This chapter provides the details on Bonds with Embedded Options.
Topics:
· Deterministic Approach for Price Based Strike
· Deterministic Approach for Rate-Based Strike
An option is a contract between a buyer and a seller in which the buyer has the right, but not the obligation, to purchase (in the case of a call option) or sell (in the case of a put option) a specified underlying asset at a specified price during or at the end of a specified period. The option seller, or writer, grants this right in return for the option price, or premium. The option buyer is long the contract; the seller is short.
FSI_D_BORROWINGS, FSI_D_LOAN_CONTRACTS, and FSI_D_INVESTMENTS are the instrument tables that support the embedded options functionality. The indicator in the instruments tables in the EMBEDDED_OPTION_FLG column. The FSI_D_EMBEDDED_OPTIONS table and FSI_D_EMBEDDED_OPTIONS_SCH tables need to be populated for all exercise types. Other relevant tables and the list of values for embedded options are as follows:
· FSI_D_EMBEDDED_OPTIONS
|
Column Name |
Display Name |
Description |
|---|---|---|
|
AS_OF_DATE |
As of Date |
The date at which the data is current, for example, “30-SEP-10” |
|
EXERCISE_TYPE_CD |
Exercise Type Code |
This attribute stores the exercise type code or option style of the embedded option. The list of valid values is 1 (American), 2 (Bermudan), 3 (European). |
|
ID_NUMBER |
ID Number |
Unique record identifier such as account number. |
|
OPTION_START_DATE |
Option Start Date |
This attribute stores the options start date and is valid for the American style of options. |
|
OPTION_TYPE_CD |
Option Type Code |
This attribute stores the option type of the embedded option. The list of valid values is 1 (Call) and 2 (Put). |
|
RATE_LOOKUP_CD |
Rate Lookup Code |
This attribute stores the rate lookup code. Depending upon the rate lookup, the rate of the appropriate term is compared against the strike rate. For instance, if the rate lookup code is Payment Frequency, the Strike IRC term point of payment frequency is compared against the strike rate. List of valid values is 1 (Remaining Term), 2 (Original Term), 3 (Payment Frequency), and 4 (Reprice Frequency). |
|
STRIKE_IRC_CD |
Strike Interest Rate Code |
This attribute stores the coded value of the interest rate curve which is linked to the strike. |
|
STRIKE_TYPE_CD |
Strike Type Code |
This attribute stores the strike type code of the embedded option. A strike type of price assumes that the price of the instrument is used as the strike. A strike type of rate assumes that the interest rate of the instrument is used as the strike. The list of valid values is 1 (Price) and 2 (Rate). |
· FSI_D_EMBEDDED_OPTIONS_SCH
|
Column Name |
Display Name |
Description |
|---|---|---|
|
AS_OF_DATE |
As of Date |
The date at which the data is current, for example, “30-SEP-10” |
|
ID_NUMBER |
ID Number |
Stores Identifier Number. |
|
INSTRUMENT_CODE |
Instrument Code |
Stores the instrument code. |
|
OPTION_EXPIRY_DATE |
Option Expiry Date |
This attribute stores the expiry date of the option. |
|
STRIKE_VALUE |
Strike Value |
This attribute stores the strike rate (for example, entering “3.56” equals 3.56% ) or price (for example, 102.15) depending on the strike type of the option specified in FSI_D_EMBEDDED_OPTIONS. STRIKE_TYPE_CD. |
· FSI_OPTION_DECISION_TYPE_MLS
|
OPTION_DECISION_TYPE_CD |
OPTION_DECISION_TYPE |
Description |
|---|---|---|
|
1 |
Cashflow to Maturity |
Cashflow to Maturity. |
|
2 |
Cashflow to Exp Date |
Cashflow to First Expiry Date. |
|
3 |
Rate Path Dependent |
Rate Path Dependent |
|
0 |
None |
None |
|
OPTION_TYPE_CD |
OPTION_TYPE |
Description |
|---|---|---|
|
1 |
Call |
Call |
|
2 |
Put |
Put |
|
-1 |
None |
None |
· FSI_OPTION_EXERCISE_MLS
|
OPTION_EXERCISE_CD |
OPTION_EXERCISE |
Description |
|---|---|---|
|
1 |
American |
American |
|
2 |
Bermudan |
Bermudan |
|
3 |
European |
European |
· FSI_OPTION_STRIKE_TYPE_MLS
|
OPTION_STRIKE_TYPE_CD |
OPTION_STRIKE_TYPE |
Description |
|---|---|---|
|
1 |
Price |
Price |
|
2 |
Rate |
Rate |
· FSI_OPTION_RATE_LOOKUP_MLS
|
OPTION_STRIKE_TYPE_CD |
OPTION_STRIKE_TYPE |
Description |
|---|---|---|
|
1 |
Price |
Price |
|
2 |
Rate |
Rate |
NOTE:
Floating Rate and Adjustable Rate Instruments are not supported for Bonds with Embedded Options. Embedded options would be ignored and the instrument would be treated as a normal bond.
Embedded Options is only supported for Amortization type code of 700 (Non-amortizing or bullet bond).
For New Business, Embedded Options modeling through Product Characteristics is not supported.
For the deterministic approach, the Cash Flow Engine recognizes the option type, reads the exercise schedule of the Option, checks if the option is exercisable (Callable/Puttable), and outputs the cash flows accordingly.
· Depending on the Call/Put option, the corresponding cash flows are bucketed, the financial measures (market value, Duration, Modified Duration, and YTM) are calculated and the RES_DTL table financial elements are also calculated
The required discount method to use for embedded option valuation is Forecast Remaining Term. The rationale detailed as follows: In the case of fixed-rate instruments when we create different scenarios, the difference in NPV would be from the changes in the discounting IRCs. For OFSALM to support this, spot input, and spot IRC methods cannot be used, as the scenarios created through forecast rates are not applicable. Forecast Remaining Term and Forecast Original Term are the methods that retain the shock scenarios defined as part of the forecast rate scenarios and use them for discounts. However, in the case of Forecast Original Term, all cash flows are always discounted with the original term of the instrument, which would have a significant effect on the bond NPV. So, forecast remaining term in the discount rates rules is the viable solution.
· If the option is exercised, the RESULT_MASTER outputs such as Duration, Modified Duration, and Yield to Maturity are calculated with the cashflows between the as of the date and option exercise date and the maturity amount/call amount. YTM would be the Yield to Call (functional), rather than YTM.
· If the Embedded Option Decisioning is selected as Cashflows to Maturity – none of the FE's of Bonds with Embedded Options would be outputted in the RES_DTL and process cash flows. The process will ignore the embedded option and calculate cashflows to the maturity of the instrument.
A European expiry may be exercised only at the expiry date of the option, that is, at a single pre-defined point in time.
Call Option
· Firstly, the underlying bond has to be priced for the given 'As of Date'.
Description of PCP Formula follows
Where,
it= Interest rate at time t
C = F * c = coupon payment
Where, F = Face Value of the bond
c = Coupon rate
N = number of payments
M = maturity value of the bond
PCP= Clean price of the bond
PDP= dirty price of the bond
LDP = Last Payment Date
AOD = As of Date
· Calculate the present value of the coupon payments during the life of the option. ( Coupon payments between the As of Date and the Option Expiry Date(OED))
Description of formula to calculate the PDP
· Calculate the Bond Forward Price as of the Option Expiry Date
Description of formula to calculate the P Forward-Dirty follows
Where,
T is the Option Expiry Date – As of Date
r is the rate of interest for Option Expiry Date
· Calculate the PForward - Clean as equal to
Description of formula to calculate the P Forward-Dirty follows
· If Strike Price is less than PForward - Clean
then the Call Option can be exercised.
· Market Value when the option on the instrument is exercised is as follows:
Market Value – Dirty is calculated as the sum of Present values of
Coupon cashflows between As of Date and Option Exercise Date
Accrued Interest between Option Exercise Date and next payment date after OED
Option – Strike Price
Market Value – Clean will be the Market Value –Dirty less the Accrued Interest as of the AOD
· Market Value when the option is not exercised: will be the Market Value of the underlying instrument.
Note: If Strike Price is greater than PForward - Clean then the Put Option can be exercised. The rest of the procedure for calculating Put Option is the same as that for Call Option.
A Bermudan option is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. This is intermediate between a European option—which allows exercise at a single time, namely expiry—and an American option, which allows exercise at any time.
The Forward induction method is used for valuing the embedded option in the case of Bermudan expiry. This method would work from the first option expiry date, closest to the as of date, and determine if it is exercisable (in the money) by considering the remaining cash flows to maturity. If not, it would move to the next execution date and again discount the remaining cash flows to maturity. If the option is in the money for an expiration date, the option would be executed, and no further decisioning made.
An American option can be exercised at any time after the options start date and before the option expiry date.
For valuing the embedded option in the case of American expiry, the Bond is treated as a Bermudan Expiry Bond option with Exercise Dates on every bucket start date. Therefore, the more granular the bucket definitions, the more precise the American option decisioning will be.
The rate-Based approach is comparing the Strike Rate against the Strike IRC from the FSI_D_EMBEDDED_OPTIONS table. And, the term selection is a user input – Payment Frequency, Reprice Frequency, Remaining Term of the Instrument, and Original Term of the Instrument.
Depending on the Rate lookup selection by the user, the term is chosen and compared against the Strike Rate.
· Depending on the Strike IRC defined in the EMBEDDED_OPTIONS table and the forecast rules as per the forecast rules definition, the rates are forecasted for Strike IRC.
· Depending on the Rate lookup selection by the user, the term is chosen and compared against the Strike Rate.
· Bucket Rates in which the option exercise date falls are to be used.
For Assets and Liabilities, if the Strike Rate > Forecasted Rate ->Then the instrument is callable.
For Assets and Liabilities, if the Forecasted Rate > Strike Rate -> Then the instrument is Puttable.
Bermudan and American Expiry follow the same approach as the European expiry. Just that the check against the Strike Rate has to be done at all the exercise dates for each of the scenarios defined from the forecast rules.