Jean-Luc Prigent

Portfolio optimization and performance analysis

UTILITY AND RISK ANALYSIS Utility Theory Preferences under uncertainty Expected utility Risk aversion Stochastic dominance Alternative expected utility theory Risk Measures Coherent and convex risk measures Standard risk measures STANDARD PORTFOLIO OPTIMIZATION Static Optimization Mean-variance analysis Alternative criteria Further reading Indexed Funds and Benchmarking Indexed funds Benchmark portfolio optimization Further reading Portfolio Performance Standard performance measures Performance decomposition Further reading DYNAMIC PORTFOLIO OPTIMIZATION Dynamic Programming Optimization Control theory Lifetime portfolio selection Further reading Optimal Payoff Profiles and Long-Term Management Optimal payoffs as functions of a benchmark Application to long-term management Further reading Optimization within Specific Markets Optimization in incomplete markets Optimization with constraints Optimization with transaction costs Other frameworks Further reading STRUCTURED PORTFOLIO MANAGEMENT Portfolio Insurance The option-based portfolio insurance The constant proportion portfolio insurance Comparison between OBPI and CPPI Further reading Optimal Dynamic Portfolio with Risk Limits Optimal insured portfolio: discrete-time case Optimal insured portfolio: the dynamically complete case Value-at-risk and expected shortfall-based management Further reading Hedge Funds The hedge funds industry Hedge funds performance Optimal allocation in hedge funds Further reading References

Weak convergence of financial markets

Throughout this chapter, the following problem is examined: assume that a discrete time financial model and a continuous one can both explain the dynamics of given statistical financial data: This means that the discrete time primitive assets S n weakly converge to the continuous ones S, under the statistical probabilities ℙ n when periods between trades shrink to zero:

An Autoregressive Conditional Binomial Option Pricing Model

{({S_{n,t}})_t}\mathop \Rightarrow\limits^{\mathcal{L}(({\mathbb{R}^p}))|{\mathbb{P}_n})} {({S_t})_t}

An Empirical Investigation in Credit Spread Indices

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Convergence of discrete time option pricing models under stochastic interest rates

We compare the performances of the two standard portfolio insurance methods: the Option Based Portfolio Insurance (OBPI) and the Constant Proportion Portfolio Insurance (CPPI), when the volatility of the stock index is stochastic. In this framework, we provide a quite general formula for the CPPI portfolio value. We use criteria such as comparison of payoffs functions at maturity and various quantiles. We emphasize in particular the role of the insured percentage of the initial investment.

Standardized versus Customized Portfolio: A Compensating Variation Approach

This paper offers an option pricing framework grounded in econometric microstructure modelling. We consider a model where stock price dynamics follow a pure jump process with constant jump size similar to a binomial setting with random time steps. Jump arrival times are described as an Autoregressive Conditional Duration (ACD) process while conditional probabilities of up-moves and down-moves are given by the logistic transformation of an autoregressive prices. We derive no-arbitrage pricing formulae under the minimal martingale measure and illustrate the use of our Autoregressive Conditional Binomial (ACB) option pricing model on intraday IBM stock date.

Hedging global environment risks: An option based portfolio insurance

This paper examines the impact of a random number of price changes on the options valuation. The model introduces the structure of the general marked point processes MPP. This kind of model allows us to take account of more general distributions of interarrival times than usual jump-diffusion models. In particular, stock price variations can be correlated with the times of transactions. Thus, the investors can decide to trade according to the history of market values and the sizes of price variations can also depend on the past times of transactions. By using the special decomposition of predictable processes, with respect to a marked point process, the determination of all risk-neutral probabilities is detailed. Derivative prices are calculated in this context with different basic examples.

A general subordinated stochastic process for the derivatives pricing

We study the dynamics of the spread between U.S. corporate and Treasury bonds. We focus on Aaa and Baa corporate yield indices and estimate nonparametrically the dynamics of the spreads assuming that they follow a univariate diffusion process. Using techniques developed for interest rate processes we try to infer from the data what acceptable process can be used to model aggregate credit spreads for option pricing or risk management purposes. We find that there is significant evidence of mean reversion especially for higher rated spreads and that the volatility of Aaa spreads exhibit a U-shape while the volatility of Baa spreads is monotonically increasing in the level of spreads. Based on these observations and on the evidence of jumps in the series, we propose a new model for credit spread indices (an Ornstein-Uhlenbeck with jumps) and estimate it by maximum likelihood.