Serving the Quantitative Finance Community

 
User avatar
donal
Topic Author
Posts: 2
Joined: April 14th, 2010, 1:53 pm

Valuing a tricky Equity linked note

November 5th, 2011, 9:50 am

Hi all,Currently looking at a structure with a few features which are leaving me a little stuck in terms of how to value. Your thoughts would be much appreciated.Product is an investment in a fund which invests in various equities. You invest 100 in the fund, receive 100% capital protection and participate in 65% of the positive performance of the share basket. Now, there are two elements that are causing me difficulties: (1) there is no maturity on the investment i.e. In theory could be held indefinately, and (2) is puttable by the holder at any time.If there was a maturity then I would price as a callable note linked to a basket. With no maturity, I am somewhat unsure what to do from a theoretical perspective, as I'm left with a perpetual, callable equity linked note.Thanks in advance for any suggestions.Cheers,Donal
 
User avatar
daveangel
Posts: 5
Joined: October 20th, 2003, 4:05 pm

Valuing a tricky Equity linked note

November 5th, 2011, 10:02 am

i think the principal protection bit is just a CPPI structure. What price is it puttable at ?
knowledge comes, wisdom lingers
 
User avatar
donal
Topic Author
Posts: 2
Joined: April 14th, 2010, 1:53 pm

Valuing a tricky Equity linked note

November 5th, 2011, 10:06 am

If you put it back then you get your original 100 plus 65% of the basket performance if positive.
 
User avatar
daveangel
Posts: 5
Joined: October 20th, 2003, 4:05 pm

Valuing a tricky Equity linked note

November 5th, 2011, 10:54 am

I am incorrect - its not a CPPI. i thought the buyer of the fund has limited capital protection down to 65%.
knowledge comes, wisdom lingers
 
User avatar
list
Posts: 0
Joined: October 26th, 2005, 2:08 pm

Valuing a tricky Equity linked note

November 5th, 2011, 11:43 am

QuoteOriginally posted by: donalIf you put it back then you get your original 100 plus 65% of the basket performance if positive.For example, let a basket has two assets S1 (t) = 100 , S2 (t) = 10 and S1 (t+1) = 80 , S2 (t +1) = 20. Then at t+1 the price of the basket is guaranteed ( if put applied ) to be 110 + 10 =120.Here 110 is original basket price qnd 10 is the gain of the second asset. The problem is how much one should pay for such protection?
Last edited by list on November 4th, 2011, 11:00 pm, edited 1 time in total.
 
User avatar
Alan
Posts: 3050
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

Valuing a tricky Equity linked note

November 5th, 2011, 1:51 pm

QuoteOriginally posted by: donalHi all,Currently looking at a structure with a few features which are leaving me a little stuck in terms of how to value. Your thoughts would be much appreciated.Product is an investment in a fund which invests in various equities. You invest 100 in the fund, receive 100% capital protection and participate in 65% of the positive performance of the share basket. Now, there are two elements that are causing me difficulties: (1) there is no maturity on the investment i.e. In theory could be held indefinately, and (2) is puttable by the holder at any time.If there was a maturity then I would price as a callable note linked to a basket. With no maturity, I am somewhat unsure what to do from a theoretical perspective, as I'm left with a perpetual, callable equity linked note.Thanks in advance for any suggestions.Cheers,DonalIf those were truly the terms, why is it not an arbitrage opp? I will guess the answer is that there are additional terms that you have not disclosed, such as a very risky counter-party or a minimum holding period, or various fees, etc.
 
User avatar
list
Posts: 0
Joined: October 26th, 2005, 2:08 pm

Valuing a tricky Equity linked note

November 5th, 2011, 2:56 pm

QuoteOriginally posted by: listQuoteOriginally posted by: donalIf you put it back then you get your original 100 plus 65% of the basket performance if positive.Let us assume for simplicity the portfolio can be exercised at discrete moments. Then on the algebraic level the value of the portfolio can be represented as P ( t ) + I {P = t + 1}0.65q ( t + 1 ) + ... + I {P = t + k} 0.65q ( t + k ) + ... where P ( t ) is the value of the portfolio at t ,I { P = t + k} is the indicator that put to the portfolio will be applied at t + k ,q ( t + k ) = max{ 0 , P ( t + k ) - P ( t ) } The market value of the premium is 0.65*[ B( t , t + 1)q ( t + 1 ) + ... + B(t , t + k} q ( t + k ) + ... ]To specify model we need to specify conditions when put would be applied, then to make an assumption about portfolio dynamics, and say something about value of risk that could not be admitted. The the calculated upfront coupon will be conditioning on these assumptions.It might be more reasonable to design floating periodic payments that under some conditions can be stopped. It is possible that it would decrease risk. For example let your assets are Greek's bonds of different maturities? No one can say something reasonable what will happen in 2-5 years ahead.
Last edited by list on November 4th, 2011, 11:00 pm, edited 1 time in total.
 
User avatar
daveangel
Posts: 5
Joined: October 20th, 2003, 4:05 pm

Valuing a tricky Equity linked note

November 5th, 2011, 3:51 pm

what about thisfund = 0.65 * spot + perpetual american put struck @ 100 ?
knowledge comes, wisdom lingers
 
User avatar
list
Posts: 0
Joined: October 26th, 2005, 2:08 pm

Valuing a tricky Equity linked note

November 5th, 2011, 4:17 pm

QuoteOriginally posted by: daveangelwhat about thisfund = 0.65 * spot + perpetual american put struck @ 100 ?0.65*(of the positive performance at the date of put exercised ) ?
 
User avatar
ppauper
Posts: 11729
Joined: November 15th, 2001, 1:29 pm

Valuing a tricky Equity linked note

November 7th, 2011, 10:49 am

so if the price of the basket is B, and we say that the initial basket price is 100, the payoff is 100+.65*max(B-100,0)perpetual zero coupon floating rate note paying 100 (and therefore worth 100) combined with a perpetual American option paying .65 max(B-100)Is this for work or a school project ?If it's just a school project, I'd price the perpetual floating rate option using the time-independent BS equation, and the way to do that is in Professa' Wilmott's books