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Fixed Income Market
Fixed Income Market Products Variable Rate Mortgage-Backed Securities 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. The purpose of the first calculator is to determine the fair value of a VRMBS that is eligible for the new CMB program. This calculator will be used to assist the CHT when purchasing a VRMBS. Local Vol 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. FX Option Valuation via BGM Monte Carlo Simulation for BGM 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. Multi-currency BGM Model 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. 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. GIC Coupon Rate The model assumes that the GIC holder receives deterministic payments on specified payment days, and the embedded put option is exercised by the GIC holder when the redemption value exceeds the holding value. GIC Redemption Option Greeks 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. Prime GIC has a three year maturity. Over two respective 30 day windows, which start on inception anniversary dates, the holder has an option to redeem the principal and accrued interest less penalty interest based on the call rates assigned to the respective windows. Flexible is a one year maturity GIC whose holder has an option to redeem the principal and accrued interest without any penalty from one month after inception till maturity. If the holder chooses to redeem the GIC within the first 30 days after inception, a zero call rate is applied. Cancelable Swap The valuation model is a “disconnected” tree discretization of a two-factor, risk-neutral Black-Karazinski (BK) short-interest rate process; in particular, the SDEs governing the short-interest rate process admit respective deterministic mean reversion and volatility parameters. The disconnected tree discretization above is non-recombinant by design, but employs an interpolation scheme to approximate short-interest rate values at tree nodes along a time slice. Calibration of the model parameters is accomplished by matching, in a least squares sense, the model price against the market price for each respective European style payer swaption or caplet in a cache of calibration securities. American Swaption A disconnected tree discretization of the short-rate process above is non-recombinant by design, but employs an interpolation scheme to approximate short-rate values at tree nodes along a time slice. Calibration is accomplished by matching, in a least squares sense, the model price against the market price for each respective European style payer swaption in a cache of calibration securities. The volatility break points are related to the forward start times of the respective swaptions in the calibration portfolio (see Section 4.2 for a typical specification). Government Bond Curve 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. The Canadian zero curves generated will be used to generate particular risk measures, for example DV01’s. Moreover, the zero rate curves are not intended for use in pricing (P&L) applications GIC Option A valuation model is presented for pricing a pool of GICs with an embedded redemption option. The model covers 1) pricing of a closed (non-redeemable) GIC, 2) penalty calculation for Redeemable and Premium GIC, 3)embedded option valuation, 4) numerical convergence of the embedded option pricing procedure. Inflation Swap and Cap 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. CMS Rate Convexity Adjustment 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. We model the probability density of a CMS rate, under the forward swap measure, by a certain weighted sum of three log-normal densities. The defining parameter values for the log-normal densities above are determined by matching, in a least squares sense, the market price for various European style swaptions. 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. 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. 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; upon exercise 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. |