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Interest Rate Product
Rate Derivatives CMS Spread Option To evaluate CMS spread option, we require the SDE followed by the forward exchange rate process under domestic T-forward measure. This is derived by changing measure from foreign delta-forward measure, to domestic risk-neutral measure, to domestic -forward measure. Forward Starting Option The valuation requires two interest rate curve inputs. One curve, called the “hedge curve”, is specified by a list of n term and continuously compounded zero rate pairs and is intended for use in computing forward equity values. Brownian Bridge 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. Cap Implied Volatility A cap/floor is quoted by implied volatilities but not prices. An interest rate cap volatility surface is a three-dimensional plot of the implied volatility of a cap as a function of strike and maturity. The term structures of implied volatilities which provide indications of the market’s near- and long-term uncertainty about future short- and long-term forward interest rates. A crucial property of the implied volatility surface is the absence of arbitrage. 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. 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. Quanto Option A quanto option is a financial contract where payment is made in a currency other than that of the underlying security. It can help investors to buy foreign stocks to hedge their foreign asset risk as well as exchange rate risk. Zero Coupon Bond Zero coupon bonds are issued at a deep discount and repaid the face value at maturity. The greater the length of the maturity is the cheaper price a bond has. Unlike other bonds, the investor’s return is the difference between the purchase price and the face value. An investor preferring a long-term investment may purchase zero coupon bonds such as saving money for children’s college tuition. The deep discount helps the investor grow a small amount of money into a sizable sum over several years. Normally investors buy zero coupon bonds when interest rates are high. Pricign 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. 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. Callable Bond A callable bond can therefore be considered a vanilla underlying bond with an embedded Bermudan style option. Callable bonds protect issuers. Therefore, a callable bond normally pays the investor a higher coupon than a non-callable bond. Rainbow Option Rainbow options are appealing to investors due to its natural risk diversification, cost efficiency, and weighted average on the best or worst performing assets. The best version offers higher returns, whereas the worst version is normally cheap. 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 Collateralization Model Default for ordinary contractual payments is deemed to have happened as soon as the payment is missed as the size and timing of the payment is defined precisely by the contract. In contrast, the size of collateral transfers is subject to legitimate dispute. This is because collateral levels are a function of portfolio value, and for all but the simplest portfolios, portfolio value is a function of future payments whose amount or even existence is uncertain. 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. 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. Callable Floating Coupon Note Callable floating coupon note usually pay a higher coupon or interest rate to investor. Institutions may issue callable floating coupon notes to fund expansion or to pay off loans. This type of note is in demand among investors when interest rates are low and expected to rise. 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. |