,464 |
| $200 | +$9,260 | +$200 | +$9,456 | -$9,464 |
The expiry line does not price an early exit
Before expiration, the bullish position is worth N × (Ct - Pt), where Ct and Pt are current values for these exact contracts. Its mark-to-market P&L is N × [(Ct - Pt) - (c - p)] minus accrued costs. Unlike the piecewise-linear expiry payoff, those option values generally change nonlinearly with spot, remaining time, each leg's IV and rates. Equal entry premiums do not cancel gamma, vega or theta.
- For a hypothetical closing sale of the call at $1.00 and purchase of the put at $3.00, the original bullish trade loses 100 × [(1 - 3) - (2.40 - 2.00)] - 4 = $244, assuming $4 covers all fees. The spot could still be inside the expiry plateau; these closing inputs are not inferred from spot alone.
- Use the long leg's available bid and the short leg's available ask as conservative closing inputs, then record actual fills. Midpoints and model values are not assured executions, and quotes must be contemporaneous.
- A European Black-Scholes estimate can illustrate sensitivity under its assumptions. It does not establish the fair American exercise value, predict assignment or guarantee fills. A skew quote change alone cannot determine this position's P&L.
Assignment changes the stock and cash position
OIC states that an open short American-style option can be assigned before expiration. In the bullish example, assignment of the 95 put requires buying 100 shares for $9,500; the long 105 call does not fund that payment. In the bearish version, assignment of the 105 call requires delivering 100 shares for $10,500; the long 95 put does not supply shares.
- If the bearish trader has no shares, call assignment can create a short-stock position subject to broker and borrow requirements. If shares already cover the call, include those shares in the whole-position P&L; long stock plus long put plus short call is a collar.
- Reserve the cash or broker-required margin separately from the opening premium. Requirements can change, and a broker liquidation before expiration can prevent the planned expiry result.
- Check exercise cutoffs, dividend dates and final assignment notices. Near-strike exercise decisions and after-hours moves can leave stock exposure after the option expires. A zero-intrinsic-value row does not certify an empty account.
- Once either leg is exercised, assigned or closed, record the new share and option balances. Physical settlement cash flows and intrinsic-value P&L are alternative accounting views; do not deduct the same economic loss twice.
Build the structure, then preserve the input evidence
In TradingView Options, create a custom strategy with one bought 105 call and one sold 95 put on the same available underlying and expiration. Set each size to one contract and enter the hypothetical $2.40 and $2.00 prices. Confirm the multiplier, use the expiration P&L view and compare $80, $100 and $120 with the pre-fee values -$1,540, -$40 and +$1,460. Account for the $4 fee separately if absent from the chart.
- TradingView supports changing leg direction, strike, expiry and price basis. Keep a separate copy for the bearish direction and distinguish bid, ask, midpoint and theoretical prices. If the exact contract is unavailable, retain this as a hypothetical worksheet.
- Pineify AI Stocks & Options Picker has an options-chain view grouped by expiry and strike, with call/put bid, ask, IV and delta where supplied. Inspect available inputs and verify their timestamp, contract terms and executable prices with the broker. The implementation can return a partial chain or missing fields; absence is not a zero premium.
- In Trading Journal plan notes, retain both identifiers, directions, quantity, multiplier, expiry, quote source/time, premium basis, fees, margin assumptions and intended assignment response. In review notes, add actual fills and final stock holdings.
- These steps support research and recordkeeping. A scenario curve is not a historical multi-leg backtest, and a displayed chain does not establish a fill, complete FX volatility surface or automatic assignment reconciliation.
