Synthetic Forward Strategy
Replicate a long or short stock/futures position using options. Buy an ATM call and sell an ATM put for bullish exposure, or reverse for bearish exposure. Capital-efficient way to gain directional exposure.
Overview
The synthetic forward strategy replicates the payoff of owning (or shorting) stock using options. A long synthetic combines a long ATM call with a short ATM put at the same strike and expiration.
By put-call parity, this combination produces a payoff identical to a forward contract: f_T = S_T - K - H, where H is the net debit/credit. When options are fairly priced, H is typically very small.
Traders use synthetic forwards for capital efficiency (lower margin than stock), to avoid borrowing costs on short positions, or when the underlying is hard to borrow. The strategy provides full directional exposure with defined risk.
Key Insight
Research
Research on options replication, put-call parity, and synthetic positions in derivatives markets.
The Mathematics
In Plain English
The math behind this strategy is straightforward. Here's what you're actually doing:
- 1Long synthetic forward: Buy an ATM call and sell an ATM put at strike K = S₀. You profit dollar-for-dollar as the stock rises, lose as it falls.
- 2Short synthetic forward: Buy an ATM put and sell an ATM call at strike K = S₀. You profit as the stock falls, lose as it rises.
- 3Net cost H: The premium paid (debit) or received (credit). By put-call parity, H is typically near zero for ATM options.
- 4Breakeven: For long synthetic, breakeven is K + H. For short synthetic, breakeven is K - H.
That's it. The formulas below just express this process precisely.
1Long Synthetic Payoff
Long call payoff minus short put payoff minus net debit. Simplifies to stock return minus strike minus cost.
2Long Synthetic Breakeven
Stock price where long synthetic breaks even at expiration.
3Long Synthetic Max Profit
No cap on upside—profit increases dollar-for-dollar with stock price.
4Long Synthetic Max Loss
Maximum loss if stock goes to zero. Equals strike plus net debit.
5Short Synthetic Payoff
Long put payoff minus short call payoff minus net debit. Profits as stock declines.
6Short Synthetic Breakeven
Stock price where short synthetic breaks even at expiration.
7Short Synthetic Max Profit
Maximum profit if stock goes to zero. Equals strike minus net debit.
8Short Synthetic Max Loss
No cap on downside—loss increases dollar-for-dollar as stock rises.
Put-Call ParityNote
By put-call parity: C - P = S - Ke^(-rT). When K = S₀ and options are fairly priced, the net cost H of a synthetic forward is approximately the cost of carry (interest minus dividends). This makes synthetics nearly equivalent to owning stock.
Strategy Rules
Long Synthetic Setup
- 1Select ATM strike K ≈ current stock price S₀
- 2Buy 1 ATM call option at strike K
- 3Sell 1 ATM put option at strike K (same expiration)
- 4Net debit H = call premium - put premium
- 5Typically H ≈ 0 for ATM options (small debit or credit)
Short Synthetic Setup
- 1Select ATM strike K ≈ current stock price S₀
- 2Buy 1 ATM put option at strike K
- 3Sell 1 ATM call option at strike K (same expiration)
- 4Net debit H = put premium - call premium
- 5Provides short exposure without borrowing shares
Position Management
- Monitor delta—should be approximately ±100 (like stock)
- Roll position before expiration if maintaining exposure
- Be aware of early assignment risk on short option
- Consider dividend dates—short calls may be assigned early
- Adjust strike if stock moves significantly from K
Exit Strategies
- Close both legs simultaneously to exit
- Let expire ITM for automatic stock delivery/assignment
- Roll to new expiration to extend exposure
- Set profit target: close when stock reaches target price
- Stop-loss: close if stock moves X% against position
Implementation Guide
Implementing a synthetic forward involves buying one ATM option and selling the other at the same strike and expiration. The position replicates stock ownership with different margin requirements.
Determine Direction
Decide if you want long exposure (bullish) or short exposure (bearish). Long synthetic = buy call + sell put. Short synthetic = buy put + sell call. Both use the same ATM strike.
- Long synthetic for bullish view without owning stock
- Short synthetic to avoid hard-to-borrow fees
- Consider synthetic when stock margin is unfavorable
Select Strike and Expiration
Choose an ATM strike (K ≈ S₀) for the purest synthetic. Select expiration based on your time horizon. Longer expirations have higher premiums but less frequent rolling.
- ATM strike gives delta ≈ ±100 (stock-equivalent)
- Monthly or quarterly expirations are most liquid
- Avoid expiration around dividend dates for short calls
ITM or OTM strikes will have different deltas and may not perfectly replicate stock exposure.
Execute Both Legs
Enter both options simultaneously as a combo order if your broker supports it. This ensures you get filled on both legs at the expected net debit/credit. Legging in separately adds execution risk.
- Use "combo" or "spread" order type for simultaneous execution
- Check bid-ask spreads on both legs
- Execute during high liquidity periods (market open, not lunch)
Monitor and Manage
Track your position delta and P&L. The synthetic should move approximately dollar-for-dollar with the stock. Watch for early assignment risk on the short option, especially around dividends.
- Delta should stay near ±100 throughout the trade
- Be prepared for assignment on short put (long synthetic)
- Roll before expiration if maintaining the position
Margin Requirements
Synthetic positions typically require less margin than buying stock outright since the short option is covered by the long option. However, margin requirements vary by broker. Some brokers recognize the synthetic and margin it like a forward; others margin each leg separately.
Helpful Tools & Resources
Strategy Variations
Explore different ways to implement this strategy, each with its own trade-offs and benefits.
Collar
Own stock + long OTM put + short OTM call. Similar structure but with existing stock position.
Risk Reversal
OTM call vs OTM put. Similar to synthetic but with different strikes, leaving a gap around current price.
Conversion/Reversal
Arbitrage strategy combining synthetic with actual stock to lock in mispricing.
Jelly Roll
Calendar synthetic—different expirations on call and put legs. Trades the term structure.
Risks & Limitations
Short synthetic has unlimited loss potential if stock rises. Same risk as short stock.
Short option may be assigned early, especially around dividends. Be prepared to manage stock position.
Near expiration, if stock is near strike, unclear which option will be exercised/assigned.
Wide bid-ask spreads on options can make entry/exit costly. Stick to liquid underlyings.
Short calls on dividend-paying stocks may be assigned early to capture the dividend.
References
- Stoll, H. R. (1969). The Relationship Between Put and Call Option Prices. Journal of Finance, 24(5), 801-824 [Link]
- Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654 [Link]
- Ofek, E., Richardson, M., & Whitelaw, R. F. (2004). Limited Arbitrage and Short Sales Restrictions. Journal of Financial Economics, 74(2), 253-284 [Link]
- Cremers, M., & Weinbaum, D. (2010). Deviations from Put-Call Parity and Stock Return Predictability. Journal of Financial and Quantitative Analysis, 45(2), 335-367 [Link]
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