Financial Rate Products

  1. GIC Pooling

Guaranteed investment certificate provides investors a guaranteed interest rate for a fixed amount time. Interest is accrued daily on GIC. Accrued interest will be reported annually

Science gic pooling

Gitbook gic pooling

Core gic

2. Quanto Himalayan Option

Himalayan options are a form of European-style, path-dependent, exotic option on a basket of equity underliers, in which intermediate returns on selected equities enter the payoff, while the equities are subsequently removed from the basket.

Science quanto Himalayan

Gitbook quanto Himalaya

Core QH

3. Local Volatility Model for Callable Quanto Option

We review a model for computing the price, in the domestic currency, of European standard call and put options on an underlying foreign equity (stock or index) with tenor of up to 7 years. The function implements a local volatility based pricing method.

Science local quanto

Gitbook local quanto

Core quanto

4. Forward Starting Option

Forward start option is an option whose strike will be determined at some later date. Unlike a standard option, the strike price is not fully determined until an intermediate date before expiration. Cliquet option consists of a series of forward start options.

Science forward starting

Gitbook forward starting

Core start

5. Three Factor Convertible Bond

The owner of a convertible bond (CB) receives periodic coupon payments from the issuer, but can also convert the CB into the issuer’s stock.  The convertible bond may also include call and put provisions, which respectively allow the issuer to buy back the convertible bond and the owner to put the convertible bond for respective preset amounts. 

Science 3-factor

Gitbook 3-factor

Core convertible

6. Mutual Fund Securitization

The purpose of the model is to determine, from a projected stream of future cashflows, whether all Commercial Paper used to fund the commissions to brokers for the sale of mutual funds will be repaid within a period.  Here a broker charges the Partnership a commission on the net asset value of the mutual funds sold.  The buyer of the mutual funds, however, pays nothing up front; instead, a deferred sales charge, which depends on when the mutual funds are redeemed, is assessed.

Archive mutual fund

Gitbook mutual fund

Core mf

7. Hull-White Convertible Bond Model

A convertible bond pays the holder periodic coupon payments from the issuer, but can also convert it into the issuer’s stock.  The model uses a two-factor trinomial tree for pricing the convertible bond, where the two factors are

  • the short term interest rate and
  • the issuer’s stock price.

Science hw convertible

Gitbook hw convertible

Core convertbile

8. Brownian Bridge

The Brownian bridge algorithm has been implemented for stress testing within the Risk Management framework. It is used for generation of multidimensional random paths whose initial and ending points are predetermined and fixed.

Archive BB

Gitbook BB

Core BB

9. Exchangeable Convertible Bond

A convertible bond issuer pays periodic coupons to the convertible bond holder. The bond holder can convert the bond into the underlying stock within the period(s) of time specified by the conversion schedule. The bond issuer can call the bond and the holder can put it according to the call and put provisions.

Science exchangeable convertible

Gitbook exchangeable convertible

Core bond

10. Asset Backed Senior Note

We consider a securitization deal, which allows the holder to purchase co-ownership interests in a revolving pool of credit card receivables. To fund the acquisition of the interests in the revolving pool, the trust issued Asset-Backed Notes, in a number of different series. A share of future collections of credit charge receivables, to which the trust is entitled, is used to pay the interest and the principal of the notes.

Archive abs

Gitbook ABS

Core ABS

11. Hull White Volatility Calibration

Hull White model is a short rate model that is used to price interest rate derivatives, such as Bermudan swaption and accumulator exotics. We map implied Black’s at the money (ATM) European swaption volatilities into corresponding Hull-White (HW) short rate volatilities.

Science HW vol

Gitbook HW vol

Core vol

12. Bond Curve Bootstrapping

We discuss a method for bootstrapping a set of zero rates from an input set of US government money market securities and bonds. The government bond bootstrapping procedure requires to input a set of financial instruments, of the type below, sorted by order of increasing time to maturity:

Science bond curve

Gitbook bond curve

Core curve

13. GIC Pricing

Guaranteed investment certificate (GIC) is a financial instrument that offers a return based on a corresponding GIC rate and the performance of a basket of certain stock and bond market indices.

Science gic pricing

Gitbook gic pricing

Core gic

14. Extendable Swap

An extendable swap represents a forward swap agreement with an option of extending the swap for another term (swaption). Other irregular swaps include accumulator swap

Science extendable swap

Gitbook extendable swap

Core swap

15. Callable Inverse Swap

A Callable Inverse Floating Rate Swap is a forward swap agreement with an option of canceling the swap each year starting from several years in future. The deal is priced with a two factor Black-Karasinski model.

Science callable inverse

Gitbook callable inverse

Core callable

16. Flexible GIC

A flexible GIC is an investment with an embedded option to redeem the principal and accrued interest at any time after 30 days from the date of purchase. In other words, the holder of GIC has an option to redeem the principal and accrued interest at any time after 30 days of from the date of purchase. No interest is paid if the investment is redeemed within first 30 days from the purchase date.

Science flexible gic

Gitbook flexible gic

Core flexible

17. American Bond Option

A valuation model is presented for pricing an American style call option on the yield of Treasury bond. The payoff is positive if the yield exceeds a predetermined strike level. The model assumes the yield of an American Treasury bond to be a log-normally distributed stochastic process and uses Monte-Carlo simulation to price the deal as a European call option.

Science American Bond

Gitbook American Bond

Core bond

18. Martingale Preserving Tree

An important feature of the popular three factor trinomial tree is that it uses a deterministic approximation of the interest rates for constructing the stock tree. The preservation of the martingale property of the stock price is thus not guaranteed.  and may potentially represent a problem.

Science tree

Gitbook tree

Core tree

19. Arrear Quanto CMS

An arrear quanto constant-maturity-swap (CMS) is a swap that pays coupons in a different currency from the notional and in arrears. The underlying swap rate is computed from a forward starting CMS.

Science arrear cms

Gitbook arrear cms

Core option

20. Black-Karasinski Short Rate Tree

The Black-Karasinski model is a short rate model that assumes the short-term interest rates to be log-normally distributed. We implement the one factor  Black-Karasinski model as a binomial or trinomial tree.

Science BK tree

Gitbook BK tree

Core tree

21. Variable Rate Swap

Variable rate swap is a special type of interest rate swap in which one leg of the swap corresponds to fixed rate payments while the other involves fixed rate payments for an initial period of time and a floating rate for the rest. The floating rate on that portion is defined as a minimum of two index rates.

Science variable swap

Gitbook variable swap

Core swap

22. CMS Spread Option

A constant maturity swap (CMS) spread option makes payments based on a bounded spread between two index rates (e.g., a GBP CMS rate and a EURO CMS rate).  The GBP CMS rate is calculated from a 15 year swap with semi-annual, upfront payments, while the EURO CMS rate is based on a 15 year swap with annual, upfront payments.

Science cms option

Gitbook cms option

Core option

23. Early Start Swap

An early start swap is a swap that has an American style option for the counterparty of starting the swap early, within a period of three month. Otherwise, the swaps are plain vanilla fixed-for-floating swaps.

Science early swap

Gitbook early swap

Core swap

24. Quanto Total Return LIBOR Swap

A quanto total return Libor Swap is a swap where one leg is a regular floating leg paying LIBOR less a constant spread and the other leg makes a single payment at the swap’s maturity equal to a leveraged non-negative return on USD-for-EURO exchange rate paid in CAD. The main focus of the valuation model is the quantoed total return on the FX rate.

Science quanto trs

Gitbook quanto trs

Core correlation

25. Daily Digital LIBOR Swap

A daily digital LIBOR swap is an interest rate swap whose reference interest rate is three-month USD Libor BBA. For each accrual period in the swap, one party receives the reference rate, and pays the reference rate plus a positive spread, but weighted by the ratio of the number of calendar days in the period that the reference rate sets below an upper level to the total number of calendar days in the period.

Science daily digital

Gitbook daily digital

Core digital

26. Ratchet Swap

A ratchet swap is an interest rate swap with two legs. One leg is a standard floating leg and the other leg is a ratchet leg. The ratchet leg pays a ratchet floating rate.

The ratchet floating rate coupon is based on an index, e.g., 6-month EURIBOR. The rate is further subject to a minimum decrease of 0 bps and a maximum increase of a threshold, such as, 15 bps. These rates are reset two business days prior to the first day of each coupon period.

Science ratchet swap

Gitbook ratchet swap

Core fx swap

27. LIBOR Rate Model

LIBOR Rate Model is used for pricing Libor-rate based derivative securities. The model is applied, primarily, to value instruments that settle at a Libor-rate reset point.  In order to value instruments that settle at points intermediate to Libor resets, we calculate the numeraire value at the settlement time by interpolating the numeraire at bracketing Libor reset points.

Science libor model

Gitbook libor model

Core ois