1,720,980 research outputs found
A new class of multidimensional Wishart-based hybrid models
Full text linkIn this article, we present a new class of pricing models that extend the application of Wishart processes to the so-called stochastic local volatility (or hybrid) pricing paradigm. This approach combines the advantages of local and stochastic volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multidimensional specifications for the stochastic volatility component. Our work tries to fill the gap: we introduce two hybrid models in which the stochastic volatility dynamics is described by means of a Wishart process. The proposed parametrizations not only preserve the desirable features of existing Wishart-based models but significantly enhance the ability of reproducing market prices of vanilla options
Calibration and advanced simulation schemes for the Wishart stochastic volatility model
Full text linkIn this article, we deal with calibration and Monte Carlo simulation of the Wishart stochastic volatility model. Despite the analytical tractability of the considered model, being of affine type, the implementation of Wishart-based stochastic volatility models poses non-trivial challenges from a numerical point of view. The goal of this article is to overcome these problems providing efficient numerical schemes for Monte Carlo simulations. Moreover, a fast and accurate calibration procedure is proposed
Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities
Full text linkWe present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes
Optimal investment strategies with a minimum performance constraint
Full text linkWe consider the optimal investment problem of a fund manager in the presence of a minimum guarantee constraint on the fund performance. The manager receives a fee which is proportional to the liquidation value of the portfolio or of the surplus over the guarantee in case it is positive and zero otherwise, eventually augmented by a constant fee. Her remuneration is reduced through the application of a penalty if the value of the fund at maturity is below a specified-in-advance threshold (minimum guarantee). We deal with two different settings: a continuous time economy with constant instantaneous interest rate and the case where the interest rate evolves as the Vasicek model. Explicit formulas for the optimal investment strategy are presented. We compare our portfolio strategies to the Merton portfolio and to the Option Based Portfolio Insurance strategy
Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options
Full text linkThe Wiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a Lévy process, such as the maximum, the minimum and hitting times. Here we propose a constructive procedure for the computation of the Wiener-Hopf factors, valid for both single and double barriers, based on the combined use of the Hilbert and the z-transform. The numerical implementation can be simply performed via the fast Fourier transform and the Euler summation. Given that the information in the Wiener-Hopf factors is strictly related to the distributions of the first passage times, as a concrete application in mathematical finance we consider the pricing of discretely monitored exotic options, such as lookback and barrier options, when the underlying price evolves according to an exponential Lévy process. We show that the computational cost of our procedure is independent of the number of monitoring dates and the error decays exponentially with the number of grid points
ESG ratings explainability through machine learning techniques
No full textEnvironmental, Social, and Governance (ESG) scores are quantitative assessments of companies' commitment to sustainability that have become extremely popular tools in the financial industry. However, transparency in the ESG assessment process is still far from being achieved. In fact there is no full disclosure on how the ratings are computed. As a matter of fact, rating agencies determine ESG ratings (as a function of the E, S and G scores) through proprietary models which public knowledge is limited to what the data provider effectively chooses to disclose, that, in many cases, is restricted only to the main ideas and essential principles of the procedure. The goal of this work is to exploit machine learning techniques to shed light on the ESG ratings issuance process. In particular, we focus on the Refinitiv data provider, widely used both from practitioners and from academics, and we consider white-box and black-box mathematical models to reconstruct the E, S, and G ratings' assessment model. The results show that it is possible to replicate the underlying assessment process with a satisfying level of accuracy, shedding light on the proprietary models employed by the data provider. However, there is evidence of persisting unlearnable noise that even more complex models cannot eliminate. Finally, we consider some interpretability instruments to identify the most important factors explaining the ESG ratings
Option pricing, maturity randomization and distributed computing
No full textWe price discretely monitored options when the underlying evolves according to different exponential Lévy processes.
By geometric randomization of the option maturity, we transform the -steps backward recursion that arises in option pricing into an integral equation. The option price is then obtained solving n independent integral equations by a suitable quadrature method. Since the integral equations are mutually independent, we can exploit the potentiality of a grid computing architecture. The primary performance disadvantage of grids is the slow communication speeds between nodes. However, our algorithm is well-suited for grid computing since the integral equations can be solved in parallel, without the need to communicate intermediate results between processors. Moreover, numerical experiments on a cluster architecture show the good scalability properties of our algorithm.We price discretely monitored options when the underlying evolves according to different exponential Levy processes. By geometric randomization of the option maturity, we transform the n-steps backward recursion that arises in option pricing into an integral equation. The option price is then obtained solving n independent integral equations by a suitable quadrature method. Since the integral equations are mutually independent, we can exploit the potentiality of a grid computing architecture. The primary performance disadvantage of grids is the slow communication speeds between nodes. However, our algorithm is well-suited for grid computing since the integral equations can be solved in parallel, without the need to communicate intermediate results between processors. Moreover, numerical experiments on a cluster architecture show the good scalability properties of our algorithm. (C) 2010 Elsevier B.V. All rights reserved
Pricing Discretely Monitored Asian Options by Maturity Randomization
No full textWe present a new methodology based on maturity randomization to price discretely monitored arithmetic Asian options when the underlying asset evolves according to a generic Lévy process. Our randomization technique considers the option expiry to be a random variable distributed according to a geometric distribution of a parameter independent of the underlying process. This allows one to transform the pricing backward procedure into a set of independent integral equations. Numerical procedures for a fast and accurate solution of the pricing problem are provided
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