The arbitrage principle is one of the cornerstones of modern finance, and it’s being used widely, from derivative pricing to hedging, trading, and risk management. Theoretically, there is only one arbitrage principle. Practically, however, there are other types of arbitrage, some of which are relaxed forms of the strictest one.

Reference [1] examined two seemingly simple trading strategies: the first one is based on the put-call parity, and the second one is the put-write strategy. These strategies are simple, but they can stimulate some interesting thoughts regarding practical aspects of the arbitrage principle,

*Coming back to the scheme for deriving trading strategies described in the introduction, both strategies started with stating assumptions on the financial market. For the put-call-parity this meant postulating that the no-arbitrage principle holds, for the put-write strategy pricing of options under certain model assumptions was considered. In a further step theoretical results were inferred. The put-call-parity itself in the first case and implicit volatility or expected returns of options in the latter. Testing on real market data quickly showed deviations for both theories.*

The author first investigated a trading strategy based on the put-call parity and concluded that it is not profitable. The author then examined the put-write strategy and concluded that it works better and can yield an excess return,

*…the outcome of the two methods differed vastly. Whilst the deviations for the put-call-parity were too low to gain any noteworthy economical success when considering market frictions like margins and transaction costs, the put-write strategy looked much more promising.*

The article’s results lead us to the following thoughts,

- The put-call parity strategy is one of the simplest examples of trading using the risk-neutral non-arbitrage principle. According to the author, it does not work. This is consistent with our experience that from the buy-side, it’s impossible to exploit mispricings in the risk-neutral world. Generally, we believe that this conclusion is applicable to more complex trading strategies as well.
- Put-write is one of the simplest strategies that exploit the volatility risk premium, and it works well, though with high risks. This strategy can be viewed as arbitrage between the risk-neutral vs. physical measures, which is a relaxed form of the non-arbitrage principle.
- Arbitrage is still possible but must be done mostly in the physical world, e.g. using some forms of statistical arbitrage and/or exploiting the risk premium.

Let us know what you think.

**References**

[1] A. Brunhuemer, *Computer-Supported Testing of Option Strategies*, Johannes Kepler University, July 2020