Explanation:
A is correct. The fundamental theorem of asset pricing states that the arbitrage-free price of any derivative, such as an option, is precisely equal to its expected future payoff discounted at the risk-free rate, calculated using risk-neutral probabilities.
B is incorrect. One of the main advantages of arbitrage-free pricing (and risk-neutral valuation) is that it is independent of the risk preferences of individual investors. Prices are determined by the no-arbitrage condition and the cost of replicating the derivative.
C is incorrect. In the "imaginary" risk-neutral economy, investors are assumed to be risk-neutral. Consequently, they do not penalize securities for risk, and they do price all securities exactly at their expected discounted value using the risk-free rate.
D is incorrect. The core premise of the risk-neutral pricing framework is that the price derived in the imaginary risk-neutral economy must be exactly the same as the price in the real economy; otherwise, arbitrage opportunities would exist.
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Q.1629 The price of a derivative in the real economy may be computed as the discounted value under the risk-neutral probabilities. Which of the following statement about the price of an option is correct?
A
The arbitrage-free price of the option equals its expected discounted value under the risk-neutral probabilities.
B
The price of a security that is priced by arbitrage-free depends on investors' risk preferences.
C
Investors in the imaginary economy penalize securities for risk and do not price securities by expected discounted value.
D
The price of an option does not necessarily need to be the same in the real and imaginary economies.