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EdwinAfitile
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Arbitrage conditions in Put Call Parity with a Structured Product

September 26th, 2016, 5:22 pm

P  + K = Bond + Call, however when we consider a structured product where participation in an Index can be as great as 120% of the Index in a Call Option, this does not hold. The implication is that P + K < Bond Call?
Am I wrong here?
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 26th, 2016, 8:15 pm

A classically defined put/call parity is a very robust concept, so alleged violations usually come down to mis-interpretation, most often of the forward price and/or the discount factor. So, a put and a call struck at the forward price should have the same value. For a general strike, a portfolio that is long a call, short a put (of that same strike) and short a forward will produce a payout at maturity that is identical to that of a (long or short) zero coupon bond, and should therefore be relatively easy to value. If you have leverage involved in the options, you just need to apply it consistently to all the relevant components.
 
EdwinAfitile
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 26th, 2016, 9:02 pm

 Thanks Bearish, however when the Index Option has that high participation it is not possible to secure the leverage on the Put, especially because the put and the call will usually have different strike prices
 
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bearish
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 27th, 2016, 1:08 am

Then why are you talking about put/call parity?
 
EdwinAfitile
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 27th, 2016, 2:45 pm

I have attached my working sheet. In sheet one BS Pricer I show how the ELN (written Call) returns the highest performance. Since for my example the strikes are the same, this violates Put - Call parity.

I am wondering if someone can help me introduce leverage into the Put + Fund side to try and see if it can't equal the ELN?
Attachments
Structured Product.xlsm
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list1
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Joined: July 22nd, 2015, 2:12 pm

Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 27th, 2016, 10:25 pm

P  + K = Bond + Call, however when we consider a structured product where participation in an Index can be as great as 120% of the Index in a Call Option, this does not hold. The implication is that P + K < Bond Call?
Am I wrong here?
I could not understand the equality P + K = Bond + Call if we put the time moment be equal expiration date T assuming that put, call and bond expirations are equal to T
 
EdwinAfitile
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Joined: September 5th, 2016, 12:22 pm

Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 28th, 2016, 6:43 am

Hi List, I cannot understand what you are saying
 
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list1
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 28th, 2016, 4:18 pm

P  + K = Bond + Call, however when we consider a structured product where participation in an Index can be as great as 120% of the Index in a Call Option, this does not hold. The implication is that P + K < Bond Call?
Am I wrong here?
I could not understand the equality P + K = Bond + Call if we put the time moment be equal expiration date T assuming that put, call and bond expirations are equal to T
At T that is expiration for put, call, and bond equality P  + K = Bond + Call  should be transformed to   max{ K  - S ( T ) , 0 } + K = 1  + max { S ( T ) - K , 0 } . Such identity does not obvious and looks rather wrong. In order to verify it we should consider two scenarios : K > S ( T ) and  inverse one. If we see equality of both parts the formula is correct otherwise one should recognize that formula incorrect.
 
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outrun
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 28th, 2016, 5:39 pm

Replace S(t) with the bond, the bond matures *after* the option expiration date?
 
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list1
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Re: Arbitrage conditions in Put Call Parity with a Structured Product

September 28th, 2016, 9:45 pm

Replace S(t) with the bond, the bond matures *after* the option expiration date?
Let To < T b  be options and bond expirations then the put-call parity formula at To is equal to
 max{ K  - B ( To , Tb ) , 0 } + K  =  B ( To , Tb ) + max { B ( To , Tb ) - K , 0 }
which also does not obvious true one. It might be correct if K on the left put on the right and B ( To , Tb )  from the right place in the left hand side.