Strategy #0000000004 · Options and payoff structures
Synthetic forward
Pair a call and a put to recreate a forward-like position.
Buy a call and sell a put at the same strike and expiry. Their combined payoff is forward-like, while rates and option premiums determine the fair forward level.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Jack and Rose recreate a forward contract with two tickets and a calculator.
Rose wants exposure to EUR/USD at a future date. Jack shows her a call and a put with the same strike and expiry. “Two tickets for one journey?” she asks. At expiry, the long call gains above the strike and the short put loses below it; together, the payoff moves linearly like a long forward.
The option premium is not automatically zero. Put–call parity links the call, put, spot, interest rates and time to expiry. In FX, both domestic and foreign rates matter. Jack writes the carry terms on a napkin; Rose asks whether the napkin is regulated. It is not, so the inputs need a proper source.
A synthetic forward is a payoff relationship, not a free arbitrage. Funding, collateral, early exercise, settlement conventions, spreads and counterparty terms can all change the real trade.
| Underlying at expiry | Underlying P/L | Options P/L | Total | What happens |
|---|---|---|---|---|
| 0.9800 | −$46.10 | −$1.33 | −$47.43 | The combined payoff falls linearly below the strike. |
| 1.0274 | +$1.33 | −$1.33 | −$0.00 | At the strike, carry and option premium still matter. |
| 1.1200 | +$93.90 | −$1.33 | +$92.57 | Above the strike, the combined payoff rises linearly. |
Illustrative figures only. They exclude fees, tax, financing and other costs unless stated. They are not live prices or a recommendation.
The mechanics · payoff and exposure
Put–call parity gives C − P = S₀e⁻ʳᶠᵀ − Ke⁻ʳᵈᵀ for FX options. Funding the net premium produces the theoretical forward; market conventions and costs create deviations.
C and P are call and put values; S₀ is spot, K the shared strike, rᵈ the domestic rate, rᶠ the foreign rate and T the time to expiry.
Greeks: the directional intuition
- Delta
- Measures first-order sensitivity to the underlying price.
- Gamma
- Measures how quickly delta changes as the underlying moves.
- Vega
- Measures sensitivity to implied volatility.
- Theta / Rho
- Measures sensitivity to implied volatility.
Put–call parity gives C − P = S₀e⁻ʳᶠᵀ − Ke⁻ʳᵈᵀ for FX options. Funding the net premium produces the theoretical forward; market conventions and costs create deviations.
Practical context · published observations
Synthetic forward · parity-based model: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
This is a modelled replay using stated assumptions, not observed option fills. Source ↗ · Methodology ↗
What if the underlying expires here?
Adjust the inputs to see a theoretical expiry payoff. The starting values are teaching assumptions, not live quotes.
Calculation model: This simplified expiry model excludes early close-out value, assignment timing, funding, tax, dividends and transaction costs.
Variants · same family, different risk levers
Three related angles reverse exposure or examine parity and funding.
A shared strike and expiry are the synthetic forward’s backbone. Reverse a leg and the exposure flips; test prices and the question becomes one of market frictions.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Short synthetic forward | Opposite direction · same structure | Buy a put and sell a call at the same strike; expiry payoff is K − Sₜ, like a short forward. | It gains on a fall and loses as the underlying rises; collateral, borrow and upside risk still need managing. |
| Implied funding from synthetic forwards | Pricing signal · across strikes | Infer a discount curve or market funding cost from forward prices implied by several call–put pairs. | It needs clean, synchronised quotes and suitable discount and dividend assumptions; liquidity and credit frictions can distort the estimate. |
| Put–call parity with short-sale constraints | Market-friction research | Compare synthetic short exposure with actual shorting in hard-to-borrow shares to study parity gaps. | Reliable borrow fees and executable quotes are essential; a measured gap may not be arbitrageable by a typical investor. |
The source groups long and short synthetic forwards in one family. Implied funding and short-sale constraints are adjacent pricing research, not one fixed trading rule.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01Options Industry Council, Put/Call Parity — source and methodologyofficial
- 02Options Industry Council, Synthetic Long Stock — source and methodologyofficial
- 03Federal Reserve Board via FRED, U.S. Dollars to Euro Spot Exchange Rate [DEXUSEU].data
- 04Federal Reserve Bank of New York via FRED, Secured Overnight Financing Rate [SOFR].data
- 05European Central Bank, Euro short-term rate (€STR) series metadata and downloads.data
- 06Azzone & Baviera (2021), “Synthetic forwards and cost of funding in the equity derivative market,” Finance Research Letters.research
- 07Ofek, Richardson & Whitelaw (2004), “Limited arbitrage and short sales restrictions: Evidence from the options markets.”research
- 08Kakushadze & Serur (2018), 151 Trading Strategies, §§2.10–2.11. Author version.source