Difficult interview question

I was looking at some old interview questions on the WSO company database, and I came across these two from a person who interviewed at Rothschild.

1) Walk me through how you might derive the black-scholes formula by using a real options approach

2) Argue for the right discount rate to apply to 338-related amortization tax shields

Those seem out of left field. Can you answer them? This was for M&A. I feel like OP may have had a strong finance background to have been asked these. 

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