Variable rate swap is an interest rate swap that has two legs: one fixed rate leg and a variable rate leg. The variable leg 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.

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.

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.

We propose a three-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).

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…[Read more]

A flexible GIC represents a financial instrument paying an annual coupon and provides an option for the holder to redeem the principal and accrued interest during the thirty days following the first and second coupons.

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 model estimates the swap price as a risk-neutral expectation of the difference between the bond price whose yield-to-maturity is the swap rate and the bond’s par. The swap rate is considered a log-normally distributed random variable.

The payoff at maturity from a GIC can be shown equal to the invested principal plus principal times the sum of the minimum guaranteed interest rate and the payoff from a European call option on the arithmetic average of the basket price, where the basket price is given by a weighted sum of the index levels.

We present a method for bootstrapping a set of zero rates from an input set of US government money market securities and bonds. We detail the calculations used to convert ACT/365 continuously compounded zero rates to the rates.

We present an approach that calculates the Hull White (HW) volatility to make the swaption price calculated on a HW tree match Black’s price for the same swaption at each grid point. We priced the payer swaption using our benchmark Black’s model and then priced the same swaption, using our benchmark HW trinomial tree model, based on the c…[Read more]

The valuation makes the assumption that the future values of these parameters will be unchanged until the final payment date. Subsequently, the calculator performs a deterministic computation consisting of calculating the future cashflows in the waterfall and discounting them.

A convertible bond with exchangeable feature, which can be converted into a stock issued by a party different from the bond issuer. Assume that the stock conversion is vulnerable. If the bond-issuer has defaulted by a time, t , then the stock price is zero. If, on the other hand, the bond-issuer has not defaulted by time t , then the stock price…[Read more]