In the context of option pricing, what does a synthetic put consist of?

A synthetic put can be created using a combination of financial instruments that effectively replicate the payoffs of a conventional put option. In constructing a synthetic put, one can utilize a long position in the underlying stock and a short position in a call option.

To understand why the correct answer involves the put and stock adjusted for the present value of the exercise price, consider that holding a stock gives you ownership, while selling a call option provides you with income (the premium) and obligates you to sell the stock at the strike price if the option is exercised. When you combine these positions and consider the potential outcomes, you essentially create the same risk and payoff profile as a standard put option.

In detail, if the stock price falls below the exercise price, you are protected because you can cover your short call obligation with the stock you own, effectively limiting your loss, which is akin to the protective nature of a put option. Conversely, if the stock price rises beyond the exercise price, the loss on the call will be offset by the gains on the stock.

This interplay between using both the stock and the call option, and accounting for the present value of the exercise price—recognizing that the value of future cash flows needs to be discounted—helps illustrate