# Derivatives

Interactive derivatives widgets for options strategies, synthetic positions, put-call parity, collars, risk reversals, delta equivalence, and FX option identities.

Canonical URL: https://exclam.ai/derivatives/

Options strategies visualized

Interactive payoff widgets for synthetic forwards, put-call parity, covered calls, collars, risk reversals, delta equivalence, and FX option identities.

12 widgets

Options Strategies, Vol IV LM1

Synthetic and equivalent payoffs side by side

Code-authored curriculum examples

## Widget Browser

Curated interactive visuals for this subject — new widgets ship with the app.

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arbitragecollarcovered callcurrencydeltaforwardsgreekshedgingoptionsparityposition equivalenciesprotective putput writingrisk reductionshort sellingshort stockskewvolatility

### Synthetic Long Forward

Vol IV · LM1

Long call + short put, same strike and expiry, behaves exactly like a long forward.

optionsforwardsposition equivalencies

### Synthetic Short Forward

Vol IV · LM1

Short call + long put, same strike and expiry, behaves exactly like a short forward — or a short stock with no borrow.

optionsforwardsposition equivalenciesshort selling

### Synthetic Long Put

Vol IV · LM1

Short the stock, buy a call at the short-sale price — the payoff is exactly a long put.

optionsposition equivalencieshedging

### Synthetic Long Call

Vol IV · LM1

Long stock + long put — the protective put — behaves exactly like a long call.

optionsprotective putposition equivalencies

### Put–Call Parity

Vol IV · LM1

Stock + put and call + bond both pay Max(S\_T, X) — the identity behind every synthetic in LM1.

optionsparityposition equivalenciesarbitrage

### Put–Call–Forward Parity

Vol IV · LM1

A fiduciary call and a synthetic protective put both pay Max(S\_T, X) — so parity prices them identically.

optionsforwardsparityposition equivalencies

### Covered Call = Writing a Put

Vol IV · LM1

The most popular retail options trade and the least popular one are the same risk profile.

optionscovered callput writingposition equivalencies

### Options on a Short Position

Vol IV · LM1

Short the stock, then buy a call (loss capped at 1.13) or write a put (income, cushion of only 0.65).

optionsshort stockrisk reduction

### Delta Equivalence

Vol IV · LM1

ATM covered call, ATM protective put, and long stock + short half-forward: all delta +50 per 100 shares.

optionsdeltagreeksposition equivalencies

### The Collar

Vol IV · LM1

Stock + put below + short call above — slide the strikes together and equity turns into fixed income.

optionscollarrisk reductionposition equivalencies

### Long Risk Reversal

Vol IV · LM1

Long OTM call + short OTM put: a split-strike synthetic forward with a premium shelf in the middle.

optionsvolatilityskewposition equivalencies

### FX Option Identity

Vol IV · LM1

A call on one currency IS a put on the other — the same contract quoted from the other side.

optionscurrencyrisk reduction