# Put-Call Parity

The put-call parity is useful as part of a hedging/ speculative strategy for a trader who wants to participate in the futures market. The put-call parity explains the relationship between the prices of put and call options in the same category-in other words, options with the same strike price, expiration date and underlying price.

In general, the value of a put option implies a fair value for the corresponding call, and vice versa. Thus, the price of one option cannot move very far without the price of the corresponding option changing accordingly. The parity is violated when there is a large price difference between the put and call options. Although the parity concept is strictly confined to European options, the relationship is applicable to American options as well (adjusting for dividends and interest rates).

From a trading perspective, the put-call parity reveals an arbitrage opportunity if there is a divergence between the value of calls and puts in the same category-in other words, if the parity is violated. If an option pricing model that produces put and call prices does not satisfy the parity, it can open up arbitrage opportunities. Arbitrageurs can profit until the gap between the put and call narrows. Although arbitrage strategies are not considered useful for the average trader, the corresponding synthetic relationship in the options market can reveal trading strategies. Conversion and reversal strategies are the most commonly used arbitrage techniques that profit from the put-call parity.

## Put/Call Ratio

The put/call ratio is simply the ratio of the volume of put options to the volume of call options traded during a given period of time, where the call and put options are based on the same underlying asset. For instance, the daily put/call ratio of an asset is calculated as the volume of put options traded during a given day divided by the volume of call options, where the put and call options have the same underlying asset. A put/call ratio over 1 means that more put options than call options on a given asset were traded. Conversely, a put/call ratio below 1 means that more call options than put options for this asset were traded.

The put/call ratio can be used by investors and traders as a technical indicator in two ways. In the first approach, an increasing put/call ratio might mean that more investors and traders are buying protection against depreciation in the anticipation of the market turning lower. This could be read as a bearish shift in sentiment. In such a situation, it is important to not only look at the ratio as a whole but to dig deeper into what is driving the change. An increase in the ratio caused by an increase in the volume of puts might be more bearish than an increase in the ratio caused by a decrease in the volume of calls.

The second approach to using the put/call ratio is a contrarian one. In this approach we look for extremes in the ratio. An extremely low reading would mean that the volume of calls is significantly higher than the volume of puts. This could be the case when the market is excessively optimistic and bets on higher prices are made by purchasing call options. So, an extremely low reading on the put/call ratio could be a contrarian bearish indication. On the other side of the spectrum, an extremely high reading on the ratio would mean that put volume is significantly higher than call volume. This could be the case when the market is excessively bearish and the puts bought as insurance against declines are the main factor. In such a situation, an extremely high reading of the put/call ratio could be a contrarian bullish sign telegraphing a potential bottom in the market.

## Put-Call Parity in Gold

The put-call parity in the yellow metal works accordingly to the template described above. It describes a relationship that holds in the gold options market. The put-call parity in gold explains the relationship between the prices of gold put and call options with the same characteristics, in particular with the same strike price and expiration date. The price of a gold put option cannot move very far without the price of the corresponding gold call option changing accordingly. The parity is violated when there is a large price difference between the put and call options.

One way of using put-call parity in the gold market is as follows: suppose the put-call parity is violated, the call side of the parity is undervalued and the put side of the parity is overvalued. Then one could theoretically sell a gold put option and short gold, while simultaneously buying a gold call option with the same characteristics and the risk-free asset. Such a combination should allow one to make an arbitrage profit.

## Put-Call Parity in Silver

Silver put and call options are also subject to put-call parity. Again, this means that the price of a silver put option cannot move away from the corresponding silver call options price following suit. Relatively large differences in the prices of silver put and call options might mean that there are arbitrage opportunities in the market. Apart from that, the put/call ratio can be used as an indicator for the silver market (or the gold market) in the ways described above. Indications from the put/call parity might translate into signal for the underlying silver (or gold) market itself.

In much the same way as for gold, when the put-call parity is thrown out of balance traders could act on this. If the call side is worth less than the put side, then traders could short silver, sell silver puts but at the same time buy silver calls and the risk-free asset. Such a portfolio should, in theory, produce an arbitrage profit.