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Exercise Set 9, question 8

Exercise Set 9, question 8

by Miguel Silva André Rocha Gouveia -
Number of replies: 1

Hi professor,

In question 8 of the Exercise Set 9, we are suppose to price a put option with a binomial tree. The solutions price it using the replicating portfolio, which makes total sense, but also it's given to us the probability of the price going up or down.


If we calculate it by:

Price(put) = (prob(u)*payoff(u) + prob(d)*payoff(d))/(1+rf)

=(70%*0 + 30%*3)/(1+2%) = $ 0.88, 

we get a different result than from the replicating portfolio. Should we explore that there's an arbitrage opprotunity here? Also, if both ways work, the market price of the option should be the cheaper one, as buyers would only buy for $ 0.88.


Also, it's given the MRP. What's the use of it?

In reply to Miguel Silva André Rocha Gouveia

Re: Exercise Set 9, question 8

by Martijn Boons -

The big insight from our option classes is that you can price them without using probabilities or risk premia. Rather, we replicate. Hence, all the additional info is useless. Indeed, even if you had the probabilities, you would have needed to know the discount rate of the option, which is not the risk-free rate. The CAPM would say the beta of the option is related to the beta of the stock, which is also not given. (In fact, to use the CAPM, you'd first need to replicate anyway.)

Cheers, Martijn