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In page 59 of his book Option Volatility and Pricing, Natenberg argues that the forward price of an underlying security is essentially the market's consensus expected value for that security, otherwise an arbitrage opportunity exists:

In a sense, the marketplace must think that the forward price is the most likely future value for the underlying contract. If we assume that the underlying market is arbitrage-free, the expected value for the underlying contract must be equal to the forward price.

So if the two month forward price for a stock with a spot value of $100 with interest rates at 12% is $102, that's the expected value of that security in two months.

This assumption makes no sense to me. The forward price of a stock takes into account only interest rates and time and is only a measure of what I'd pay now to receive the stock in two months. It seems to me that the expected value of that stock in two months should take into account volatility and other factors. Why does this assumption hold?

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  • $\begingroup$ Volatility plays no role, you can check out this answer, which shows that a synthetic forward (combination of call and put option) gives the same result, irrespective of IV. $\endgroup$
    – AKdemy
    Commented Aug 13, 2023 at 7:28
  • $\begingroup$ Oops, forgot the link. This result relies on @dm3's answer. $\endgroup$
    – AKdemy
    Commented Aug 13, 2023 at 8:59

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Strictly speaking the book is not accurate. The forward price is equal to the expected future price only in the risk- neutral world (usually denoted by the pricing measure $Q$). In the real world (often denoted by $P$) the expected value of the stock at some future date is generally higher, to account for the riskiness of the stock (see the Capital Asset Pricing Model for example).

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