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As for the pricing of stock, we can use the DCF method. For the pricing of bonds, we can also use the DCF method.

As i understand, for the pricing of stocks and bonds, to use the DCF method, we must know the "risk premium" in order to discount the future cashflows.

I am wondering what difference between stocks/bonds and options that prevent us from using pricing method for stocks/bonds (like DCF) to price options ?

Moreover, i often see that they use DCF method to price stock and bond, which means that they can determine which "risk premium" to use for stocks and bonds. Why can't they do the same thing (i.e. determine the risk premium) as for options ?

Thank you for your help!

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    $\begingroup$ You could price options by adding the expected cash flows and using the right discount rate. It’s just awfully difficult to find the right discount rate. These methods are also called absolute pricing. Stocks and bonds are fundamental assets whose prices are determined from equilibrium models. Based on these prices (taking them as given), we can value options by replication under the no-arbitrage assumption. That’s a much, much weaker assumption than equilibrium, and a very powerful tool in finance. $\endgroup$
    – Kevin
    Oct 12 at 13:07
  • $\begingroup$ Everything in finance is just cashflows (CF) that need to be discounted to the valuation date. For vanilla bonds, coupons are part of the contract, for stocks, predicting dividends is harder, figuring out the expected CF for derivatives is even harder. However, any Monte Carlo (MC) pricing tool is essentially just doing that. If you use for example Bloomberg's DLIB (derivatives library), it's "simply" defining CF as per contract terms, and running MC simulations to determine what the expected value of the underlying (s) is (are) to get expected CF. These are discounted (at a desired rate). $\endgroup$
    – AKdemy
    Oct 12 at 13:42
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    $\begingroup$ @InTheSearchForKnowledge Equilibrium pricing refers to finding the "right" discount rate (e.g., using the CAPM). The value of a call option equals the discounted expected cash flows the option generates. You can do this with DCF (if you know the right discount rate). Pricing by replication allows you to avoid finding the right discount rate. It's very difficult to find the rate discount rate. That's why derivatives are (almost) always priced by no arbitrage (if possible). $\endgroup$
    – Kevin
    Oct 12 at 13:56
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    $\begingroup$ Pricing by replication means to find option prices such that there is no arbitrage by trading options, spot and bond markets. That's all that's behind the maths. Even if stocks are mispriced (agents use the wrong discount rates), the option is still correctly valued in the sense that any other option value would introduce arbitrages. For the BS formula to hold, stocks do not need to be priced correctly and market do not need to be in equilibrium. These conditions are necessary for the CAPM though. That's why derivative pricing models are more successful than traditional asset pricing model. $\endgroup$
    – Kevin
    Oct 12 at 14:00
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    $\begingroup$ In theory, the CAPM prices everything (stocks, bonds, options, etc.). Finding good models for discount rates (i.e., a good model for the SDF) is very difficult. If you're interested in applications, you may want to check out a reduced-form factor model approach. The seminal Fama and French (1993) paper suggests two pricing factors for bonds: a term structure premium and credit premium. That seems a sensible place to start (in my opinion). $\endgroup$
    – Kevin
    Oct 12 at 16:06
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If we were to price an opion with the DCF method, we would have to contend with 2 problems:

  1. We don't know the cash flow. So we would have to make an assumption that it comes from a specific probability distribution, say $\mathbb P$, and then take an expectation of that.

  2. We need to know the discount factor. Since we made an assumption about $\mathbb P$, we know the level of risk embedded in it, so we could use, say, CAPM, to obtain the appropriate discount rate.

If we do the above, we arrive at precisely the Black-Scholes model, see this answer and the paper linked there, or the original BS papers.

People just don't like to think about valuation of derivatives in these terms, because it's difficult to find objective grounds on which to choose $\mathbb P$, and CAPM is also a very strong assumption, with empirical shortcomings. So the preferred approach is to use the risk-free valuation, which imposes a specific risk-free distribution $\mathbb Q$ and dictates the use of the risk-free rate for the discount factor to go along with it. In the end, we arrive at an equivalent result, on stronger theoretical grounds.

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  • $\begingroup$ Hi, thanks for your answer. It is great. However, could you explain more why when we make an assumption about $P$, we know the level of risk embedded ? and is it right to think that the distribution $P$ is the distribution of price of the stock or is it the distribution of the "payoff" of the option ? Thank you very much! $\endgroup$ Oct 13 at 5:04

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