Dynamic Hedging Using Generated Genetic Programming Implied Volatility Models

The purpose of this paper is to improve the accuracy of dynamic hedging using implied volatilities generated by genetic programming. Using real data from S&P500 index options, the genetic programming's ability to forecast Black and Scholes implied volatility is compared between static and dynamic training-subset selection methods. The performance of the best generated GP implied volatilities is tested in dynamic hedging and compared with Black-Scholes model. Based on MSE total, the dynamic training of GP yields better results than those obtained from static training with fixed samples. According to hedging errors, the GP model is more accurate almost in all hedging strategies than the BS model, particularly for in-the-money call options and at-the-money put options.Comment: 32 pages,13 figures, Intech Open Scienc

Accelerated American option pricing with deep neural networks

Given the competitiveness of a market-making environment, the ability to speedily quote option prices consistent with an ever-changing market environment is essential. Thus, the smallest acceleration or improvement over traditional pricing methods is crucial to avoid arbitrage. We propose a method for accelerating the pricing of American options to near-instantaneous using a feed-forward neural network. This neural network is trained over the chosen (e.g., Heston) stochastic volatility specification. Such an approach facilitates parameter interpretability, as generally required by the regulators, and establishes our method in the area of eXplainable Artificial Intelligence (XAI) for finance. We show that the proposed deep explainable pricer induces a speed-accuracy trade-off compared to the typical Monte Carlo or Partial Differential Equation-based pricing methods. Moreover, the proposed approach allows for pricing derivatives with path-dependent and more complex payoffs and is, given the sufficient accuracy of computation and its tractable nature, applicable in a market-making environment

Model uncertainty and its impact on the pricing of derivative instruments

Model uncertainty, in the context of derivative pricing, can be defined as the uncertainty on the value of a contingent claim resulting from the lack of precise knowledge of the pricing model to be used for its valuation. We introduce here a quantitative framework for defining model uncertainty in option pricing models. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk measurement and management, we propose a method for measuring model uncertainty which verifies these properties and yields numbers which are comparable to other risk measures and compatible with observations of market prices of a set of benchmark derivatives. We illustrate the difference between model uncertainty and the more common notion of "market risk" through examples. Finally, we illustrate the connection between our proposed measure of model uncertainty and the recent literature on coherent and convex risk measures.decision under ambiguity; uncertainty; option pricing; risk measures; mathematical finance

A Characterization of Stochastically Stable Networks

Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.Network formation, Pairwise stability, Stochastic stability

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Applying Dynamic Training-Subset Selection Methods Using Genetic Programming for Forecasting Implied Volatility

International audienceVolatility is a key variable in option pricing, trading, and hedging strategies. The purpose of this article is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training-subset selection methods. These methods manipulate the training data in order to improve the out-of-sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models, which are not adapted to some out-of-sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training-subset selection methods are proposed based on random, sequential, or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases' errors. Using real data from S&P500 index options, these techniques are compared with the static subset selection method. Based on mean squared error total and percentage of non-fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, especially those obtained from the adaptive-random training-subset selection method applied to the whole set of training samples

Pricing and hedging of a portfolio of options in the presence of stochastic volatility

Dopo aver fatto pricing di un basket di opzioni sul S&P500 sia con black-scholes che Heston, vengono effettuate diverse strategie di hedging dinamico (Delta, Delta-Gamma, Delta-Gamma-Vega

WAMI: a web server for the analysis of minisatellite maps

Abouelhoda M, El-Kalioby M, Giegerich R. WAMI: a web server for the analysis of minisatellite maps. BMC Evolutionary Biology. 2010;10(1): 167.Background Minisatellites are genomic loci composed of tandem arrays of short repetitive DNA segments. A minisatellite map is a sequence of symbols that represents the tandem repeat array such that the set of symbols is in one-to-one correspondence with the set of distinct repeats. Due to variations in repeat type and organization as well as copy number, the minisatellite maps have been widely used in forensic and population studies. In either domain, researchers need to compare the set of maps to each other, to build phylogenetic trees, to spot structural variations, and to study duplication dynamics. Efficient algorithms for these tasks are required to carry them out reliably and in reasonable time. Results In this paper we present WAMI, a web-server for the analysis of minisatellite maps. It performs the above mentioned computational tasks using efficient algorithms that take the model of map evolution into account. The WAMI interface is easy to use and the results of each analysis task are visualized. Conclusions To the best of our knowledge, WAMI is the first server providing all these computational facilities to the minisatellite community. The WAMI web-interface and the source code of the underlying programs are available at http://www.nubios.nileu.edu.eg/tools/wam