Describe the trading position created in which a call option...

Describe the trading position created in which a call option is bought with strike price $K_2$ and a put option is sold with strike price $K_1$ when both have the same time to maturity and $K_2>K_1$. What does the position become when $K_1=K_2$ ?

Key Concepts

Call Option

A call option is a financial contract that gives the holder the right, but not the obligation, to purchase an underlying asset at a specified strike price before or at expiration. It is used in trading strategies to take advantage of potential price increases in the underlying asset without having to commit the full capital required to own the asset outright.

Put Option

A put option is a derivative contract that provides the holder with the right, but not the obligation, to sell an underlying asset at a predetermined strike price within a specific time frame. Traders use put options to hedge against or profit from declines in the value of the underlying asset.

Synthetic Forward Contract

A synthetic forward contract is created by combining options in such a way that their net payoff replicates the payoff of a traditional forward contract. Specifically, a long call and a short put with the same strike price and expiration yield a synthetic long forward position, which effectively simulates holding the underlying asset and being exposed to its price movements.

Put-Call Parity

Put-call parity is a key principle in options pricing that defines a specific relationship between the prices of European call and put options with the same strike price and expiration. This relationship shows that the combined positions of buying a call and selling a put produce a payoff equivalent to that of a forward contract, thereby allowing traders to construct synthetic forward positions.

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