Assume that a trader has sold $10,000$ European call options with strike price of $$34$ on a non$-$dividend paying stock. Immediately after the sale $($week $0)$ the stock price is $$33\mathrm{.}13$ dollars, and the delta of the option is $0\mathrm{.}491.$ After one week, the share price moves to $$33\mathrm{.}24,$ and the delta of the option is $0\mathrm{.}496.$ Assume that the trader makes his portfolio delta neutral immediately after the sale $($week $0)$ and rebalances after the first week $($week $1).$ What are the costs of the purchased or sold shares immediately after the sale and after one week?

Question $1$Answer

a$.$

week $0$: sell shares for $$162,668,$ week $1$: sell shares for $$164,330.$

b$.$

week $0$: purchase shares for $$162,668,$ week $1$: purchase shares for $$1,662.$

c$.$

week $0$: purchase shares for $$162,668,$ week $1$: purchase shares for $$164,330.$

d$.$

week $0$: purchase shares for $$162,668,$ week $1$: sell shares for $$1,662.$