P1.T3 Chapter13 Practice Questions

[thanhtam92]

Hi @David Harper CFA FRM , regarding question Hull 11.22, can you please explain how you gets to the arbitrage strategy below?

 

[Sixcarbs]

Long Put+Short Call= Short Stock

You must get comfortable with the different synthetic combinations!

I norrmally like to draw little graphs, but I am not that good with them on Excel. Closing Price on x-axis, value of option on y-axis. Do calls, do puts, long and short, then start combining them. My little table below ignores interest and dividends, but you can see conceptually how it works. It's making money dollar for dollar as the stock drops, like short stock.

As trader's we used to use for quick and dirty:

X+C-P=S+i-D
Strike+Call-Put=Stock+Interest-Dividend.

Interest would just be simple interest over the time period of the Strike.

But the left side is your Synthetic Stock, which equals the real stock on the right side, adjusted for interest and dividends. (No dividend, even easier!, Interest rates so low nobody cares, great!)

So in the example above it is the put that is cheap, so you are going to employ a strategy that involves buying the put. We call that position above a "Coversion." Normally your biggest risk with a Conversion is "Pin Risk" where the stock pins at the strike on expiration. The opposite, Long Calls+Short Puts+Short Stock is called a "Reverse Conversion." The Reverse has other risks including dividend increases, special dividends, and the stock becoming hard to borrow.

 

[Eustice_Langham]

Very interesting..thankyou. I have a question concerning Reverse Conversion...a number of institutions mainly banks declared dividends then revoked the dividend, was there a discernible issue when it came to valuing optons?

 

[Sixcarbs]

Very interesting..thankyou. I have a question concerning Reverse Conversion...a number of institutions mainly banks declared dividends then revoked the dividend, was there a discernible issue when it came to valuing optons?

A risk of the Reverse Conversion is a dividend increase or a special dividend. So a dividend cut should be beneficial to holding the Reverse.

Remember someone who is short stock needs to pay the dividend to the lender of the stock.

 

[David Harper CFA FRM]

That's super cool @Sixcarbs! Another thing you can do, and I guess it's more of a trick-shortcut is use the signs (+/-) in put-call parity where (+) is long and (-) is short. I always start with protective put equals call plus cash: p + S = c + K*exp(-rT, it's the only one I memorize.. In this case, solving for p:

p = c + K*exp(-rT) - S; and that's exactly the formula uses to value the mis-priced put. By solving for $4.50, we've identified an inequality:

p < c + K*exp(-rT) - S
$3.00 < [c + K*exp(-rT) - S] = $4.50 <-- for me, this is the key, to see that the put's replication has a higher price than the put.

having identified ...
put @ $3.00 is cheap > put replication @ 4.50 is expensive

we can buy the cheap thing (the put) and sell the expensive thing which is [c + K*exp(-rT) - S]. To sell, just negate with "-":

[c + K*exp(-rT) - S] <-- this is "buy call, long cash [i.e., invest], short stock" and now we are negating:
-[c + K*exp(-rT) - S] = -c - K + S <-- this is "short call, short cash (borrow), and buy the stock." b/c the (+) is long and the (-) is short. I hope that's interesting ...

 

[Sixcarbs]

[c + K*exp(-rT) - S] <-- this is "buy call, long cash [i.e., invest], short stock" and now we are negating:
-[c + K*exp(-rT) - S] = -c - K + S <-- this is "short call, short cash (borrow), and buy the stock." b/c the (+) is long and the (-) is short. I hope that's interesting ...

I like this because I am always having to think about which way the cash is going. This works!