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Exercise 3.4. This problem refers to the model of Example 3.1.2, whose Radon-Nikody'm...

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Accounting

Exercise 3.4. This problem refers to the model of Example 3.1.2, whose
Radon-Nikody'm process Zn appears in Figure 3.2.1.
(i) Compute the state price densities
3(HHH).
3(HHT)=3(HTH)=3(THH).
3(HTT)=3(THT)=3(TTH),
3(TTT)
explicitly:
(ii) Use the numbers computed in (i) in formula (3.1.10) to find the time-zero
price of the Asian option of Exercise 1.8 of Chapter 1. You should get
(4,4) computed in part (ii) of that exercise.
(iii) Compute also the state price densities 2(HT)=2(TH).
(iv) Use the risk-neutral pricing formula (3.2.6) in the form
V2(HT)=12(HT)E2[3V3](HT),
V2(TH)=12(TH)E2[3V3](TH)
to compute V2(HT) and V2(TH). You should get V2(HT)=v2(4,16) and
V2(TH)=v2(4,10), where v2(s,y) was computed in part (ii) of Exercise
1.8 of Chapter 1. Note that V2(HT)V2(TH).
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