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In this paper we investigate the profitability of’ skewness trades’ and ‘kurtosis trades’ based on comparisons of implied state price densities versus historical densities. In particular, we examine the ability of SPD comparisons to detect structural breaks in the options market behaviour. While the implied state price density is estimated by means of the Barle and Cakici Implied Binomial Tree algorithm...
Financial institutions are making a concerted effort to measure and manage credit risk inherent in their large defaultable portfolios. This is partly in response to regulatory requirements to have adequate capital to meet credit event contingencies, but risk managers are also concerned about the sensitivity of the value of their portfolios to potential deteriorating credit quality of issuers. These...
High price volatility is a long-standing characteristic of world oil markets and, more recently, of natural gas and electricity markets. However, there is no widely accepted answer to what the best models and measures of price volatility are because of the complexity of distribution of energy prices. Complex distribution patterns and volatility clustering of energy prices have motivated considerable...
This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.
We explore the applicability of bootstrap unit root tests to time series with heavy-tailed errors. The size and power of the tests are investigated using simulated data. Applications to financial time series are also presented. Two different bootstrap methods and the subsampling approach are compared. Conclusions on the optimal bootstrap parameters, the range of applicability, and the performance...
This paper analyzes stable Paretian models in portfolio theory, risk management and option pricing theory. Firstly, we examine investor’s optimal choices when we assume respectively either Gaussian or stable non-Gaussian distributed index returns. Thus, we approximate discrete time optimal allocations assuming different distributional assumptions and considering several term structure scenarios. Secondly,...
We review optimal quantization methods for numerically solving nonlinear problems in higher dimensions associated with Markov processes. Quantization of a Markov process consists in a spatial discretization on finite grids optimally fitted to the dynamics of the process. Two quantization methods are proposed: the first one, called marginal quantization, relies on an optimal approximation of the marginal...
The seminal work of Mandelbrot and Fama, carried out in the 1960s, suggested the class of α-stable laws as a probabilistic model of financial assets returns. Stable distributions possess several properties which make plausible their application in the field of finance — heavy tails, excess kurtosis, domains of attraction. Unfortunately working with stable laws is very much obstructed by the lack of...
The high computational complexity of many problems in financial decision-making has prevented the development of time-efficient deterministic solution algorithms so far. At least for some of these problems, e.g., constrained portfolio selection or non-linear time series prediction problems, the results from complexity theory indicate that there is no way to avoid this problem. Due to the practical...
The paper compares portfolio optimization approaches with expected regret and Conditional Value-at-Risk (CVaR) performance functions. The expected regret is defined as an average portfolio underperformance comparing to a fixed target or some benchmark portfolio. For continuous distributions, CVaR is defined as the expected loss exceeding α-Value-at Risk (VaR), i.e., the mean of the worst (1-α) 100%...
The paper gives a survey on recent developments on the use of numerical methods in rating based Credit Risk Models. Generally such models use transition matrices to describe probabilities from moving from one rating state to the other and to calculate Value-at-Risk figures for portfolios. We show how numerical methods can be used to find so-called true generator matrices in the continuous-time approach,...
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