| Investment Knowledge |
 |
 |
 |
 |
|
Core Equity
Derivatives Asian Basket Relative Performance Option We test the model via several trades (transactions). In these sample transactions, Monte Carlo simulation associated with stratified sampling variance deduction is employed to evaluate the option. In the first sample transaction, there are six stocks, one as a reference, and the other five in a basket with equal weight. These underling stocks and the option are all measured in CAD. A strike share table is provided so that a share number can be interpolated based on the relative performance. The initial price for each asset is 100. The calculated option value is 96.5776 when 2000 simulations and 2000 samples in stratified sampling are used. Keeping the 2000 stratified samples unchanged, calculations with more simulations are conducted. Table 1 shows the simulated results. Bet Option Our test is based on several trades or transactions. In this sample transaction, Monte Carlo simulation associated with stratified sampling variance deduction is employed to evaluate the option. There are three underlying assets whose prices are correlated, and five reset dates. Binary Return Note The Monte Carlo method for computing expectations consists in simulating the cashflow sequence M times (where M is a large number) and taking the average. If the valuation date is later than a reset date, then the realized return rate should be used. Quasi Mote Carlo (QMC) method (Sobol low discrepancy sequences and Brownian bridge path generation) is used. Such a method has an improved convergence speed. We also use crude Monte Carlo for comparison. For the main issues that arise when computing sensitivities. It is known that Gamma requires a high number of simulations. Bond Option We present a pricing model for bond options. Assuming that the bond price at the maturity of the option is lognormal, the model adopts the Black’s analytical closed-form solution. In market, both the underlying spot price of bond and the strike price are clean prices (quoted prices), while dirty prices are used in the price dynamic and the closed-form solution. Bond Futures Option We test the bond futures option model in several cases. The first case is a call option, with the value date of 20031212 10:54, the futures price of 111.0, the risk free interest rate of 0.01, the volatility of the futures price of 0.05, and the option maturity of 20040221 10:54. The second case is a put option with the same inputs as the first case except that the volatility is 0.10. Callable Asian Option Pricing of callable Asian options involve two stages. The first stage is for the cases when the current value date is prior to the call date. This is our focus. The second is for the cases when the current value date is beyond the call date; in these cases, either the option was called and therefore deceased, or the remaining is just a regular Asian option, which is not in our scope. Credit Default Swap Once calibration of a term structure of hazard rates is completed, the target swap can be priced. Currently, the model only allows fee payment at payment dates and does not allow accrued fee when default occurs. If a payment date in the target default swap falls between two calibration pay dates, linear interpolation is employed in the model to find the hazard rate associated with the target payment date. This is equivalent to using a time-weighted average of hazard rates in a payment period of the target swap as a flat hazard rate for that period, so long as the length of each payment period of the target swap is the same as that of the swaps for calibration. Floating Rate Convertible Bond Following general market pricing practice, pricing of convertible bonds uses lattice trees for the stock price with the interest rate curves static just like pricing a conventional bond. This is the so-called one-factor (stock price) model. The call/put feature of the bond therefore has price effect mainly contributed by the stock price movement rather than the interest rate movement. A two-factor tree model may be considered if the call/put option on bond has considerable weight on the convertible price. Convertible Bond with Refix Feature The single-factor version of the model is found to be accurate for the purposes of pricing convertible bonds which possess the refix feature. This includes situations multiple dates upon which the conversion ratio/conversion price is reset. In addition, the asset swap spread adjustment was verified to function according to design. Non Quanto Convertible Bond In a non-quanto convertible bonds, the spot stock price in foreign currency is converted into an amount in domestic currency using the spot exchange rate. This amount is then adjusted by the current value of predicted future discrete dividends, measured in domestic currency. The domestic risk-free interest rate is employed as the drift rate for the translated stock. Convertible Bond Model with Soft Call A convertible bond is a coupon paying corporate bond that can be converted into company stock at the discretion of the holder. Pricing convertible bond is a challenging task, because it is a hybrid instrument with an equity component and a bond component. These two components are subject to different credit risk, because a company can always issue more of its stock, but not necessarily come up with sufficient cash to meet bond obligations. Furthermore, in reality, even the most basic convertible bonds often incorporate various additional features, such as call and put provisions, strike reset features, mandatory or restricted conversion, etc. Correlation Swap Model We developed a conventional mark-to-market/pricing model for a new product Correlation Swap. The payoff of the correlation swap at maturity is the difference between the realized correlation (of a basket of stock indices) and the strike. The realized correlation has two main components: historical correlation part and future realized correlation part. We use the current correlation swap strike level on the market (available for exactly the remaining swap period) as the expectation of future realized correlation part. This way the essential part needed for the mark-to-market model becomes a direct input. The market level should be verified independently by middle office. Capping (flooring) can be included in the definition of the realized correlation (making part of payoff option-like, but this conventional MTM model extends its simplified view to such actions too). Generic FX Option Model We present a generic FX option model that allows currency as a random object type. The main implication is that European and Asian FX (foreign exchange) options can now be priced. Decreasing Basket Asian Option Model Decreasing-Basket-Asian option, also called Himalayas option is an option that records the highest return at the end of each reset period among the stocks left in the basket for calculation of the payoff. The stock with either the highest return or the lowest return, based on the specification, will then be eliminated from the basket for the rest reset periods. Dividend Enhancement Common Stock Model A dividend enhancement common stock (or DECS) instrument is a portfolio of stock options and a fixed coupon stream. The DECS is developed to price a corporate financing structure with the option that the debt principal can be converted to the underlying common stock at maturity date. A dividend enhancement common stock (or DECS) instrument is a portfolio of stock options and a fixed coupon stream. The DECS is developed to price a corporate financing structure with the option that the debt principal can be converted to the underlying common stock at maturity date. Eurodollar Futures Option Model Option on Eurodollar futures is a European type of call/put option on the Eurodollar futures price or put/call option on the 3-month LIBOR forward interest rate referred by the futures contract. Standard Black’s model can be used to price the options on LIBOR forward interest rate. The price of the option on Eurodollar futures is related to the price of options on LIBOR forward with a ratio adjustment. Fixed Forward Option Model The fixed forward call/put contracts are options on forward equity contracts. The option buyer has the right, but not obligation to enter into an equity forward contract, which starts on the expiration date of the option and matures on a later date further into the future. The fixed forward call/put contracts can be priced using standard option pricing methodologies such as closed form Black-Scholes model or lattice tree model. Futures Fair Value Model The proposal for the new methodology to calculate the fair value of equity-index futures was reviewed. The proposed method attempts to improve traditional method by taking into consideration the dynamic rebulanching of the position (tail hedge) over the life of futures contract. We find the model adequate for the purposes of the fair value adjustment. We present our conclusions below. Equity Forward with Dividend Reinvestment We developed a pricing model to calculate unwinding values of equity forward with dividend reinvestment. Swap Curve Construction The swap curve construction is an algorithm based on the assumption that the term forward rate curve must exhibit minimal quadratic variation. The Curve Construction Algorithm contains the following main features: |