Consider 10 assets, each defaults with probability p, independent of each other. These assets are bundled into one asset, and this asset defaults if...

Consider 10 assets, each defaults with probability p, independent of each other. These assets are bundled into one asset, and this asset defaults if two or more of the original assets default.

a) Calculate the probability (using Python) that the bundled asset defaults for p = 0.01,0.02,...,0.1.

Hint: Let Li ∼ Bin(1,p) be i.i.d., so that Li = 1 if asset i defaults.

Let Y =Summation of L from i=1 to n, with n = 10.

Then Y ∼ Bin(n,p) and P(Bundle defaults) = P(Y > 1) = 1−P(Y ≤ 1).