| Investment Knowledge |
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Risk Management Knowledge One of the central tenets of financial economics is the necessity of some trade off between risk and expected return. Because high risk is associated with high reward, investor may potentially obtain higher profits only if he is willing to accept a higher chance of losses. Risk-return trade-off is one trading principal in financial markets. Risk management is a process to identify and measure risk. The goal of risk management solution is to ensure that risk is under limit and there is no surprise in future. In capital markets, risk management is accountable for oversighting and monitoring the profit and loss, market risk, credit risk, liquidity risk and valuation risk activities of a firm. We provide some valuation and risk mangement research results. Pricing Collateralized OTC Derivatives Credit Valuation Adjustment (CVA) and Wrong Way Risk Pricing Convertible Bond Lattice Algorith for LMM Jump diffusion for pricing convertibles Collateralization examination Impact of Default Dependency IRC Approach Multilateral Credit Risk Bilateral Defaultable Pricing Defaultable Swap Pricing CDS with Counterparty Risk Derivatives CVA Vanilla and Exotic Financial Derivatives Analytics: Reference Vanilla and Exotic Financial Derivatives Analytics: Reference Index Linked Bond An index linked bond is one whose cash flows are linked to movements in a specific price index, with the aim of providing investors with a means to protect the real value of their savings. The bonds are usually indexed to a broad measure of prices, typically a domestic Consumer Price Index (CPI). Monte Carlo Acceleration A new procedure is presented to accelerate the convergence of Monte Carlo simulations using the Default Correlation model. It is found that the modifications have been implemented correctly, and that the modifications result in a substantial improvement in the convergence rate of the Monte Carlo simulation models. Implied Correlation The implied correlations for the CDO index tranches are the correlations backed out by the market quoted prices using CDO valuation models available in the credit library, namely, the Poisson model and the Normal Copula model. Base Correlation The model serves the purpose of finding an appropriate correlation to value a collateral debt obligation (CDO) tranche from market information via base correlations. The model includes: 1. Normal Copula Semi-closed Form Solution; 2. New Method of Base Correlation Calibration; 3. Extrapolation of Base Correlation Curve. Loss Trigger Leveraged Super Senior Tranche The loss trigger leveraged super senior tranche (LT-LSS) valuation model is presented. A leveraged super senior tranche trade is a credit linked note, which provides investors with a leveraged exposure to the super senior tranche in a synthetic CDO transaction. The note holder earns the risk premium associated with selling protection on the entire senior exposure when the protection it provides is limited to only the funded principal amount which is just a fraction of the entire exposure. Normal Copula As a well known default correlation model, the normal copula provides an alternative method to the Poisson model in generating correlated default events of a collateral pool. It is implemented using the Monte Carlo (MC) simulation. The testing was conducted by implementing an independent test model using the MC simulation. The results of two sample trades, generated by the test model and the model, respectively, were compared. The MC implementation was also verified by the closed form solutions and the Poisson model. Giant First Loss Compared to the standard first loss model with the same collateral pool and tranche structure, the new model predicts smaller B/E spreads for each tranche. Further, it is more sensible to the interest rate and the sensitivity to the interest rate term structure changes dramatically. The B/E spreads for each tranche calculated by both models converge when the hazard rates of the obligors become very small. Basket Default Swap A pricing model is presented to calculate Mark-to-Market (MTM) and all sensitivities for basket default swaps and Collateral Debt Obligations (CDOs) (FirstNofM, GiantFirstLoss, GiantFirstLossPayEnd, Caribou, and Reindeer). It is composed of the credit library, BulkCurveGenerator, five outstanding pricing templates, and Scenario Manager. Weighted Monte Carlo Sensitivity The model is a non-parametric approach to value complex CDO structures that need to be priced using the market information on tranche losses at multiple points of time. Currently, the model is being used for the valuation of forward starting CDO trades (FSCDO) and loss-trigger leverage super senior tranches Repo Curve A repo curve is defined as an adjustment to the discount curve in the pricing of a bond/FRN, when the credit default swaps (CDS) market implied default probability of the issuer is used in the pricing. We have changed the repo curve generation methodology. Credit Delta and Credit VaR Credit VaR (CVaR) is defined as the potential change in market value over a 1-day period at the 99% confidence level due to changes in credit spreads. Weighted Monte Carlo A regular Monte Carlo (MC) simulation algorithm assigns each simulation scenario, or path, an identical probability weight. A weighted Monte Carlo (WMC), however, allows a different probability to be assigned to each simulation path. For example, we can choose the probabilities of each path in a manner such that the simulation is guaranteed to reproduce the prices of “benchmark” securities, whose prices are known from market data. A simulation thus calibrated to benchmarks will then price off-market securities in a realistic manner. Capped Accumulated Return Call Volatility Surface A pricing model for capped-accumulated-return-call (CARC) with volatility surface is presented. Proprietary approaches to interpreting volatility surface are employed during pricing. To accelerate the convergence when low discrepancy sequences are used in Monte Carlo simulation (Quasi-Monte Carlo simulation), the Brownian Bridge Path Construction has been employed in some CARC transactions Fair Value Adjustment A modified calculation approach is presented for the fair value of an equity index futures contract. The modified calculation takes into account the funding required to support the tail hedge that was not considered previously. |