A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price and maturity. Describe the trader's position. Under what circumstances does the price of the call equal the price of the put?
The trader's position in this scenario is known as a synthetic long position in the underlying asset. By buying a European call option, the trader has the right to buy the underlying asset at the strike price at maturity. On the other hand, by selling a European put option, the trader is obligated to buy the underlying asset at the strike price if the option is exercised.
By combining these two options, the trader effectively replicates the payoff of owning the underlying asset itself. This is because the call option allows the trader to participate in any upside potential, while the put option provides downside protection by offsetting losses if the price of the underlying asset falls below the strike price.
The price of the call option will equal the price of the put option under certain circumstances. Specifically, it occurs when there is no opportunity for arbitrage in the market, and the options are fairly priced. This equilibrium state, where the prices are the same, is known as a put-call parity. It happens when the prices of the options, together with their strike prices and the price of the underlying asset, satisfy a specific mathematical relationship. This relationship is derived from the concept of no-arbitrage and helps ensure that there are no riskless profit opportunities in the options market.
In summary, the trader's position is a synthetic long position in the underlying asset. The price of the call option equals the price of the put option under the condition of put-call parity, which ensures market equilibrium and prevents arbitrage opportunities.