Pablo Olivares

Pricing two dimensional derivatives under stochastic correlation

In this paper, we develop a framework for pricing two dimensional derivatives under stochastic correlation. Closed form approximations for the price of these derivatives are provided based on Taylors expansions of known price function under constant correlation. Two families of stochastic dynamics for the correlation are considered. The framework is applied in the pricing of spread options and compo options.

A multivariate default model with spread and event risk

Abstract We present a new portfolio default model based on a conditionally independent and identically distributed (CIID) structure of the default times. It combines an intensity-based ansatz in the spirit of Duffie and Gârleanu (2001). Risk and valuation of collateralized debt obligations. Financial Analysts Journal, 57(1), 41–59. with the Lévy subordinator concept introduced in Mai and Scherer (2009). A tractable multivariate default model based on a stochastic time-change. International Journal of Theoretical and Applied Finance, 12(2), 227–249. We aim at exploiting the computational advantages of the CIID framework for evaluating multiname credit derivatives, while incorporating two central drivers for credit products. More precisely, we allow for both a dynamic evolution of the portfolio credit default swap (CDS) spread (unlike static copula models) and cataclysmic events allowing for simultaneous defaults (unlike intensity-based portfolio loss processes). While the former feature is considered to be crucial for consistently hedging credit products, the second property is supposed to take into account default clusters and the market’s fear of extreme events. For applications, the model is approximated by a related top-down representation of the portfolio loss process. It is shown how to coherently calculate hedging deltas for collateralized debt obligations (CDOs) w.r.t. portfolio CDS and how to consistently calibrate the model to the two products. Both tasks solely require the computation of one-dimensional (Laplace inversion) integrals and can be carried out within fractions of a second. Illustrating the stability and functionality of the pricing approach, the new model and the models it is related to are calibrated to a daily time-series of iTraxx Europe index CDS and CDOs. We find the fitting results of the presented model to be very promising and conclude that it may be used for the dynamic pricing and hedging of credit derivatives.

Pricing Basket Options by Polynomial Approximations

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort.

Risk Management Under A Factor Stochastic Volatility Model

In this paper, we study risk measures and portfolio problems based on a Stochastic Volatility Factor Model (SVFM). We analyze the sensitivity of Value at Risk (VaR) and Expected Shortfall (ES) to the changes in the parameters of the model. We compare the positions of a linear portfolio under assets following a SVFM, a Black–Scholes Model and a model with constant dependence structure. We consider an application to a portfolio of three selected Asian funds.

Risk Management and Portfolio Selection using α-stable Regime Switching Models

This article tries to enhance the current Gaussian distribution paradigm for modeling asset returns by emphasizing two points. It proposes a model which captures fat tails and skewness, and takes into account distinct market regimes. Therefore, an alpha-stable regime-switching model is proposed. The implications of this model on asset management are shown. The alpha-stable regime-switching model is employed for applications in risk management and portfolio selection. An empirical study shows that the model is better suited than Gaussian and Gaussian regime-switching models to measure risk accurately. A portfolio optimization case study for a traditional stocks and bonds investor is pursued. In this study, the model leads to less risky and more diversified portfolios. In particular, the model avoids huge losses in times of crisis and thus leads to a better (adjusted) Sharpe ratio and Omega.

Estimation of Risk Measures for Large Credit Portfolios

In this paper, saddle point techniques are used in the computation of risk measures for large mark-to-market credit portfolios with stochastic recovery and correlation between obligors depending on the state of the economy. We compare the efficiency of the saddle point approach with existing methods such as plain Monte Carlo simulation and large deviation theory. By measuring run time and accuracy of calculations of the value-at-risk and the conditional value-at-risk for different significance levels we analyze the quality of these approximation approaches. Furthermore, the approximation quality over the whole portfolio loss distribution function is analyzed. The results show that the saddle point approximation performs not only very quickly but also very accurately over the whole loss distribution function. This result is not limited to large portfolios and can also be achieved for small portfolios.

Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process

The log-likelihood of a nonhomogeneous Branching Diffusion Process under several conditions assuring existence and uniqueness of the diffusion part and nonexplosion of the branching process. Expressions for different Fisher information measures are provided. Using the semimartingale structure of the process and its local characteristics, a Girsanov-type result is applied. Finally, an Ornstein-Uhlenbeck process with finite reproduction mean is studied. Simulation results are discussed showing consistency and asymptotic normality.