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State price deflators. Sep 2013 Q6

V

vegan

Member
Hi in the examiners solution of the above question, the state price deflator of the middle node (Aud and Adu) have been combined together. r=0.02 and p=0.7. Why is their denominator multipied by 2 (i.e. 2*0.7*0.3*1.02^2). As the denominator for Auu and Aud are each 0.7*0.3*1.02^-2 , would you not still get 0.7*0.3*1.02^-2 when you add them together, since common denominators do not change upon adding? The same is seen with September 2011 question 7 but I do not understand why we multiply by 2 if we r just adding two common denominators.
 
Hi
I don't think that there are any fractions being added together here. The denominator of the state price deflator contains the real world probability of a particular node being reached. The middle node that you've identified can be reach via two routes, and so the total real-world probability of arriving there is 2*0.7*0.3. The numerator is just the risk-neutral version, which again contains the total probability of reaching that point in the tree.
Hope that helps :)
Let me know if I haven't understood you correctly.
 
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