Assume currently the price of a stock is $$20$ and a bank sold $10,000$ call options on this stock with a strike price of $$15.$ The bank wants to use delta hedging to protect itself.

The price changes and the corresponding deltas of the option are as follows over the first three weeks. $($The bank rebalances every week$).$ The risk free rate is $5\%.$

Time Price Delta

$0200\mathrm{.}70$

$1210\mathrm{.}72$

$2180\mathrm{.}63$

$3160\mathrm{.}51$

Create a table that shows the stock positions necessary to delta hedge every week and the weekly and cumulative costs of delta hedging.