I created a new post about this because the previous one is already in the "older posts" section. To refresh your memory, this is about 2005, II.4.
Here are my 2 cents, let me know if it makes sense:
Answer to first question: you can use CAPM to estimate expected excess returns of options under certain assumptions: HARA class of utility functions.
Answer to second question:
(Preliminary note: CAPM is about expected excess returns and and is mute about price levels. B&S is about arbitrage free price levels and is mute about expected excess returns.)
Role of Beta in CAPM: quantifies the amount of the priced factor in an asset, to measure its expected excess return. The price of risk is given by the expected market premium.
In that sense, sigma in B&S is analogous to the expected market premium and not to beta. The delta of an option is analogous to beta. Making sigma = 0, the option is worth its intrinsic value (something analogous to the risk free rate).
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4 comments:
I'd like to ask a clarifying question here. If you have HARA utility function, that doesn't lead to MV-preferences, right? I thought you needed quadratic utility for MV just from the preferences. So does HARA get you the CAPM with non-normal returns? If not, you shouldn't be able to price options with the CAPM using just HARA>
again I think you guys should take a look at Duffie Chapter 6. He relates the Black-Scholes MODEL (note forula) to beta pricing and the CCAPM. It might help.
I also think you should be careful about thinking that an equation relating returns says nothing about prices. If we know the expected return and we know the expected payoff, should we be able to get prices? Jensens inequality?
J: HARA works when you have a risk free asset, and you definitely need one when you want to price a plain vanilla option
B: Not sure about that. What is the expected payoff of an option when we are considering a CAPM world? It seems to me that idiosyncratic risk matters for an option payoff, even though in CAPM we only deal with systematic risk of an option. I have to thing more about all this...
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