Risk-neutral pricing is a theoretical framework used in finance to value financial instruments, particularly derivatives. It's based on the idea that in a perfectly efficient market, the expected value of any financial instrument, when discounted at the risk-free rate, should equal its current price. This means that investors are indifferent to risk, as they can earn the same return by investing in risk-free assets.
Here's how risk-neutral pricing works:
1. Construct a replicating portfolio: This is a portfolio of basic assets, like stocks and bonds, that has the same payoff as the derivative in every possible future state.
2. Calculate the cost of the replicating portfolio: This cost represents the fair value of the derivative.
3. Determine the risk-neutral probability: These are probabilities assigned to each future state that make the expected value of the derivative, discounted at the risk-free rate, equal to the cost of the replicating portfolio.
The key assumption in risk-neutral pricing is that all investors are risk-neutral. This....
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