An at-the-money put option has a Black-Scholes price P0=$5, with K=100,  = -0.4 and time to maturity T = 1⁄4 (year, 3-m

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An at-the-money put option has a Black-Scholes price P0=$5, with
K=100,  = -0.4 and time to maturity T = 1⁄4 (year, 3-months). The
current stock price is S0 = $100 and the risk-free rate r = 3%pa.
Today, M/s Short sells one put and delta hedges. (Assume you can
buy and sell, fractions of a stock). Assume the stock price falls
to S1 = 90 after one-week and the delta is then 1 = - 0.5. M/s
Short rebalances the hedge each week. The stock price then falls
monotonically to ST=$10. At T, M/s Short has accumulated a bank
deposit of BDT = $100.3. You may use some or all of the above
illustrative data and a diagram to answer the following questions:
a). Explain what happens in M/s Short’s hedge i) at t= 0, ii) at t
= 1-week and iii) at T. b). Briefly list the risks in the hedge.
c). Briefly explain in practice, the benefit (if any) to the trader
who initially sold the put and then delta hedged.