# Bullish risk reversal

**ADV-13a · Advanced Options · Advanced**

**Lesson question:** How does bullish risk reversal express a upside financed by a downside obligation view?

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

## By the end

- Read and reconstruct the priced ticket.
- Reconcile leg P/L with the combined graph.
- Explain the time, volatility and operational failure cases.

**Prerequisites:** OPT-F01, OPT-F02, OPT-F03, OPT-F04

A bullish risk reversal buys a call and sells a put at a lower strike. Equal premiums can make the entry cash flow zero, but the sold put supplies the financing by accepting downside risk.

## Construction: read every leg

Sell 95 put and buy 105 call at 2.00 each. Between strikes terminal gross P/L is zero. Above 105 the call gains; below 95 the put liability grows. The far-downside loss is 9,500 before costs. Different strikes distinguish it from exact synthetic stock.

## 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

Both legs contribute bullish Delta. The structure also trades relative volatility across wings, so skew matters. An increase in downside IV can hurt the sold put even when the upside call is unchanged.

## Manage the position deliberately

Ask whether the put obligation is acceptable on its own. If not, do not justify it as payment for the call. Compare a purchased call or protected spread. Reassess both legs after a thesis change.

## Priced fictional ticket

Read every leg before interpreting the combined payoff.

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

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

| SELL | 1 | put | 95 | 2026-11-20 | 2 | 100 |

| BUY | 1 | call | 105 | 2026-11-20 | 2 | 100 |

Opening option cash: 0 USD (positive received, negative paid). Entry option fees: 1.3 USD.

$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.

**Before fees:** maximum terminal profit Unbounded in this terminal model; maximum terminal loss magnitude 9,500; breakeven price(s) 95, 105.

**After entry fees:** maximum terminal profit Unbounded in this terminal model; maximum terminal loss magnitude 9,501.3; breakeven price(s) 105.013.

Zero-P/L intervals before fees: [[95.0, 105.0]]

## From opening cash to a settlement result

Read the opening instructions: sell 1 95 put at 2.00; buy 1 105 call at 2.00. 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 85.00. 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 $9,500.00, before costs. Isolated zero-P/L settlement points in the model: 95, 105; zero-P/L intervals are shown in the ticket data, not single isolated breakevens. 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.

## Calculation popup: Calculate this exact ticket

```text
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 − 2.00) = $-800.00: 95 put.

2. +1 × 100 × (0.00 − 2.00) = $-200.00: 105 call.

3. Opening fees: 1.30.

**Result:** Before costs $-1,000.00; after entry fees only $-1,001.30.

## Calculation popup: Maximum risk and breakevens

```text
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 $9,500.00, before costs.

2. Breakeven points: 95, 105; zero-P/L intervals are shown in the ticket data, not single isolated breakevens.

3. Costs shift net P/L downward without moving the strikes.

**Result:** Maximum terminal profit is unbounded in this model; maximum terminal loss magnitude is $9,500.00, before costs.

## Graph: The whole ticket at common expiry

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

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.

Complete numerical data are embedded in `scripts/advanced-options/ADV-13a.js` and displayed as an accessible table in the HTML lesson.

## The failure case

A supposedly free upside position becomes a large loss after a downside gap. No entry debit does not mean no capital at risk.

## Check your understanding

### What is whole-position terminal P/L at QLT 85.00, before costs?

**Answer:** $-1,000.00

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

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

**Answer:** No.

**Why:** It describes the specified common-settlement payoff. Product rules, stock delivery, capital and execution still matter. **Critical risk check.**

## Takeaway

Explain the intended upside financed by a downside obligation exposure, each leg's obligation and the adverse price region before using the strategy name.

## 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.

- [OIC Strategy Reference](https://www.optionseducation.org/strategies/all-strategies-en)

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