Put-Protected Stock Has the Payoff of a Long Call

Summary

The document examines whether buying an underlying asset while also buying a put creates an arbitrage opportunity. The response describes the expiration payoff: the protective put limits losses below the put strike, while gains accrue when the underlying finishes above the position’s breakeven level.

It uses put–call parity to explain that long stock plus a long put is synthetically equivalent to a long call with the same strike. Under the stated simplification of no carry cost or dividends, the described position has the same payoff as buying a call for the put-protected position’s net cost. The response concludes that this payoff structure is not an arbitrage. The explanation is limited to expiration outcomes and explicitly sets aside carry and dividends; it does not discuss transaction costs, financing, early exercise, or other real-world frictions.

Key ideas

• Long stock combined with a long put creates downside protection at the put strike.
• The response describes a locked-in loss below the put strike and gains above the position’s breakeven level.
• Long stock plus a long put is synthetically equivalent to a long call at the same strike.
• The no-arbitrage comparison assumes there are no carry costs or dividends.

Tags

# Option Arbitrage Opportunity


# Option Arbitrage Opportunity












Could you please explain me whether there is an arbitrage opportunity in this situation (added below)?

## Answer by Bob Baerker (score 1)

https://quant.stackexchange.com/a/60067

On an expiration basis, your put protected long underlying makes money above $80 and you have a locked in loss of \$5 below \$75.

Note that long underlying plus long put is synthetically equal to a long call. Pretending no carry cost or dividend, your position is the same as buying the \$75 call for \$5 and the P&L is the same as stated above.

There's no arbitrage.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.