Why Call and Put Prices Match Through Put-Call Parity
Summary
The article explains why an upward expected drift does not, by itself, make a call more valuable than a put with the same strike and expiry. It uses a toy probability example to distinguish the chance of finishing above the strike from option value, then relates the result to put-call parity: a call can be replicated with a put and the underlying asset, while a put can be replicated with a call and a short underlying position.
Under the simplified assumptions shown, equal-strike European calls and puts have equal calculated prices, and a price mismatch would allow an arbitrage between the option and its synthetic equivalent. The article supports the explanation with a Black-Scholes calculation for both contracts. Its example sets carry to zero and does not develop the effects of dividends or other real-world frictions, which it raises as a follow-up consideration. The parity argument depends on matching contract terms and the ability to trade the underlying and options consistently.
Key ideas
- Expected upward drift does not determine whether an equal-strike call or put costs more.
- A call can be replicated by combining a long put with a long position in the underlying.
- A put can be replicated by combining a call with a short position in the underlying.
- Under the example's assumptions, a price gap between an option and its synthetic equivalent implies an arbitrage opportunity.
- Dividends and other carry effects matter when applying parity beyond the simplified example.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.