Will someone look through my process and let me know if I am lookin that this wrong?

When I do Question C part one I use the Put-Call Parity,

Put Price = Call Price - Share Price + PV of Exercise price
5 = 5 - 77 + 80/1.02
0 = 1.43
So shouldn't the Cash Outflow at Time 0 be equal to -1.43 since the investor instantly made a profit by buying a put option and selling a synthetic put option?

For part B, if the put has a price of $5, then

c + PV(X) = p + s  =>  c = $3.57

So, would we prefer either the put (since 6.43 > 5.00) or the call (since 5.00 > 3.57)?  I'm a bit confused.

[NEAS: Use the following logic.

If the call is truly worth $5, the put is worth $Z. If it is selling for $5, it is either overpriced or underpriced. We should buy under-priced securities and sell over-priced securities.

If the put is truly worth $5, the call is worth $Z. If it is selling for $5, it is either overpriced or underpriced. We should buy under-priced securities and sell over-priced securities.

Substitute the figures. The result: we should buy one of the options and sell the other option.]

The question and answer gives the wrong rate of interest.  It should be 2% per quarter (.08/4) giving a 80/1.02 for the PV of the exercise price.  This is clearly stated in the problem where the risk free rate is 8% per annum, or 2% per quarter.  When the answer uses (1.08^.25) -1 = 1.0194 as the PV discount factor, it incorrectly interprets 8% as the effective annual rate.  This will be very confusing to some who may not be familiar with this topic.

[NEAS: Correct. The answer explains how different compounding intervals affect the solution.]

Ken

I agree with you here.

The investor has both (1) sold a call option and (2) bought a put option.

The investor has effectively insured herself against any volatility in the stock price.

If the stock price is less than $80 then she exercises the put option and sells the stock at $80. If the stock price is more than $80 then whoever she sold the call option to will want to buy it at $80. So again she sells it at $80.

In either case the investor sells the stock at $80 and she pays the bank $78.54. There is a risk free gain of $80-$78.54= $1.46.

I get the same answer for both C3 and C4 ($1.46)

I am still having some trouble with figuring out the net gain of C) 4.

The investor is forced to sell, but is it at $80 or the market price.

It would make more semse to me if it were at $80 because the investor looses and the buyer is the one that gains the market price - $80.

And if this is true then the investor's net gain is 80-78.54 = $1.46.

KPlunk:
C-4) At the end of 3 months, if stock prce rises > 80, say S. The put option is worthless. The buyer of call option exercise his right. The investor is FORCE to sell his share at market price S (remember S>80), and pay the buyer the difference (S-80). Investor get to keep $80. Repay the loan of 77*91.02) = 78.54, his net gain is $1.46

Or you can think of, since the stock price > 80. The buyer of the call option wants the share (he call sell it immediiately for S>80, or keep in his investment portfolio), he exercise his right, pay the investor $80 to exchange a share worth more than $80.
The investor get $80. pay off the loan of 77*(1.02), leave him with $1.46

For Part A, why are people calculating the price of the call when it is given in the information. It says the value is $5. I think this means the formula should be:

p + 77 = 5 + 80/1.02     p = 6.43

[NEAS: Yes]

Let me know what you think or why you are calculating the call. What is the $5 given supposed to be used for.

Also, how would this change the answer for part B, I have you would prefer the put becuase the ture value, 6.43 is greater than the price paid which is said to be 5.00

MC:

1) agree

2) They give us the equation: $77*1.02% = $78.54. Why did you multiply by 3?

3) You're correct that the put option is exercised. So he sells at 80$. Subtract what he pays to the bank, $78.54, get a net profit of $1.46.

4) The call option is exercised. Whoever bought the call will force the investor to sell his stock for $80. The net gain for the investor will thus be the same, either way.

This exercise demonstrates why an option will never be underpriced. If it were, we would have a quick money scheme on our hands. (I apologize if I just sounded like Brealey and Myers. I also apologize for the font changes. I'm still trying to figure this thing out.

1. you stated call value =-3 , this is nonsense.
A call option is an OPTION. Meaning that you need to pay extra to get this feature. It can't be <0.

c + pv(k) = p+ S

we are given c =5, S=77, K=80, then pv(K) = 80/1.02
=> value of put = c + pv(K) - S

[NEAS: Yes]