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Computational Finance Workshop |
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| Mark Broadie - Simulation and Calibration of Stochastic Volatility and Jump Diffusion Option Pricing Models - Strong empirical evidence against the Black-Scholes model - Models beyond Black-Scholes - Bias and variance in simulating stochastic volatility models - Discretization methods - Exact simulation using transform methods - Calibration approaches and results |
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| Peter Forsyth ¨C Dynamic Hedging Under Jump Diffusion with Transaction Costs Real assets do not follow Geometric Brownian Motion. It¡¯s important to consider jump diffusions from a risk management point of view. In order to hedge jumps, we need to construct a hedging portfolio containing the underlying asset and liquidly traded options. We devise a dynamic strategy, which minimizes jump risk and transaction costs. Simulation studies show that this strategy is effective at reducing jump risk, while not being too expensive. Theoretical analysis confirms the effectiveness of this strategy. Study also shows an optimal strategy for a hedge fund manager: maximize short term bonuses and let your investors suffer losses due to jumps. In this talk, we consider the problem of hedging a contingent claim, where the underlying follows a jump diffusion process. The no-arbitrage value of the claim is given by the solution of a Partial Integro Differential Equation (PIDE), which in general must be solved numerically. By constructing a portfolio consisting of the underlying asset and a number of liquidly traded options, we devise a dynamic hedging strategy. At each hedge rebalance time, we minimize both the jump risk and the cost of buying/selling due to bid-ask spreads. Simulations of this strategy show that the standard deviation of the profit and loss of the hedging portfolio is greatly reduced compared to the standard hedging strategy. If time permits, some theoretical results concerning this strategy will also be presented. This is joint work with Shannon Kennedy and Ken Vetzal. |
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| Qing Hou ¨C Equity Derivatives Products: Structures and Pricing Last few years have seen tremendous innovation in derivative products which has become popular for institutional as well as retail investors. We discuss, from a practitioner's viewpoint, the financial engineering process. We will highlight a few key products, hedging considerations, as well as challenges to modelling and pricing. |
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| David Li - A Transformed Gaussian Copula Function Approach To Credit Portfolio Pricing We present a fundamental modification to the current popularly used copula function approach to the credit portfolio modeling introduced by Li (2000). The original approach simply uses a copula function to create a joint survival time distribution where individual survival time distribution is already risk neutralized, and given from a single name perspective. Based on Buhlmann's equilibrium pricing model (1980) under some assumptions on the aggregate risk or the multivariate Esscher and Wang transforms we find that the covariance between each individual risk and the market or aggregate risk should be included in the measure change. In the Gaussian copula model it is shown that we simply need to adjust the asset return by subtracting an item associated with the variance risk. This discovery allows us to theoretically link our credit portfolio modeling with our classical equity portfolio modeling in the CAPM setting. This can help us solve some practical problems we have been encountering in the credit portfolio modeling. |
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| Yuying Li ¨C Robust Portfolio Solutions to Mean-Variance Portfolio Selection The Nobel prize winning work of the Markowitz portfolio selection method has difficulty performing in practice due to estimation errors in means and covariance matrix of asset returns. Recent min-max robust optimization methods promise new solutions to the old mean-variance portfolio solution problem. How well do the min-max robust optimal portfolios perform in practice? How should different robust optimization solutions be evaluated?< In this talk, we will discuss - impact of estimation error for optimal mean variance portfolio selection - min-max robust optimization methods - performance of min-max robust optimal portfolios in - sensitivity to data - efficiency in risk and return tradeoff - asset diversification - a new CVaR robust mean variance optimal portfolio selection approach - computationally efficient methods for CVaR optimizations |
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| Dan Rosen -"Valuation and Risk Management of Credit Portfolios and Structured
Credit Products" - Introduction: credit risk, credit portfolios, credit derivatives - General framework for credit portfolio models - Factor models for credit risk - Valuation models: synthetic CDOs, bespoke CDOs and cash structures - Weighted Monte Carlo methods - Examples: ABX and cash CDOs - Measuring the risk of structured credit portfolios |
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| Liuren Wu ¨C Computational Challenges in Estimating Option Pricing Models - The current state of the art in option pricing theory: A review - Capture return innovation distribution using Levy processes - Capture the stochastic variation of the innovation distribution using stochastic time changes - Design economically sensible option pricing models - Identify the sources of economic shocks - Measure the time variation of the financial responses - Estimate option pricing models for different purposes - Static versus dynamic consistency - Fast recalibration of simpler models for options market making - Dynamically consistent estimation of option pricing models for long-term statistical arbitrage - Computational challenges in estimating option pricing models - Fast Fourier transform (FFT) and fractional FFT: Trade-offs between speed, accuracy, and robustness. - Unscented Kalman filtering and particle filtering: The sequential procedure for extracting risk states - Monte Carlo simulation: Determine exotic derivative values and hedging ratios. - Embedding Monte Carlo simulation into model estimation: Models for the next generation |
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