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Equity Market
Derivatives 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. Asset Backed Senior Note We consider a securitization deal, which allows the holder to purchase co-ownership interests in a revolving pool of credit card receivables. To fund the acquisition of the interests in the revolving pool, the trust issued Asset-Backed Notes, in a number of different series. A share of future collections of credit charge receivables, to which the trust is entitled, is used to pay the interest and the principal of the notes. At this time the deal has entered its liquidation period, during which all allocable collections remaining after the payment of interest are used to repay the principal. For this reason, only the portion of the model relevant to the liquidation period 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: Brownian Bridge The Brownian bridge algorithm has been implemented for stress testing within the Risk Management framework. It is used for generation of multidimensional random paths whose initial and ending points are predetermined and fixed. 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. Hull-White Convertible Bond A convertible bond pays the holder periodic coupon payments from the issuer, but can also convert it into the issuer’s stock. The model uses a two-factor trinomial tree for pricing the convertible bond, where the two factors are 1) the short term interest rate and 2) the issuer’s stock price. Mutual Fund Securitization Under the mutual fund securitization agreement, one party may provide monthly funding for the commission to brokers selling mutual fund units, up to one year. The purpose of the model is to determine, from a projected stream of future cashflows, whether all Commercial Paper used to fund the commissions to brokers for the sale of mutual funds will be repaid within a period. Here a broker charges the Partnership a commission on the net asset value of the mutual funds sold. The buyer of the mutual funds, however, pays nothing up front; instead, a deferred sales charge, which depends on when the mutual funds are redeemed, is assessed. Three Factor Convertible Bond The owner of a convertible bond (CB) receives periodic coupon payments from the issuer, but can also convert the CB into the issuer’s stock. The convertible bond may also include call and put provisions, which respectively allow the issuer to buy back the convertible bond and the owner to put the convertible bond for respective preset amounts. The stock price process is then expressed under the bond’s coupon currency risk neutral probability measure by means of a quanto adjustment. Under the bond’s coupon currency risk neutral probability measure, then, the short interest rate, stock price and foreign exchange rate processes respectively follow geometric Brownian motion with drift, but are driven by pair-wise correlated Brownian motions. 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. Employee stock option is a forward start option. The strike price is not fixed when the employee began to work. Instead, he is promised that he will receive stock option at periodic dates in the future. The strikes of employee stock options are unknown for now, but will be set to be at the money on later dates. 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 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. Like other exotic option, Quanto Himalayan may also have cap floor constraints and barrier conditions. The barrier option may knock out the trade before maturity Equity Linked 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. Asian Commodity Swap Valuation A commodity swap is a deal where counter-parties exchange fixed payments for floating payments monthly based on a specific commodity, for example, West Texas Intermediate (WTI) crude oil. The fixed payments are specified as a given quantity times a fixed price; the floating payments are specified as a given quantity times the spot value of the commodity on the payment date. The floating payments may also be based on the arithmetic average of spot commodity price (Asian commodity-price) over the payment period or LIBOR plus a spread. The commodities swaps are based on crude and refined oil products and these swaps are typically Asian commodity-price swaps. A typical deal where one party pays fixed and receives floating is specified as follows Rainbow Partial Barrier Option Valuation A rainbow partial barrier option is an option on two assets where one asset-the trigger asset-knocks in an European call or put on a second asset; such an option is therefore European. (Unless specified otherwise, all options are European style.) The adjective partial refers to the fact that the knock in or out period is shorter than the option tenor. The adjective rainbow describes the fact that the option is on two assets and cannot be priced as equivalent option on a single asset. Rainbow partial barrier options come in eight “colors”: the trigger asset initially may be above or below the barrier knocking in or out a call or put on the other asset. European Shout Cap and Floor Valuation A European shout cap is an option giving the holder the right to “shout” a European call strike level at spot at any time during the option tenor. That is, the holder receives an at-the-money European call when they shout. If they do not shout at any time during the option tenor the holder receives a European call struck at the initial strike level. Typically the initial strike level is set to the spot level when the contract is initiated. This instrument provides a protective cap on losses in short positions without requiring additional payments. A European shout floor is similar to a shout cap. The shout floor is an option giving the holder the right to “shout” a European put strike level at spot at any time during the option tenor. That is, the holder receives an at-the-money European put when they shout. If they do not shout at any time during the option tenor the holder receives a European put struck at the initial strike level. This instrument provides a protective floor on losses in long positions without requiring additional payments |