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Structure Rate Market
Equity Products 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. Libor rate model is very useful to price callable exotics. Many derivatives have callable features. Callable exotics are among the most challenging derivatives to price. These products are loosely defined by the provision that gives the holder or issuer the right to call the product after a lock-out period 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. 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. The payoff amount can be viewed as the value of the sum of a series of daily Libor digital payoffs. Here we assume that Libor rates are log-normally distributed, and derives an analytical formula for the daily digital payoff. 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. The payoff of the leg based on the return of the foreign exchange rate is a payoff of a European call option. Its present value is given by Black’s formula for futures with the discounting factor equal to the Canadian zero-coupon bond and the future price given as 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. 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. 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. Black-Karasinski Short Rate Tree he 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. 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. Assumes that, under the coupon payment currency (SEK) risk-neutral probability measure, the forward swap rate process corresponding to each swap rate fixing follows Geometric Brownian motion with drift. Each forward swap rate process is then convexity adjusted, and is furthermore expressed under the notional currency (FRF) risk neutral-probability measure by means of a quanto adjustment. 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. We propose a two-factor tree model that implements the Hull-White and Black-Karasinski models. The new tree model does preserve the martingale property of the stock for sufficiently long terms (with accuracy better that 10-8 for terms of at least 10 years). American Bond Yield 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. At the time of maturity of the option the yield distribution is taken as y = yf exp(-0.52T + W), where yf is the bond’s forward yield (by the time T, which is the option tenor). The payoff is averaged over this distribution and discounted to the trade date. 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. 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. The Black-Karasinski class of models assumes the short term interest rates to be log-normally distributed. The spreadsheet mode used for the deal pricing has a hard-coded term structure of the mean reversion and volatility parameters, constructed as Chebyshev polynomials. Extendable Swap An extendable swap represents a forward swap agreement with an option of extending the swap for another term (swaption). The valuation model assumes the swap rates for different terms to be correlated log-normally distributed random variables and uses the Haselgrove integration method for pricing the deal. GIC Valuation 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. To determine the rate of return, the percentage change in each index level from the initial level is calculated. Here the initial level is set two days after purchase, while the final level is set to the arithmetic average of the last 11 month-ending index levels and the level one day prior to maturity. Bond Curve Government Bond Bootstrapping proceeds in two phases. The first phase uses short term instruments, which typically mature in one year or less. Consider, for example, a US government money market instrument with |