Answer:

Answer:

I know how to get the premium of European put but how to get the American? What's the difference between them? I need an explanation thanks!

A European put written on shares has strike price $8 and expires in five time steps. Using CRR notation, the underlying share prices are calculated using S=$7,u= 1.15 and d=1/u. The return on a bank investment over each time step is R= 1.05. Find the premium of the put by calculating the risk neutral probabilities and then constructing a five-step binomial pricing tree. \begin{tabular}{|l|l|r|r|r|r|} \hline Euro put & & & & & \\ \hline 0.44023756 & 0.22885431 & 0.074930962 & 0 & 0 & 0 \\ \hline & 0.88337543 & 0.538674937 & 0.2206391 & 0 & 0 \\ \hline & & 1.629199604 & 1.1880538 & 0.64968623 & 0 \\ \hline & & & 2.6536222 & 2.32604195 & 1.91304348 \\ \hline & & & & 3.6167749 & 3.39738637 \\ \hline & & & & & 4.51976285 \\ \hline \end{tabular} Find the premium of an American put with the same underlying asset, strike price and expiry as the European put. \begin{tabular}{|r|r|r|r|r|r|} \hline US put & & & & & \\ \hline 1 & 0.41028223 & 0.115334077 & 0 & 0 & 0 \\ \hline & 1.91304348 & 1 & 0.33960871 & 0 & 0 \\ \hline & & 2.706994329 & 1.91304348 & 1 & 0 \\ \hline & & & 3.39738637 & 2.70699433 & 1.91304348 \\ \hline & & & & 3.99772728 & 3.39738637 \\ \hline & & & & & 4.51976285 \\ \hline \end{tabular} A European put written on shares has strike price $8 and expires in five time steps. Using CRR notation, the underlying share prices are calculated using S=$7,u= 1.15 and d=1/u. The return on a bank investment over each time step is R= 1.05. Find the premium of the put by calculating the risk neutral probabilities and then constructing a five-step binomial pricing tree. \begin{tabular}{|l|l|r|r|r|r|} \hline Euro put & & & & & \\ \hline 0.44023756 & 0.22885431 & 0.074930962 & 0 & 0 & 0 \\ \hline & 0.88337543 & 0.538674937 & 0.2206391 & 0 & 0 \\ \hline & & 1.629199604 & 1.1880538 & 0.64968623 & 0 \\ \hline & & & 2.6536222 & 2.32604195 & 1.91304348 \\ \hline & & & & 3.6167749 & 3.39738637 \\ \hline & & & & & 4.51976285 \\ \hline \end{tabular} Find the premium of an American put with the same underlying asset, strike price and expiry as the European put. \begin{tabular}{|r|r|r|r|r|r|} \hline US put & & & & & \\ \hline 1 & 0.41028223 & 0.115334077 & 0 & 0 & 0 \\ \hline & 1.91304348 & 1 & 0.33960871 & 0 & 0 \\ \hline & & 2.706994329 & 1.91304348 & 1 & 0 \\ \hline & & & 3.39738637 & 2.70699433 & 1.91304348 \\ \hline & & & & 3.99772728 & 3.39738637 \\ \hline & & & & & 4.51976285 \\ \hline \end{tabular}