

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 


Thread Tools  Display Modes 
#1




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 6month 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




Quote:
__________________
I want to get a PhD cause I hear you get paid to TA classes. Last edited by toesockshoe; 01062017 at 02:30 PM.. 
#4




edited my response accordingly
__________________
I want to get a PhD cause I hear you get paid to TA classes. 
#5




IFYP

#6




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 (5250)  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.
__________________
Last edited by jlavec; 01062017 at 01:37 PM.. Reason: more clarification 
#8




just curious... what page are you currently on? I encountered that problem today!
__________________
I want to get a PhD cause I hear you get paid to TA classes. 
Tags 
call, option, put, short 
Thread Tools  
Display Modes  

