Please Answer all parts!

(b) Price a European Put on a risky underlying S (share price at t = 0) equals So = 100 US $, and up-tick factor u = 105%, down-tick factor d = 95%) in a two-period version of the Binomial model (with the three times t=0,t = 1/2 and t =T = 1). The maturity T is one year, the strike K = 99 US $, and in the market is a risk- less investment opportunity with a safe rate r = 3% per annum (with semi-annual compounding). (c) For the setting in 4(b), derive the replicating portfolio on each date and in each possible scenario. You may use the formulas for Option delta and safe position, n n On i Vu - Vd Sn u-d 1 uv,- dv B) = - nSn = 1+r U-d Here V,, V,denotes the future values of the option (in the case of an up- or down- tick of the underlying), given the time t = n value Sn of the underlying. (d) Explain why in general, and whether for the basis of the concrete pricing task in 4(b), an American put contract on the same asset, having the same maturity and strike, is worth more than the European counterpart. (b) Price a European Put on a risky underlying S (share price at t = 0) equals So = 100 US $, and up-tick factor u = 105%, down-tick factor d = 95%) in a two-period version of the Binomial model (with the three times t=0,t = 1/2 and t =T = 1). The maturity T is one year, the strike K = 99 US $, and in the market is a risk- less investment opportunity with a safe rate r = 3% per annum (with semi-annual compounding). (c) For the setting in 4(b), derive the replicating portfolio on each date and in each possible scenario. You may use the formulas for Option delta and safe position, n n On i Vu - Vd Sn u-d 1 uv,- dv B) = - nSn = 1+r U-d Here V,, V,denotes the future values of the option (in the case of an up- or down- tick of the underlying), given the time t = n value Sn of the underlying. (d) Explain why in general, and whether for the basis of the concrete pricing task in 4(b), an American put contract on the same asset, having the same maturity and strike, is worth more than the European counterpart