Borrowing money in the long call option replication using no-arbitrage approach and hedge ratio

CFA Level II Derivatives
#1

Hi,

in the reading 41. cash outflows are negative and cash inflows are positive.

My question concerns example 1 in this reading, but I think it will be necessary also later.

We have the equation: c = hS + PV(–hS– + c–) or rather c - hS - PV(–hS– + c–) = 0

This that hS is an outflow is very understandable. But why are the money we get from the debt to finance this transaction an outflow (PV(–hS– + c–)). Intuitively it should be an inflow…

Or is it actually cash inflow, but little bit messed up by the author of the book +PV(hS– - c–)?

I would appreciate any help from you.

EDIT:

Yeah, after reading about puts I noticed that the author does not stick to the convention he/she mentioned in the beginning… I am curious whether it has any goal.

If someone has a similar problem, then do not think that these exercises are in terms of cash flows. If you calculate how signs later offset each other you will have a correct version of inflows and outflows. Be careful in the exercises, because they are very counterintuitive.

#2

I’m trying to figure out this exact problem right now. I just want to see a filled in binomial tree with the valuation calculation for the call, and the payoff, and then a filled in binomial tree for the fractional shares of stock, factoring in the borrowed money. Also, when we borrow to buy the fractional shares, there’s no money forked out, but with a call you have to pay a premium. Very tough to understand how the very tough concepts are often not supplemented with the accompanying work and math. Do you know where I can get this answer?