This is from CFA textbook p448
Sousa’s first task is to illustrate how to value a call option on Alpha Company with a one-period binomial option pricing model. It is a non-dividend-paying stock, and the inputs are as follows.
The current stock price is 50, and the call option exercise price is 50.
In one period, the stock price will either rise to 56 or decline to 46.
The risk-free rate of return is 5% per period.
Based on the model, Rocha asks Sousa to estimate the hedge ratio, the risk-neutral probability of an up move, and the price of the call option. In the illustration, Sousa is also asked to describe related arbitrage positions to use if the call option is overpriced relative to the model.
4 For the Alpha Company option, the positions to take advantage of the arbitrage opportunity are to write the call and:
A short shares of Alpha stock and lend.
B buy shares of Alpha stock and borrow.
C short shares of Alpha stock and borrow.
I can get that the answer is B coz of the formula to replicate call option is:
C0 = hS0 + PV(-hS^- + c^-) = hS0 + PV(-hS^+ + c^+)
However, what I can’t understand is that at Time Step 1 why is the borrowing calculated as -0.6*46=-27.6 for both up and down scenario?
Txn | Time Step 0 | down occurs | Time Step 1 Up occurs
sell the call option | 4.5 | 0 | -6
buy h shares | -0.650=-30 | 0.646=27.6 | 0.656 = 33.6
borrow | -(1/1.05)[(-0.646+0]=26.287 | **-0.646=-27.6** | -0.6*46=-27.6
Net cash flow | 0.787 | 0 | 0
Thanks for helping!