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ResearchGate derivative reference
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
Payoff for equity GIC requires a dynamically created basket such that the weight factors incorporate a division by the spot levels on the issue date, which converts the payoff to one based on a basket of comparative returns (rather than basket returns). To automate feeds on a daily basis we will need to create new baskets on a daily basis.
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.
This definition is consistent with the one in the case of domestic equities, that is, in the absence of a quanto adjustment. In the quanto case, the effect of the change in the quanto adjustment resulting from a change in the volatility is ignored.
Quanto Local Volatility
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.
The equity price process satisfies a risk-neutral stochastic differential equation (SDE) when where are no dividend payments. Let St denote the equity price at time t. We assume that the process satisfies a SDE of the form under the domestic risk-neutral probability measure:
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.
In practice, option price or implied volatility surfaces are available at points on a relatively sparse grid of strike and tenor pairs. Using analytical expressions to determine the local volatility function then likely yields inaccurate results due to the numerical instability from calculating first, and especially, second derivatives.
Three Factor Model
We construct respective trinomial trees to approximate the processes for each new random variable, but with each tree based on the same time slice partition of the CB tenor. A new tree, which combines these respective trees, is then defined such that the set of nodes on a particular time slice of the combined tree equals the cross product of the set of nodes in each of the three respective trees at this time slice.
Mutual Fund Securitization
The General Account collects monthly administrative and redemption fees and, if required, a collateral infusion amount. This money is used to pay monthly program fees, as well as amortized principal and accrued interest owed from issued Commercial Paper. Any excess money is transferred to a Retention Account as future collateral.
Here monthly administration fees are set to a fixed percentage of the average of the respective current and previous month’s beginning mutual fund net asset values. Program fees are similarly set to a fixed percentage of the current month’s beginning net asset value.
Hull-White Convertible Bond
We build respective trinomial trees for the approximate stock’s price and short-term interest rate processes above. This construction is based on Hull and White’s single factor tree-building technique, but is generalized to accommodate non-uniformly spaced partitions of the interval to bond maturity. The separate trinomial trees are then combined into a joint tree using Hull and White’s two-factor tree building procedure.
Here the set of nodes at a particular time slice on the combined tree is given by the cross product of the nodes on each respective tree at this time slice. From each node on the combined tree emanate nine children; the branching probabilities are given by the product of the corresponding probabilities on the respective trees, but shifted by a certain amount so to match the correlation between the random variables associated with the combined tree node.
Brownian Bridge
In the context of stress testing this algorithm is used for efficient generation of specific scenarios subject to certain extreme and generally unlikely conditions. If paths were generated by a conventional Monte-Carlo method only a very small portion of all the paths would satisfy such conditions.
The Brownian Bridge algorithm belongs to the family of Monte Carlo or Quasi-Monte Carlo methods with reduced variance. It generates sample paths which all start at the same initial point and end, at the same moment of time, at the same final point.
Asset Backed Senior Note
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.
The following notation will be used throughout the text: the contents of the cell in row i of column A in the spreadsheet will be denoted by A(i), and similarly for other columns. Lower-case letters will be used for all other constants.
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.
The Exchangeable feature assumes that the convertible bond and the underlying stock are issued by different parties. There are two possible cases with respect to stock conversion:
Archive exchangeable convertible
Science exchangeable convertible
Hull White Volatility
Hull White model is a short rate model that is used to price interest rate derivatives, such as Bermudan swaption and callable exotics
We map implied Black’s at the money (ATM) European swaption volatilities into corresponding Hull-White (HW) short rate volatilities.
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
GIC
The payoff at maturity from a GIC can be shown equal to the invested principal plus these principal times the sum of the minimum guaranteed interest rate and the payoff from a European call option on the arithmetic average of a basket price at the 12 points above, where the basket price is given by a weighted sum of the index levels above.
We consider the pricing of this call option. We assume that each of the underlying stock and bond market indices in the basket follows geometric Brownian motion with drift under their respective risk neutral probability measures. Each index process is then expressed under the Canadian risk neutral probability measure by means of a corresponding quanto adjustment.
Extendable Swap
We use analytical formulas for forward swap and swaption valuation: the swap price is calculated as the difference between a bond par and the bond’s price, and the swaption price is evaluated from the Black’s formula.
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.
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.
Flexible GIC
We price the option of a flexible GIC with a one factor Hull-White model via a trinomial tree. The Hull-White model assumes a normal distribution for the rates. Our solution constructs a Hull-White tree. The calibration procedures take an interest rate curve as input (ignoring volatility surfaces) and assume volatility and mean reversion parameters as constants.
The initial approximation of the short rate in the middle node of a time slice is taken as a forward rate for the time interval between the given and next slices, without using the Hull-White analytical approximation, The initial value is subsequently improved by the Newton-Raphson formula.
American Bond Yield Option
The model builds a trinomial tree for the yield process to price the deal as an American option. The time slices of the tree are evenly spaced. Node transition probabilities and the time interval between slices are determined by matching the first four moments of the underlying Brownian motion. The option is priced using the backward induction.
The payoff of the option is a discontinuous function of yield, which technically represents the primary security. As a result, the delta is not defined for the intrinsic case, and it is poorly defined for small volatilities. Therefore, the use of delta is not recommended for volatilities less than 5% or for time to maturity less than 10 days.
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).
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.
The yield to maturity of a bond is the internal rate of return on a bond held until maturity. In other words, it is the discount rate that will provide the investor with a present value V equal to the price of the bond.
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.
Black-Karasinski short rate tree approach can be used to price convertible bond. Convertible bond is not only a coupon paying bond but also can be converted at the discretion of the holder within the periods of time specified by the conversion schedule.