Explanation:
A is correct: In a risk-neutral framework, the fundamental principle is 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, under the risk-neutral probability measure.
B is incorrect: A defining feature of arbitrage-free pricing and risk-neutral valuation is that the price of the derivative does not depend on the individual risk preferences of the investors.
C is incorrect: In the imaginary (risk-neutral) economy, investors are mathematically assumed to be risk-neutral. Consequently, they do not require a risk premium and do not penalize securities for taking on risk; they explicitly price all securities by their expected discounted values.
D is incorrect: The entire foundation of risk-neutral pricing relies on the fact that the price of the derivative computed in the imaginary (risk-neutral) economy precisely matches the arbitrage-free price in the real economy.
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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.