Concept check for replicating options. Can you help with the signs please!

  1. Identify the trading strategy that will generate the payoffs of taking a long position in a call option within a single-period binomial framework.
    A. Buy h = (c+ + c–)/(S+ + S–) units of the underlying and financing of – PV(–hS– + c–)
    B. Buy h = (c+ – c–)/(S+ – S–) units of the underlying and financing of – PV(–hS– + c–)
    C. Short sell h = (c+ – c–)/(S+ – S–) units of the underlying and financing of +PV(–hS– + c–)

B is correct.

  1. Identify the trading strategy that will generate the payoffs of taking a long position in a put option within a single-period binomial framework.
    A. Short sell –h = –(p+ – p–)/(S+ – S–) units of the underlying and financing of –PV(–hS– + p–)
    B. Buy –h = (p+ – p–)/(S+ – S–) units of the underlying and financing of –PV(–hS– + p–)
    C. Short sell h = (p+ – p–)/(S+ – S–) units of the underlying and financing of +PV(–hS– + p–)

A is correct

Question:

  1. For Q1, why is the sign before PV negative? aren’t we borrowing → cash inflow so it should be +PV ?
  2. For Q2, same question: shouldn’t we short sell +h not -h?
  3. Is the term financing means either borrowing or lending?

My main issue is the signs before the terms. I thought short selling h shares means directly " -hS " , so in Q2 when we say " short selling -h " , I think of it (-)*(-)h , meaning +h, meaning we buy h shares.

I definitely have something mixed up, if you can help please !