# Valuation of FID

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## Valuation of FID

 Hi, I had placed this question in some other forums, however failed to garner sufficient information till date. Presenting the same here hoping to get some insightful ideas from experts here. Typically in a Bond the Principal is constant over it's life. However I have come across a Bond whose principal is variable, say, average of S&P quote for the last one month and coupon is paid based on that, coupon rate being constant. I was looking for some idea how such bond can be priced? Any idea will be highly appreciated. Thanks and regards, _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Valuation of FID

 Hi Christofer, For this instrument its value today would be the sum of the present value (pv) of its coupons and the pv of its redemption value. You have not specified how the redemption value is determined, so I won't deal with it. Regarding the coupons, you also did not say the rate of the coupon, so let's say that is fixed, say at C (e.g. C=3%). Each coupon appears to be C x (Avg Value of the Index), which seems to be like holding C of an Average Rate Option (with a zero strike price), also called an Average Price option (in this case an Average Price Call). Since each coupon is a position in such an option, the set of coupons is a portfolio of Average Price Calls. Hull and White discuss valuation for such options, including a reference to Kemna and Vorst (1990) who treated the case when the average is calculated as a geometric average and the option is European. Hopefully this provides enough clues for you to take it from here. Best, Eric On Sun, Jun 21, 2020 at 10:47 PM Christofer Bogaso <[hidden email]> wrote: > > Hi, > > I had placed this question in some other forums, however failed to > garner sufficient information till date. Presenting the same here > hoping to get some insightful ideas from experts here. > > Typically in a Bond the Principal is constant over it's life. However > I have come across a Bond whose principal is variable, say, average of > S&P quote for the last one month and coupon is paid based on that, > coupon rate being constant. I was looking for some idea how such bond > can be priced? > > Any idea will be highly appreciated. > > Thanks and regards, > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Valuation of FID

 This sounds more like a swap contract than a bond.  The principal is some quantity of S&P (futures, index value* some initial capital, something). Perhaps look at pricing swaps. On Sun, 2020-06-21 at 23:16 +0300, Eric Berger wrote: > Hi Christofer,For this instrument its value today would be the sum of > the presentvalue (pv) of its coupons and the pv of its redemption > value.You have not specified how the redemption value is determined, > so Iwon't deal with it. Regarding the coupons, you also did not say > therate of the coupon, so let's say that is fixed, say at C (e.g. > C=3%).Each coupon appears to be C x (Avg Value of the Index), which > seems tobe like holding C of an Average Rate Option (with a zero > strikeprice), also called an Average Price option (in this case an > AveragePrice Call). Since each coupon is a position in such an > option, theset of coupons is a portfolio of Average Price Calls. Hull > and Whitediscuss valuation for such options, including a reference to > Kemna andVorst (1990) who treated the case when the average is > calculated as ageometric average and the option is European. > Hopefully this provides enough clues for you to take it from here. > Best,Eric > On Sun, Jun 21, 2020 at 10:47 PM Christofer Bogaso< > [hidden email]> wrote: > > Hi, > > I had placed this question in some other forums, however failed > > togarner sufficient information till date. Presenting the same > > herehoping to get some insightful ideas from experts here. > > Typically in a Bond the Principal is constant over it's life. > > HoweverI have come across a Bond whose principal is variable, say, > > average ofS&P quote for the last one month and coupon is paid based > > on that,coupon rate being constant. I was looking for some idea how > > such bondcan be priced? > > Any idea will be highly appreciated. > > Thanks and regards, > > _______________________________________________R-SIG-Finance@r- > > project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > -- Subscriber-posting only. If you want to post, subscribe first.-- > > Also note that this is not the r-help list where general R > > questions should go. > > _______________________________________________R-SIG-Finance@r- > project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first.-- > Also note that this is not the r-help list where general R questions > should go. -- Brian         [[alternative HTML version deleted]] _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Valuation of FID

 Christofer provided only a sketch of the structure, but presumably it is part of a general class of financial instruments called Structured Notes. There is a very short entry in Wikipedia that gives a bit of a flavor. https://en.wikipedia.org/wiki/Structured_noteStructured notes would normally have a "buyer" who pays the issuer/sponsor when the deal is entered. By contrast, swaps generally have a value of zero at initiation. (Pre the 'big bang' in the CDS market, this was true of CDS swaps also.) On Mon, Jun 22, 2020 at 3:44 PM Brian G. Peterson <[hidden email]> wrote: > > This sounds more like a swap contract than a bond. The principal is some quantity of S&P (futures, index value* some initial capital, something). > > Perhaps look at pricing swaps. > > -- > > Brian > > On Sun, 2020-06-21 at 23:16 +0300, Eric Berger wrote: > > Hi Christofer, > > For this instrument its value today would be the sum of the present > > value (pv) of its coupons and the pv of its redemption value. > > You have not specified how the redemption value is determined, so I > > won't deal with it. Regarding the coupons, you also did not say the > > rate of the coupon, so let's say that is fixed, say at C (e.g. C=3%). > > Each coupon appears to be C x (Avg Value of the Index), which seems to > > be like holding C of an Average Rate Option (with a zero strike > > price), also called an Average Price option (in this case an Average > > Price Call). Since each coupon is a position in such an option, the > > set of coupons is a portfolio of Average Price Calls. Hull and White > > discuss valuation for such options, including a reference to Kemna and > > Vorst (1990) who treated the case when the average is calculated as a > > geometric average and the option is European. > > > Hopefully this provides enough clues for you to take it from here. > > > Best, > > Eric > > > On Sun, Jun 21, 2020 at 10:47 PM Christofer Bogaso > > < > > [hidden email] > > > wrote: > > > Hi, > > > I had placed this question in some other forums, however failed to > > garner sufficient information till date. Presenting the same here > > hoping to get some insightful ideas from experts here. > > > Typically in a Bond the Principal is constant over it's life. However > > I have come across a Bond whose principal is variable, say, average of > > S&P quote for the last one month and coupon is paid based on that, > > coupon rate being constant. I was looking for some idea how such bond > > can be priced? > > > Any idea will be highly appreciated. > > > Thanks and regards, > > > _______________________________________________ > > [hidden email] > >  mailing list > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > -- Subscriber-posting only. If you want to post, subscribe first. > > -- Also note that this is not the r-help list where general R questions should go. > > > _______________________________________________ > > [hidden email] > >  mailing list > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > -- Subscriber-posting only. If you want to post, subscribe first. > > -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Valuation of FID

 Eric, Agreed that this could be constructed as a structured note. In that case there is an initial principal payment, which may be leveraged.  Additionally, the principal may be 'principal-protected', or not. A structured note may be priced like a swap (if the note is not principal protected), or it may be priced with a zero coupon bond and embedded call option (for a principal protected note) or as a more complex structure depending on the waterfall of payments to note holders.  Especially in a leveraged and non-principal-protected structure, the payoffs can be quite complex. As you point out, the OP did not give us [m]any details about the contract specification for what he is trying to price.  So I think we need more specifics to add any more clarity to this thread. -- Brian On Mon, 2020-06-22 at 15:59 +0300, Eric Berger wrote: > Christofer provided only a sketch of the structure, but presumably it > is part of a general class of financial instruments called Structured > Notes. > There is a very short entry in Wikipedia that gives a bit of a > flavor. > https://en.wikipedia.org/wiki/Structured_note> > > Structured notes would normally have a "buyer" who pays the > issuer/sponsor when the deal is entered. > By contrast, swaps generally have a value of zero at initiation. (Pre > the 'big bang' in the CDS market, this was true of CDS swaps also.) > > > On Mon, Jun 22, 2020 at 3:44 PM Brian G. Peterson < > [hidden email] > > wrote: > > This sounds more like a swap contract than a bond. The principal is > > some quantity of S&P (futures, index value* some initial capital, > > something). > > > > Perhaps look at pricing swaps. > > > > -- > > > > Brian > > > > On Sun, 2020-06-21 at 23:16 +0300, Eric Berger wrote: > > > > Hi Christofer, > > > > For this instrument its value today would be the sum of the present > > > > value (pv) of its coupons and the pv of its redemption value. > > > > You have not specified how the redemption value is determined, so I > > > > won't deal with it. Regarding the coupons, you also did not say the > > > > rate of the coupon, so let's say that is fixed, say at C (e.g. > > C=3%). > > > > Each coupon appears to be C x (Avg Value of the Index), which seems > > to > > > > be like holding C of an Average Rate Option (with a zero strike > > > > price), also called an Average Price option (in this case an > > Average > > > > Price Call). Since each coupon is a position in such an option, the > > > > set of coupons is a portfolio of Average Price Calls. Hull and > > White > > > > discuss valuation for such options, including a reference to Kemna > > and > > > > Vorst (1990) who treated the case when the average is calculated as > > a > > > > geometric average and the option is European. > > > > > > Hopefully this provides enough clues for you to take it from here. > > > > > > Best, > > > > Eric > > > > > > On Sun, Jun 21, 2020 at 10:47 PM Christofer Bogaso > > > > < > > > > [hidden email] > > > > > > > wrote: > > > > > > Hi, > > > > > > I had placed this question in some other forums, however failed to > > > > garner sufficient information till date. Presenting the same here > > > > hoping to get some insightful ideas from experts here. > > > > > > Typically in a Bond the Principal is constant over it's life. > > However > > > > I have come across a Bond whose principal is variable, say, average > > of > > > > S&P quote for the last one month and coupon is paid based on that, > > > > coupon rate being constant. I was looking for some idea how such > > bond > > > > can be priced? > > > > > > Any idea will be highly appreciated. > > > > > > Thanks and regards, > > > > > > _______________________________________________ > > > > [hidden email] > > > > > >  mailing list > > > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > > > > > > -- Subscriber-posting only. If you want to post, subscribe first. > > > > -- Also note that this is not the r-help list where general R > > questions should go. > > > > > > _______________________________________________ > > > > [hidden email] > > > > > >  mailing list > > > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > > > > > > -- Subscriber-posting only. If you want to post, subscribe first. > > > > -- Also note that this is not the r-help list where general R > > questions should go. > > _______________________________________________ > [hidden email] >  mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R > questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Valuation of FID

 With the caveat that the exact nature of this instrument is a bit proprietary, Eric's solution quite fit to this pricing problem. I am curious to understand if there is any implementation in R (or other software like python) to price such Average Price Calls option. Thanks, On Mon, Jun 22, 2020 at 7:30 PM Brian G. Peterson <[hidden email]> wrote: > > Eric, > > Agreed that this could be constructed as a structured note. > > In that case there is an initial principal payment, which may be > leveraged.  Additionally, the principal may be 'principal-protected', > or not. > > A structured note may be priced like a swap (if the note is not > principal protected), or it may be priced with a zero coupon bond and > embedded call option (for a principal protected note) or as a more > complex structure depending on the waterfall of payments to note > holders.  Especially in a leveraged and non-principal-protected > structure, the payoffs can be quite complex. > > As you point out, the OP did not give us [m]any details about the > contract specification for what he is trying to price.  So I think we > need more specifics to add any more clarity to this thread. > > -- > Brian > > > On Mon, 2020-06-22 at 15:59 +0300, Eric Berger wrote: > > Christofer provided only a sketch of the structure, but presumably it > > is part of a general class of financial instruments called Structured > > Notes. > > There is a very short entry in Wikipedia that gives a bit of a > > flavor. > > https://en.wikipedia.org/wiki/Structured_note> > > > > > Structured notes would normally have a "buyer" who pays the > > issuer/sponsor when the deal is entered. > > By contrast, swaps generally have a value of zero at initiation. (Pre > > the 'big bang' in the CDS market, this was true of CDS swaps also.) > > > > > > On Mon, Jun 22, 2020 at 3:44 PM Brian G. Peterson < > > [hidden email] > > > wrote: > > > This sounds more like a swap contract than a bond. The principal is > > > some quantity of S&P (futures, index value* some initial capital, > > > something). > > > > > > Perhaps look at pricing swaps. > > > > > > -- > > > > > > Brian > > > > > > On Sun, 2020-06-21 at 23:16 +0300, Eric Berger wrote: > > > > > > Hi Christofer, > > > > > > For this instrument its value today would be the sum of the present > > > > > > value (pv) of its coupons and the pv of its redemption value. > > > > > > You have not specified how the redemption value is determined, so I > > > > > > won't deal with it. Regarding the coupons, you also did not say the > > > > > > rate of the coupon, so let's say that is fixed, say at C (e.g. > > > C=3%). > > > > > > Each coupon appears to be C x (Avg Value of the Index), which seems > > > to > > > > > > be like holding C of an Average Rate Option (with a zero strike > > > > > > price), also called an Average Price option (in this case an > > > Average > > > > > > Price Call). Since each coupon is a position in such an option, the > > > > > > set of coupons is a portfolio of Average Price Calls. Hull and > > > White > > > > > > discuss valuation for such options, including a reference to Kemna > > > and > > > > > > Vorst (1990) who treated the case when the average is calculated as > > > a > > > > > > geometric average and the option is European. > > > > > > > > > Hopefully this provides enough clues for you to take it from here. > > > > > > > > > Best, > > > > > > Eric > > > > > > > > > On Sun, Jun 21, 2020 at 10:47 PM Christofer Bogaso > > > > > > < > > > > > > [hidden email] > > > > > > > > > > wrote: > > > > > > > > > Hi, > > > > > > > > > I had placed this question in some other forums, however failed to > > > > > > garner sufficient information till date. Presenting the same here > > > > > > hoping to get some insightful ideas from experts here. > > > > > > > > > Typically in a Bond the Principal is constant over it's life. > > > However > > > > > > I have come across a Bond whose principal is variable, say, average > > > of > > > > > > S&P quote for the last one month and coupon is paid based on that, > > > > > > coupon rate being constant. I was looking for some idea how such > > > bond > > > > > > can be priced? > > > > > > > > > Any idea will be highly appreciated. > > > > > > > > > Thanks and regards, > > > > > > > > > _______________________________________________ > > > > > > [hidden email] > > > > > > > > >  mailing list > > > > > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > > > > > > > > > > -- Subscriber-posting only. If you want to post, subscribe first. > > > > > > -- Also note that this is not the r-help list where general R > > > questions should go. > > > > > > > > > _______________________________________________ > > > > > > [hidden email] > > > > > > > > >  mailing list > > > > > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > > > > > > > > > > -- Subscriber-posting only. If you want to post, subscribe first. > > > > > > -- Also note that this is not the r-help list where general R > > > questions should go. > > > > _______________________________________________ > > [hidden email] > >  mailing list > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > > > -- Subscriber-posting only. If you want to post, subscribe first. > > -- Also note that this is not the r-help list where general R > > questions should go. > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.