Complete the following in python

Arbitrage. Financial arbitrage is the ability to earn a riskless profit. In this problem we will try to construct a portfolio that achieves an arbitrage by exploiting the price differential of a stream of cash flows; i.e., purchase underpriced bonds at the ask price, and simultaneously sell overpriced bonds at the bid price.

Assume that the following bonds are available for buying at the ask price, or for selling at the bid price. The bonds available for purchase today (Year 0) are given in the next table. All bonds have a face value of $100. The coupon is annual. For example, you can buy Bond 5 for $98 today, or sell it for $97.02. If you buy one unit of the bond, it pays back $4 in Year 1, $4 in Year 2, $4 in Year 3 and $104 in Year 4. If you sell one unit of the bond, then you have to pay $4 in Year 1, $4 in Year 2, $4 in Year 3 and $104 in Year 4. All the bonds are widely available and can be purchased or sold without affecting the stated bid and ask prices.

Bond 1 2 3 4 5 6 7 Ask Price 102.00 99.00 101.00 98.00 98.00 104.00 100 Bid Price 100.98 98.01 99.99 97.02 97.02 102.96 99 Coupon 5 3.5 5 3.5 4 9 6 Maturity 1 2 2 3 4 5 5

Assume that the riskless reinvestment rate of excess cash is 1% per year.

If arbitrage exists, the optimal solution would be to sell an infinite amount of the overpriced bonds and buy an infinite amount of the underpriced bonds. To provide a finite solution, assume that you can buy or sell at most one unit of each bond. Find whether a portfolio exists such that todays value is positive i.e., you receive money and cash flows for any future date are non-negative.