Actuarial Outpost Does shorted sale plus purchased call equal purchased put?
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#1
01-04-2017, 07:24 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for MFE College: UCSB Posts: 57
Does shorted sale plus purchased call equal purchased put?

You short an asset with a price of \$50. At the same time, your purchase a 6-month call, with an exercise price of \$50, for \$3.25. The effective annual interest rate is 6%. Determine your loss as of the expiration date of the option, when the underlying asset price on that date is \$52.

When I read the problem, I saw "short an asset" and "purchase call", so I immediately thought of this problem as purchased put. I first found the FV of the premium as 3.25 * (1+i) with i being the semiannual rate. Then, since the spot price is \$52, there's no point in selling at \$50, and so there's no gain or loss there. Therefore, I thought the final loss would just be the FV of the premium, but the book did not do this problem as a purchased put. Did I misinterpret something or is my work incorrect? Thanks in advance.
#2
01-05-2017, 01:21 AM
 toesockshoe Member Join Date: Dec 2014 Posts: 227

Quote:
 Originally Posted by mistersunnyd You short an asset with a price of \$50. At the same time, your purchase a 6-month call, with an exercise price of \$50, for \$3.25. The effective annual interest rate is 6%. Determine your loss as of the expiration date of the option, when the underlying asset price on that date is \$52. When I read the problem, I saw "short an asset" and "purchase call", so I immediately thought of this problem as purchased put. I first found the FV of the premium as 3.25 * (1+i) with i being the semiannual rate. Then, since the spot price is \$52, there's no point in selling at \$50, and so there's no gain or loss there. Therefore, I thought the final loss would just be the FV of the premium, but the book did not do this problem as a purchased put. Did I misinterpret something or is my work incorrect? Thanks in advance.
This problem aint got notin' to do with puts (well actually idk but i can solve this and i havent gotten to the put sections yet). it said you purchased a call for 50 and then the price went up to 52. of course the purchaser would stick with the exercise price.... so you are wrong that there is no point in selling at 52 dollars. if you are instead referring to the short, the short position isnt a call/put option... you HAVE to spend the 52 regardless of whether u want to or not.... answer should be 1.86787 loss....
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Last edited by toesockshoe; 01-06-2017 at 02:30 PM..
#3
01-05-2017, 01:28 AM
 Ito's Phlegm Member SOA AAA Join Date: Jan 2015 College: trump university alumni Posts: 11,018

Put Call parity can solve these sorts of questions.

Namely, C-P = Se^(dt) - Ke^(rt)

Yes, it works in real life too. Mostly.
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#4
01-05-2017, 01:45 AM
 toesockshoe Member Join Date: Dec 2014 Posts: 227

Quote:
 Originally Posted by Ito's Phlegm Put Call parity can solve these sorts of questions. Namely, C-P = Se^(dt) - Ke^(rt) Yes, it works in real life too. Mostly.
edited my response accordingly
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#5
01-05-2017, 12:00 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 6,023

Quote:
 Originally Posted by Ito's Phlegm Put Call parity can solve these sorts of questions. Namely, C-P = Se^(-dt) - Ke^(-rt) Yes, it works in real life too. Mostly.
IFYP
#6
01-06-2017, 10:19 AM
 jlavec Member SOA Join Date: May 2016 Posts: 138

To answer your theory question: I believe a written asset + a purchased call should equal a purchased put. I mentally visualized the payoffs for these and it seems right.

To answer the numerical part, it says you shorted the asset for 50. You then MUST buy back the asset at 6 months (remember, this is not an option. You don't have the option to exercise or not. An asset must be bought back if shorted). Since the effective annual interest rate is 6%, we need to convert to 6 months, or half a year, which is 1.06^(1/2). Since we shorted the asset, we receive \$50, which can then be making interest. So, to get the net gain/loss on the asset at 6 months, we have: 50*1.06^(1/2)-52 ~ -.52

We also buy a call for 3.25. We bought the call with a strike price of 50 and its price at 6 months is 52. Since the final price is greater than the strike price, we would exercise the option. But we also spent \$3.25 which could have been making interest at 1.06^(1/2). So the total net gain on the call option is (52-50) - 3.25*1.06^(1/2) ~ -1.35

Add the 2 final products to get -1.35-.52 = -1.87 (which is what toesockshoe got)

Just to note: Although you might be right about how a short asset and long call equals a long put, you're wrong about how you go about this problem. This problem gives you no information about a put. You would need the price of the put, the strike price, the time to maturity, etc... Since you have none of that, you can't solve using a put. Remember to always use what's given and never assume anything unless explicitly stated.
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Last edited by jlavec; 01-06-2017 at 01:37 PM.. Reason: more clarification
#7
01-06-2017, 05:43 PM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for MFE College: UCSB Posts: 57

Ah I see. It looks like I made some erroneous assumptions. Thank you very much guys.
#8
01-06-2017, 09:18 PM
 toesockshoe Member Join Date: Dec 2014 Posts: 227

Quote:
 Originally Posted by mistersunnyd Ah I see. It looks like I made some erroneous assumptions. Thank you very much guys.
just curious... what page are you currently on? I encountered that problem today!
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 Tags call, option, put, short

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