The put-call parity is a principle in options pricing that states the price of a call option implies a certain fair price for the corresponding put option and vice versa. The put-call parity relationship is established based on the payoff of two portfolios: a fiduciary call and a protective put. The fiduciary call consists of a risk-free discount bond and a call option, while the protective put is made up of a put option and the underlying stock. In this context, the face value of the discount bond at maturity must be equal to the strike price of the call and put options at expiration. This is because the strike price is the price at which the holder of the option can buy (in case of a call option) or sell (in case of a put option) the underlying security when the option is exercised. Hence, for the put-call parity to hold, the face value of the discount bond (which is the amount that will be returned to the bondholder at maturity) must be equal to the strike price of the call and put options.

Choice A is incorrect. The face value of the discount bond being below the strike price of call and put options would not uphold the principle of put-call parity. This is because it would imply that the risk-free return from holding a fiduciary call (bond + call option) would be less than that from holding a protective put (put option + stock), which contradicts the concept of arbitrage-free pricing in financial markets.

Choice B is incorrect. Similarly, if the face value of the discount bond were above the strike price, it would mean that there's an opportunity for arbitrage as one could earn more by investing in a fiduciary call than in a protective put, which again contradicts the no-arbitrage principle.

Choice C is incorrect. The face value of discount bond being equal to final price of options does not make sense as final prices are uncertain and depend on various factors like underlying asset's price at maturity, volatility etc., whereas face value of bond is known upfront and does not change over time.