# Interest Rate Derivatives Knowledge

1. Amortizing Floor Option

An amortizing floor option consists of 12 floorlets, or put options, on the arithmetic average of the daily 12-month Pibor rate fixings over respective windows of approximately 30 calendar days.  Furthermore the notional amount corresponding to each floorlet is specified by an amortization schedule.

Science floor

Gitbook floor

ResearchGate floor pdf

ResearchGate floor

2. Single Currency Bermudan Swaption

The underlying security of a single currency Bermudan swaption is an interest-rate swap, which is specified by respective payer and receiver legs.  Each of the legs above can pay a fixed rate, Libor or CMS rate.  The owner of the Bermudan swaption can choose to enter into the swap above at certain pre-defined exercise times

Science Bermudan

Gitbook Bermudan

ResearchGate Swaption pdf

ResearchGate Swaption

3. Arbitrary Cash-Flow

An Arbitrary Cash-Flow (ACF) security interface values future known cash-flows. These cash-flows must be in a single (potentially foreign) currency. The present value of these cash-flows is determined by prevailing market interest and foreign exchange rates.

Science arbitrary cf

Gitbook arbitrary cf

Core flow

4. Partial Payoff Swap

Partial payoff swap pays periodically, the payoff from a particular European style put option on the spread between respective ten and two-year CMS rates. Moreover, this payoff is algebraically equivalent to the sum of the spread above and the payoff from a related European style put option.

Science partial swap

Gitbook partial swap

ResearchGate swap pdf

ResearchGate swap

A method is presented to calculating a particular multiplicative factor, which appears in a formula for a CMS rate convexity adjustment.  A CMS rate convexity adjustment provides a correction term to the forward CMS rate to match the mean value of the CMS rate under the forward probability measure.

Science cms convexity

Gitbook cms convexity

ReserchGate coupon pdf

6. Inflation Swap, Cap and Floor

A model is presented for pricing swaps, caps, and floors on inflation index returns. To capture general term structures of interest rates and index volatilities, the model requires time-averaged forward rate, and volatility inputs.

Science inflation products

Gitbook inflation products

ResearchGate option

7. GIC Option

The GIC price is the sum of the price of closed GIC and the price of a put option with time-varying strike.

We assume that the GIC holder receives deterministic payments at the specified payment dates and observe how the redemption option price changes due to changes in the number of the HW tree time slices.

Science gic option

Gitbook gic option

An algorithm is presented for bootstrapping a discount factor curve. The bootstrapping procedure uses an input set of instruments with different maturities (i.e., Canadian government money market securities and bonds) to generate successive points on a discount factor curve.

ResearchGate bond pdf

ResearchGate bond

9. American Swaption

If an American swaption is exercised at a point that is not a reset date, in practice, the effective Libor rate at the point of exercise is a blended rate, which is linearly interpolated from a pair of Libor rates with respective accrual periods that bracket the remaining time interval to the next reset date.  The effective Libor rate at the exercise point is taken to be the simple interest rate implied from the zero-coupon bond price to the next reset date.  This treatment represents a compromise between accuracy and computational efficiency, since it avoids having to determine bracketing Libor rate values.

Science American swaption

Gitbook American swaption

ResearchGate cds pdf

ResearchGate cds

10. Cancelable Swap

A pricing model is presented for pricing cancelable fixed-for-floating interest rate swap.  Here, party A makes regular payments that depend on the average level of a Libor rate over a set of Asian observation points, while party B makes upfront fixed rate payments.

Science cancelable swap

Gitbook cancelable swap

ResearchGate swap pdf

ResearchGate swap

11. GIC Redemption Option Sensitivity

Redeemable GIC is a GIC where one month after inception till maturity (up to 7 years), the holder has an option to redeem the principal and accrued interest less a penalty based on the “call” rate specified by the exercise schedule; the schedule may include up to six contiguous windows with individual call rates.

Science gic Greeks

Github gic Greeks

ResearchGate option pdf

ResearchGate option

12. Swap Average Term

The average term is calculated for a swap that underlies a European style payer swaption, which is in the calibration portfolio for a Bermudan swaption with amortizing notional (i.e., the outstanding notional is reduced from time-to-time). Given the payer swaption maturity and the average swap term pair, we then look up, from a table indexed by payer swaption maturity and underlying swap term, the corresponding Black’s implied volatility.

Science swap average term

Gitbook swap average term

13. GIC Coupon Rate

We calculate the Treasury transfer coupon rate, in the case of zero coupon payment frequency, or the equivalent annualized simple rate in the case of non-zero coupon payment frequency, from which the transfer coupon rate.

Science gic coupon

Gitbook gic coupon

14. Multi-currency BGM

The Brace-Gatarek-Musiela (BGM) model is a multi-factor log-normal model. This model applies to both currencies. Its principle is to fix a tenor , for instance 3 months, and to assume that each Libor rate at date , has a log-normal distribution in the “forward-neutral” probability of maturity . The present model uses 4 factors, which we may assume independent.

Science bgm

Gitbook bgm

15. BGM Monte Carlo Simulation

Brace-Gatarek-Musiela (BGM) model, also called LIBOR Market Model, is a multi-factor log-normal model for pricing interest rate derivatives. The model is usually solved by Monte Carlo simulation.

Science MC BGM

Gitbook MC BGM

16. Pricing FX Option via BGM

The interest rate diffusion refers to the Brace-Gatarek-Musiela (BGM) model that is a multi-factor log-normal model. The model is used for pricing interest rate and FX derivatives. The method directly models the movement of the whole yield curve through the dynamics of correlated spanning forward LIBOR rates. This feature gives the BGM model much more flexibilities to model the correlation among the rates on the whole yield curve.

Science FX BGM

Gitbook FX BGM

17. Local Volatility Greeks

Calculation of the Greeks in the local volatility model is difficult because recalibrating the local volatility surface tends to result in high numerical error terms. While this appears to be OK for first order Greeks, for higher order Greeks we are forced to make some approximations. Here is the full list of Greeks.

Science local vol Greeks

Gitbook local vol Greeks

18. Variable Rate MBS

The variable rate mortgage (VRM) has provisions that allow the mortgagor to convert his mortgage, without penalty, to a fixed rate mortgage. Consequently, VRM MBS are subject to an additional source of early principal repayment.

Science variable mbs

Gitbook variable mbs

19. Credit Risk Calculator

The purpose of the credit risk calculator is to ensure that the expected loss that can occur from the guarantor’s (CMHC’s) perspective is covered by the guarantee fee. From CMHC’s perspective, the risk of loss will occur if an AAA/AA swap counterparty fails instantaneously without any rating migration to a lower state (i.e., AA to A). Under a normal rating migration, the swap counterparty to the Trust would have to collateralize its exposure.

Science credit risk

Gitbook credit risk

20. Variable Rate Mortgage-Backed Security

The Canada Housing Trust (“CHT”) will raise funds by issuing Canada Mortgage Bonds and use the proceeds to purchase VRMBS’s from Approved Sellers. For each VRMBS purchased CHT will also enter into a swap, where it pays the MBS interest and reinvestment income to the swap counterparty and receives fixed coupon cashflows, which are used to service the CMB. CHT will also pay CMHC an up-front guarantee fee for each CMB issuance. In return CMHC provides a guarantee for the CMB’s.

Science variable mbs

Gitbook variable mbs

21. Mutual Fund Cash Flow

A model for the balance between the expenses to pay back amortizing notes and the income from fees generated by mutual funds is presented. We provide two basic models, one static and the other dynamic, for the performance of the mutual fund fees. The static model assumes that the Net Asset Value (NAV) of the mutual fund grows at a predetermined rate. The alternative model assumes that the growth rate of the NAV varies either.

Science mutual fund cash

Gitbook mutual fund cash

22. Prepayment Neural Net

A model of mortgage prepayment rates based on the neural net approach is proposed. The model for insured, closed, five-year term mortgages has been developed. The neural net prepayment model behaves consistently across the training and testing sets and outperforms a simpler predictor, the linear regression model.

Science prepayment

Gitbook prepayment

23. Liquidation Rate MBS

We calculate the price of an MBS based on future cashflows that are assumed to be deterministic. One of the factors affecting future cashflows is a liquidation rate. In its current implementation the user has two options for specifying a liquidation rate, that is, it can be assumed to be constant or vary deterministically according to a Standard Vector prepayment model.

Science liquidation MBS

Gitbook liquidation MBS

24. Mortgage Pool

A model is presented for the calculation of the fair value and the hedge ratios, Delta, Vega and Gamma, with respect to pools of Canadian commercial and residential mortgages. Commercial mortgages are closed and either insured or not insured, while residential mortgages are separated into

Science mortgage pool

Gitbook mortgage pool

25. Seller Swap

One party sells mortgage pools on its balance sheet and pays the bond interest by entering into a pay-fixed swap with CHT, and receives the interest from MBS pool sold to CHT. This is a seller swap. The fixed leg is semi annual, and the float leg, MBS coupons, is monthly. In addition, the MBS sold to the trust generates principal cash flows. CHT buys new-pooled mortgages from the party with this principal flows every month until the maturity of the swap.

Science seller swap

Gitbook seller swap

26. Mortgage Transfer Coupon Rate

With respect to a closed commercial mortgage certificate, the transfer coupon rate is defined as an annualized, monthly compounded interest rate, such that the fair value of the closed mortgage certificate, from Treasury’s point of view, is par. The model calculates the transfer coupon rate for forward starting, closed Canadian commercial mortgage certificates.

Science mortgage coupon

Gitbook mortgage coupon