You have a portfolio of derivatives II that is A-neutral but has the following Gamma, I(II)...

Transcribed Image Text:

You have a portfolio of derivatives II that is A-neutral but has the following Gamma, I(II) = -30. In the market there is a derivative U1 with I'(U1) = 0.4 and A(U1) = 0.5. Explain how you should modify your portfolio (using U1 and the underlying asset) to make it both A- and I'-hedged. Give the precise numerical quantities involved. If the price of U1 is 1.50 and the price of the underlying is $2, what is the total cost of this modification? Formulas that may be potentially useful: F = Soe(r-5)T F = SoeT - FVr(Div) C-P = PV(F – K) R = E P(0, T,)F(T,) E P(0, T;) elr-5)h – d Snh = Sod" (u/d)X, X~Bin(n, q) u = elr-5)h+ovh d= e(r-6)h-ovh u-d A = e-5h Cu - Ca PS - "S B =e-rh (uC4 – dC,) (u – d) C = e=rh(qCu + (1- 4)Ca) C = AS + B Co = e-ST SoN(d1) – Ke-r™N(d2) log(So/K) + (r-6)T ± o²T/2 aVT Po = KerT N(-dz) -e-6T SoN(-d1) -8T d1,2 = Acall =e-ST N (d1) APut = -e-dT N(-d1) %3D S = Soe(r-6-a*/2)t+ovie, en N(0, 1) E[S] = Soe(r-5)t %3! You have a portfolio of derivatives II that is A-neutral but has the following Gamma, I(II) = -30. In the market there is a derivative U1 with I'(U1) = 0.4 and A(U1) = 0.5. Explain how you should modify your portfolio (using U1 and the underlying asset) to make it both A- and I'-hedged. Give the precise numerical quantities involved. If the price of U1 is 1.50 and the price of the underlying is $2, what is the total cost of this modification? Formulas that may be potentially useful: F = Soe(r-5)T F = SoeT - FVr(Div) C-P = PV(F – K) R = E P(0, T,)F(T,) E P(0, T;) elr-5)h – d Snh = Sod" (u/d)X, X~Bin(n, q) u = elr-5)h+ovh d= e(r-6)h-ovh u-d A = e-5h Cu - Ca PS - "S B =e-rh (uC4 – dC,) (u – d) C = e=rh(qCu + (1- 4)Ca) C = AS + B Co = e-ST SoN(d1) – Ke-r™N(d2) log(So/K) + (r-6)T ± o²T/2 aVT Po = KerT N(-dz) -e-6T SoN(-d1) -8T d1,2 = Acall =e-ST N (d1) APut = -e-dT N(-d1) %3D S = Soe(r-6-a*/2)t+ovie, en N(0, 1) E[S] = Soe(r-5)t %3!

Answer rating: 100% (QA)

Part b What is the approach behind it At present the portfolio gamma is 30 to make it gamma neutral ... View the full answer