Skip to content
All library documents

Put-Call Parity and Apparent Arbitrage in Futures and Options Data

Article Quant Q&A · Author: Denis
Read the original

Summary

The document presents an apparent arbitrage using a call, a put, and a futures contract with the same expiry and strike. The proposed position is long the call, short the put, and short the future; the questioner sees a positive initial cash balance and believes the portfolio leaves no underlying exposure. The example is meant to test whether the resulting payoff contradicts arbitrage-free pricing.

The responses explain that data timing can make the quoted prices inconsistent: real-time or delayed observations may not be synchronized, and options may stop trading before futures at the end of the day. They give the put-call parity relationship for estimating the implied forward from the strike and call and put premiums, assuming no cost of carry, and suggest using an at-the-money strike. Thus the apparent profit may reflect mismatched inputs rather than an executable arbitrage. The discussion is brief and does not quantify transaction costs, financing, or other market frictions.

Key ideas

  • A long call, short put, and short future at a matching strike and expiry can appear to lock in a gain when quotes are inconsistent.
  • Futures and options prices should be observed at synchronized times before assessing parity.
  • Options may stop trading before futures, making end-of-day quotes difficult to compare directly.
  • Under the stated no-cost-of-carry assumption, the call and put premiums imply a forward price relative to the strike.
  • The response does not establish that the example is executable after market frictions.

Tags

OptionsFuturesArbitrageDerivatives pricing
Full text
# Arbitrage free option prices: real life example


# Arbitrage free option prices: real life example












I would like to be sure of my correct understanding of some basic principles.

I have following example, data from Euronext:

1 Month maturity, future and options are same day expiry. Strike 5400.

Future price: 5407. Put: 28.8 Call: 20.1

We construct following portfolio: Long Call, Short Put, Short Future. This yields zero underlying exposure, and $+28.8-20.1=+8.7$ index points in cash equivalent. Now whatever the final spot is at maturity date, I am effectively gathering 15.2 index points:

Final spot 5400:+7 on Futures + 8.7 in cash

Final spot at 5447. Call +47, +8.7 in cash, -40 on Futures. etc...

Am I missing something? In school was told this shouldn't happen in real life

## Answer by user7877408 (score 1)

https://quant.stackexchange.com/a/34376

There are usually a couple of problems with reconciling futures / options data from sources like Euronext

- Real time / Delayed Data is not always asynchronous ....

- EOD Options Data ... Options usually stop trading before Futures ... therefore not comparing apples with apples

... assuming no Cost of Carry .... then the implied Forward for any expiry can be estimated by Strike + Call Premium - Put Premium ... better to use ATM strike

## Answer by user28079 (score -2)

https://quant.stackexchange.com/a/34363

Impied future = strike + call - put

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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