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# 74 price 1025 on average you lose from holding this

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Unformatted text preview: means the price of the security is 0.74/1.025 The actual probability is 0.7=1-0.3 What is the expected return? .7 − 1.74 E [payoﬀ] − price .025 = = −3.04% .74 price 1.025 On average you lose from holding this security (particularly since you can get 2.5% without risk.) That’s OK – it pays you when you would like to get money! Risk-Neutral Pricing Although we derived risk-neutral pricing for the binomial pricing model, it holds much more generally: If one of the following hold: There is no-arbitrage Each agent chooses optimal portfolios The economy is in equilibrium Then: there exists a diﬀerent probability measure so that any security can be priced as price = E Q [payoﬀT ] (1 + r )T Notice that we have two ways to think about the pricing problem: 1 People think about the actual expected payoﬀ and adjust their discounting to compensate for risk. 2 People discount everything at the risk-free rate, but adjust their expectations so that, for the purpose of pricing, they think “bad” events are more likely and “good” events are less likely. Summary of Risk-Neutral Pricing This is a major accomplishment! We can now: 1 Do computations to ﬁgure out option prices 2 We know the price is right unless there is arbitrage We can interpret how the pricing works 3 People up-weight the probability of ”bad” events After making this adjustment,...
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