Hi Friends,
As per BSM’s interpretation call option can be viewed as leveraged stock investment where stocks are purchase using borrowed funds!
How does it make sense with plain put call parity relation where call option = stock + borrowing + holding a put option
What confuses me is that the BSM’s interpretation ignores long position in put option for replicating call option?
Can any one pls guide
Is it because BSM assumes that call will always have some value meaning put will always be out of money and hence zero value?
Pl answer this someone thanks
If assumption is up-market then yes, owning a call is equivalent to a levered position in the underlying. Now if markets plummet, a long at-the-money put would be necessary, along with the levered underlying purchase, to replicate the payoff of a call option on the stock. At least this is how I interpret it.
I too think the same for now… can someone confirm… smagician???
s2000magician pls clarify
I haven’t thought about this one.
I’ll ponder it and get back to you.
I think you are correct above when you said if the call has value, the put should be worthless and hence equal to zero, assuming both call and put strikes are equal.
The put/call parity is: S+P=C+PV(x) where PV(x) is the present value of the strike (discounted at risk-free rate). If you sub this into the BSM model, you get the following:
Call: S(Nd1) - Xe-rT(Nd2) --> this is the same as rearranging the put/call parity formula above to: C=S-PV(x)+P where P would be zero if the call is in-the-money, so essentially not included
Put: Xe-rT(-Nd2) - S(-Nd1) --> this is the same as rearranging the put/call parity formula above to: P=PV(x)-S+C where C would be zero if the put is in-the-money, so essentially not included
This isn’t correct. There’s time value you’re missing. If a stock is currently 50 and you look at a strike of 55 for a put and a call… They both actually have value unless time has expired to zero. Same with a strike at 45.
In fact, out of the money options could have a lot of value, such as a LEAPS.
You are right that might not be a perfect explanation… How abt the assumption that the holder of the leveraged stock may actually default on the loan with whatever the value may be for the stock… (Which replicates a put option type feature)
That’s a very fair point. I guess I’ll have to defer to someone to help explain the original question because I’m not sure of the answer.
Is the answer that you can’t really view the BSM in the same context as put/call parity? BSM is really a valuation tool (like the binomial model) whereas put/call parity really concerns itself with how you would replicate different derivative strategies.
Going back to what I posted before, if you sub the BSM formulas into the put/call parity, here is what you get:
Call = (S(Nd1) - Xe-rT(Nd2)) + (Xe-rT(-Nd2) - S(-Nd1)) --> the first term is the BSM call formula and the second is the BSM put formula. Maybe this will help get the conversation started on getting to an actual answer.
This isn’t specific to BSM, its also present in the binomial; the value of the call option involves the stock and the bond, but no put value
C = hS0 + (-hS++C+)/(1+Rf)
Exactly - I think this is mixing apples and oranges. BSM/binomial are really valuation tools while p/c parity is an exercise on how to structure derivatives strategies. That being said, I could be missing something so will let smarter folks opine.
And if CFAI starts going down this rabbit hole on the test, I’m toast, so not really focusing on this level of detail. But I doubt they’d go this deep on an already complex topic.
Sorry to keep moving this topic up in the queue, but I think I figured out an answer via a mock I took last night. I stumbled through the answer, but it ended up being correct even though rationale is explained differently (I’ve bolded and underlined relevant data in the vignette for ease of review):
Exhibit 1: Exchange-Traded Options on Pioneer Stock
Maturity X Call Price Call Delta Put Option Price
1-month $40 $2.84 0.54 $2.67
3-month $40 $5.00 0.58 $4.50
6-month $40 $7.14 0.61 $6.15
9-month $40 $8.81 0.63 $7.34
She also concludes that the 9-month put option is mispriced relative to the 9-month call option, and an arbitrage opportunity is possible, but that the 3-month put option is correctly priced relative to its comparable call option.
Is Nolte correct in her analysis of the relative pricing of the 3-month put option and the 9-month put option?
The answer is B and rationale is:
Both the 3-month and the 9-month put options are correctly priced according to put-call parity. Note that you are given the continuously compounded risk-free rate, so you have to use the continuous version of put-call parity.
Therefore, she’s correct that the 3-month put is not mispriced, but incorrect in her conclusion that the 9-month put is mispriced.
I solved it by using BSM and backing into the Nd2 value (and by extension -Nd2 for the put) using the price of the call, spot price, strike, delta (which is Nd1), time to expiration, and risk-free rate. Once you have Nd2, you can use those inputs to solve for what the put price should be. If it’s different from what is listed in the table, you could conclude the option is mispriced relative to the call. So basically, what I think this means is, put/call parity can be used to solve for this type of problem (much easier approach and probably recommended). However, you can use BSM to also get there as calls and puts on the same stock at the same strike / expiration are intrinsically linked (via put/call parity). So you can use the same inputs in BSM for Nd1 and Nd2 with a call to get to what a put w/ same strike and expiration should be trading for. You wouldn’t explicitly set the BSM to the put/call parity, but you could use the same principles of what pricing should be for a given call/put using the corresponding put/call.
Hope that helps / makes sense / is correct line of thinking.
Well, BSM is all about continues compounding. The problem you’re referring to has an arbitrage opportunity because of the difference in compounding risk free vs continuous compound of risk free.
The binomial model just uses general compounding and still wouldn’t have the put value. I stop thinking about this problem, waiting for magicians’ ponder.