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Investment / Financial Markets Old Exam MFE Forum

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  #1  
Old 02-08-2017, 06:34 PM
ilikesoldat ilikesoldat is offline
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Default MFE currency option question

Please help!!!

Alright, I'm really confused about this. Been spending all day on it and still can't figure anything out, there's so much things getting jumbled up for me.

If you are given:
Spot exchange rate is 1.5$/pound
Risk-free cont. compounded rate in $ is 6%
Cont. Comp. rate in pounds in 3%
A 6-month dollar-denominated European put option ON pounds with a strike price of 1.5$/pound costs $.03

And you're told to find two things

1.) the premium in pounds of a 6-month pound-denominated european call option ON dollars with a strike of (1/1.5)pounds/dollar
2. the premium in pounds of a 6-month pound-denominated European put option on dollars with a strike of (1/1.5)pounds/dollar

Then, here's what's confusing me to no end:

What does a call option/put option ON dollars/ON pounds mean. Key word: ON. That word is haunting me.

I understand if it's phrased like "a 6-month dollar denominated call option to buy one pound at a strike price of $1.5/pound". Then I know what the call option is doing.

According to the solution, the 6-month dollar-denominated put option ON pounds pays $1.5 for one pound, which is equivalent to a call option ON dollars paying $1.5 per 1 pound. Shouldn't a call option on dollars be, like, purchasing DOLLARS?! If a call option is on an asset, I thought I can be rest assured I'm purchasing that asset by exercising the call??

To put this as clearly as possible, if you were told you have a put option on pounds, would you actually be able to read that as selling $ to get pounds? It seems ultra-counterintuitive, don't know how I'd remember that.

In addition, I would like to know, if the 6 month put option is on pounds, and strike price is 1.5$/pound, how are the arguments filled out? P(1.5$/pound, 1.5$/pound, 1/2)?? This seems weird to me, which argument am I actually selling to get which argument? Typically you're selling the second to get the first, here I don't know how to make sense of this. The manual's solutions has it where they just put P(one currency, other currency, 1/2) and you don't even know how much it is of each.

By the way, it's ASM 9th edition for MFE

Thank you!!!

Last edited by ilikesoldat; 02-08-2017 at 06:56 PM..
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  #2  
Old 02-09-2017, 11:18 AM
Beardown9755 Beardown9755 is offline
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Quote:
Originally Posted by ilikesoldat View Post
Then, here's what's confusing me to no end:

What does a call option/put option ON dollars/ON pounds mean. Key word: ON. That word is haunting me.
The "ON" is standard for call and put options (i.e., a call on a stock, compound options are described as "call on put, call on call, etc.")


Quote:
Originally Posted by ilikesoldat View Post
According to the solution, the 6-month dollar-denominated put option ON pounds pays $1.5 for one pound, which is equivalent to a call option ON dollars paying $1.5 per 1 pound. Shouldn't a call option on dollars be, like, purchasing DOLLARS?! If a call option is on an asset, I thought I can be rest assured I'm purchasing that asset by exercising the call??
All of this seems correct. Due to option duality: P(S, K, T)=C(K, S, T). The call is an option to give up S at time T in order to get K; the put is the option to give up S to get K. Thus in this context: P(1pound, $1.5, .5)=C($1.5, 1pound, .5). I've found that these concepts can get confusing if you focus too much on phrases like "option to buy" and "option to sell" fwiw.

The call option on dollars is an example of buying $1.5 for giving up 1 pound.


Quote:
Originally Posted by ilikesoldat View Post
To put this as clearly as possible, if you were told you have a put option on pounds, would you actually be able to read that as selling $ to get pounds? It seems ultra-counterintuitive, don't know how I'd remember that.
Whenever I encounter problems of this type I write them out in option notation, so this option would be P(1pound, $X, T). Then convert it to a call [C($X, 1pound, T)] through duality or think through what's being exchanged in the put. The underlying asset is 1 pound (just as S is the underlying asset in P(S, K, T)), and for a put you have the option to receive the strike for the asset, so you are not selling, i.e., giving up, dollars; you're selling (or giving up) pounds for dollars.

Quote:
Originally Posted by ilikesoldat View Post
In addition, I would like to know, if the 6 month put option is on pounds, and strike price is 1.5$/pound, how are the arguments filled out? P(1.5$/pound, 1.5$/pound, 1/2)?? This seems weird to me, which argument am I actually selling to get which argument? Typically you're selling the second to get the first, here I don't know how to make sense of this. The manual's solutions has it where they just put P(one currency, other currency, 1/2) and you don't even know how much it is of each.
For a Put option you aren't "selling the second"; you'd be selling the first term, e.g., P(S,K,T) means that you have the option to sell the stock for K.

As for the "on dollars" I'm not entirely sure why the text uses "dollars" instead of "a dollar".

I hope that helps.
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  #3  
Old 02-09-2017, 02:43 PM
ilikesoldat ilikesoldat is offline
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Thanks for your help. However, are you sure you wrote all that correctly?

Quote:
Originally Posted by Beardown9755 View Post

All of this seems correct. Due to option duality: P(S, K, T)=C(K, S, T). The call is an option to give up S at time T in order to get K; the put is the option to give up S to get K. Thus in this context: P(1pound, $1.5, .5)=C($1.5, 1pound, .5). I've found that these concepts can get confusing if you focus too much on phrases like "option to buy" and "option to sell" fwiw.

The call option on dollars is an example of buying $1.5 for giving up 1 pound.
First part that was confusing is you wrote P(S,K,T)=C(K,S,T), which while that is true you proceeded to explain that The call you give up S to get K, and the put you give up S to get K. Looking at the order you wrote the notation in on each side of the equation I agree... but now... later you go on to say "in this context: P(1pound, $1.5,.5) = C($1.5, 1 pound, .5)". In this context, shouldn't it be P($1.5, 1pound, .5)??? And C(1pound, $1.5, .5)???

Later, you go on to say

"I write them out in option notation, so this option would be P(1pound, $X, T)." Well by the way you just said of how you do it, it would be P($, pounds, T), otherwise you are indeed selling pounds to get dollars, which is my original problem in the first place. Reading put option on pounds makes me think you're selling pounds to get $, and it seems you did the same exact thing as me.

Are you sure you fully know how to understand put ON pounds? And call option ON dollars? I would think the "ON" is the underlying asset, the first argument, but it happens to be the second argument (kind of like you yourself started filling it out). Should I just cope with the fact that "ON" something always means its the second argument?

Hope I didn't confuse you further, haha don't want to drag you into this like I dragged myself into it. But there's definitely some extra confusion here, and I think even you made some errors.

Now, ignore this until you are done with your response (if you do respond haha). But, imagine an extra layer of confusion when the textbook states put option on pounds and strike is ($1.5/pound). Seems to clarify things right? But what if, what IF the textbook said put option on pounds and strike is 1/1.5(pounds/$)? Well now I'd be confused. Is the put on one pound, a different amount, or perhaps the put is now in fact returning dollars if exercised?

And just to be clear, the textbook does do this. Look at the first question. Call option on dollars with a strike of (1/1.5)pounds/$. So, seems like you would be spending 1/1.5 pounds to get a $, when in fact this call option is receiving POUNDS!!!

EDIT: to make matters more "interesting", in the solution to the second question (a put on dollars), the notation is P($,pounds,1/2) LOL.

FINAL EDIT: Ok, I did some extra thinking about it all. The solution manual had one bit in there that was throwing me off. It's so easy to get confused off of a mistake like that, but this has never, ever happened to this degree before in my life. Basically, a put on pounds is definitely P(pounds, $, 1/2). A call on $ is definitely C($, pounds, 1/2). But an error in the manual confused the living daylights out of me. Thanks for your help

Last edited by ilikesoldat; 02-09-2017 at 03:23 PM..
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  #4  
Old 02-09-2017, 06:37 PM
Beardown9755 Beardown9755 is offline
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Sorry for muddying the waters further. I'd hope to clarify the matter, not add to the confusion! But I think my original post was correct even if it wasn't clear.


Quote:
Originally Posted by ilikesoldat View Post
Thanks for your help. However, are you sure you wrote all that correctly?

First part that was confusing is you wrote P(S,K,T)=C(K,S,T), which while that is true you proceeded to explain that The call you give up S to get K, and the put you give up S to get K. Looking at the order you wrote the notation in on each side of the equation I agree... but now... later you go on to say "in this context: P(1pound, $1.5,.5) = C($1.5, 1 pound, .5)". In this context, shouldn't it be P($1.5, 1pound, .5)??? And C(1pound, $1.5, .5)???
From option duality, both of the following are true:

P(1pound, $1.5, .5)=C($1.5, 1pound, .5)
P($1.5, 1pound, .5)=C(1pound, $1.5, .5)

When I referred to the first equation "in this context" it was because you'd noted the problem stated a put on pounds was the same as a call on dollars. I was just trying to show that the manual's solution made sense.

I think my use of P(S,K,T)=C(K,S,T) made the matter less clear.




Quote:
Originally Posted by ilikesoldat View Post
Are you sure you fully know how to understand put ON pounds? And call option ON dollars? I would think the "ON" is the underlying asset, the first argument, but it happens to be the second argument (kind of like you yourself started filling it out). Should I just cope with the fact that "ON" something always means its the second argument?
I agree; the "ON" is the underlying asset, i.e., the first argument of the function.
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  #5  
Old 02-09-2017, 06:50 PM
Beardown9755 Beardown9755 is offline
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Quote:
Originally Posted by ilikesoldat View Post
Now, ignore this until you are done with your response (if you do respond haha). But, imagine an extra layer of confusion when the textbook states put option on pounds and strike is ($1.5/pound). Seems to clarify things right? But what if, what IF the textbook said put option on pounds and strike is 1/1.5(pounds/$)? Well now I'd be confused. Is the put on one pound, a different amount, or perhaps the put is now in fact returning dollars if exercised?
I too think that exchange options can have awkward and odd wording, but I think if you can keep straight what the underlying asset is, things get clearer. For example, the wording of the strike price seems weird, but an exchange rate of 1/1.5(pounds/$) is the same as the rate $1.5/pound, so why does it matter which form it's written in? As long as you know what the underlying asset is, it shouldn't matter.
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