Consider an European Put option within a binomial tree model. The Put expires in 5 months...

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Consider an European Put option within a binomial tree model. The Put expires in 5 months and has strike K = 100. Today's stock price is So = 100, the interest rate is r = 0.07, the dividend yield is 8 = 0.02 and the volatility is o = 0.3 (all monthly). Using a binomial tree with step h of 1 month, find the replicating portfolios of this Put for all tree nodes at t = 4 months. Put your answers into a little table listing possible values of S(4), the corresponding stock position and the corresponding bank position. Sketch the resulting Delta and Bank account positions as a function of S(4). Note: the full tree is very BIG but you don't need to compute it. All I am asking about are the nodes at t = 4. Formulas that may be potentially useful: E, P(0, T;)F(T;) E P(0, T;) F = Soer-syr F = SoeT – FVr(Div) C -P = PV(F - K) R = elr-5)h – d Snh = Sod" (u/d)x, X~ Bin(n, q) = e(r-6)h+ovh d= er-5)h-aVh u - d C = e-rh(qCu+ (1– 4)Ca) A = e-6h Cu – Ca Su - Sa B = e-rh (uCa – dC,) (u - d) C = AS + B Co = e-8T S,N(d) – KeTN(d2) log(So/K) +(r- 8)T ±0²T/2 oVT Po = Ker"N(-d2) – e-ST. "SoN(-di) d1,2 ACall = e-8T N(d1) APut = -e-8T N(-d1) S = Soe(r-8-o*/2)ttovie, E N(0, 1) E[S.] = Soe(r-s)t %3D Consider an European Put option within a binomial tree model. The Put expires in 5 months and has strike K = 100. Today's stock price is So = 100, the interest rate is r = 0.07, the dividend yield is 8 = 0.02 and the volatility is o = 0.3 (all monthly). Using a binomial tree with step h of 1 month, find the replicating portfolios of this Put for all tree nodes at t = 4 months. Put your answers into a little table listing possible values of S(4), the corresponding stock position and the corresponding bank position. Sketch the resulting Delta and Bank account positions as a function of S(4). Note: the full tree is very BIG but you don't need to compute it. All I am asking about are the nodes at t = 4. Formulas that may be potentially useful: E, P(0, T;)F(T;) E P(0, T;) F = Soer-syr F = SoeT – FVr(Div) C -P = PV(F - K) R = elr-5)h – d Snh = Sod" (u/d)x, X~ Bin(n, q) = e(r-6)h+ovh d= er-5)h-aVh u - d C = e-rh(qCu+ (1– 4)Ca) A = e-6h Cu – Ca Su - Sa B = e-rh (uCa – dC,) (u - d) C = AS + B Co = e-8T S,N(d) – KeTN(d2) log(So/K) +(r- 8)T ±0²T/2 oVT Po = Ker"N(-d2) – e-ST. "SoN(-di) d1,2 ACall = e-8T N(d1) APut = -e-8T N(-d1) S = Soe(r-8-o*/2)ttovie, E N(0, 1) E[S.] = Soe(r-s)t %3D

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