Papers by Farshid Mehrdoust
Stock markets around the world are growing rapidly and vulnerability created by default risk of o... more Stock markets around the world are growing rapidly and vulnerability created by default risk of option holders has become a serious issue. In such circumstances, this paper suggests the pricing of vulnerable European and barrier options when the underlying asset follows the uncertain stock model. According to the uncertainty theory, we present closed-form analytic formulas of these options prices and use the residuals method to estimate the uncertain stock model parameters. Ultimately, based on the estimated parameters, we evaluate the effect of the vulnerable option parameters on its price.
Australian & New Zealand industrial and applied mathematics journal, Mar 25, 2011
The problem of obtaining the smallest and the largest generalised eigenvalues using quasi Monte C... more The problem of obtaining the smallest and the largest generalised eigenvalues using quasi Monte Carlo algorithm is considered. We first study the results of Dimov and others using three algorithms based on the power method combined with Monte Carlo and quasi Monte Carlo methods for evaluating extremal eigenvalue of real matrices. We present a quasi Monte Carlo algorithm for computing both the smallest and the largest generalised eigenvalues using Sobol, Halton sequences and the rand function in Matlab. We finally compare the efficiency of three employed generators in our algorithm for different pencils.
Computational and Applied Mathematics
Journal of Computational and Applied Mathematics, 2021
Annals of Financial Economics, 2020
This paper considers a class of Levy process namely the variance gamma (VG) process to offer a mo... more This paper considers a class of Levy process namely the variance gamma (VG) process to offer a more realistic way to model the dynamics of the logarithm of stock prices. Then, we verify the uniqueness and existence of the solution to the stochastic differential equation of the model. We also examine the valuation of multi-asset American options under VG model when the correlation coefficient is governed by the modified Ornstein–Uhlenbeck process. Various simulation experiments are presented and the achieved results are tested empirically for option prices using S&P 500 data.
Mathematics and Financial Economics, 2021
Jump in electricity prices is often due to shock in electricity demand or shock in existing elect... more Jump in electricity prices is often due to shock in electricity demand or shock in existing electricity supplies, which can be caused by sudden changes in temperature or production and system failure. Since jumps in electricity dynamics are directly related to the regime switch, we model them via the chain itself and consider a regime switching model for electricity spot price dynamic. Next, we determine an equivalent measure by Esscher transform and through it we evaluate the electricity forwards and risk premium. We apply expectation maximization algorithm to estimate parameters of the model. Furthermore, we use the real data of Nord Pool market to calibration of the proposed model. Using the characteristic function of model, we obtain a closed-form for forward contracts of Nord Pool market. Finally, we provide forward surfaces which show the months, quarters and seasons-ahead prices.
Chaos, Solitons & Fractals, 2020
Uncertain differential equation (UDE) has been widely applied in the financial market, and many o... more Uncertain differential equation (UDE) has been widely applied in the financial market, and many option pricing formulas are derived based on UDE. But the existing literature don't consider the parameter estimation of UDE, and the parameters are just assumed as some given constants. This paper will present an approach to estimate the unknown parameter of UDE from discretely sampled data via α-path method for the first time. And the concepts of forecast value and confidence interval are introduced to predict the future value in a UDE. As five special UDEs, the parameters estimations of arithmetic Liu process, geometric Liu process, uncertain Ornstein-Uhlenbeck process, uncertain mean-reverting process, and uncertain exponential Ornstein-Uhlenbeck process are also derived, and the corresponding numerical examples are given. Furthermore, this paper proposes a means to estimate unknown parameters for the general geometric Liu process, and as an application, this method will be successfully used in Alibaba stock.
Bulletin of the Iranian Mathematical Society, 2019
Assuming that the volatility process follows the uncertain Cox-Ingersoll-Ross (CIR) model, this p... more Assuming that the volatility process follows the uncertain Cox-Ingersoll-Ross (CIR) model, this paper presents a new version of the uncertain exponential Ornstein-Uhlenbeck interest rate model. The prices of the interest rate ceiling and the interest rate floor based on the model are derived using the Yao-Chen formula. Some algorithms are designed to calculate the prices of these derivatives numerically. We present some numerical experiments which illustrate the behaviour of the proposed model. Keywords Exponential Ornstein-Uhlenbeck model • Uncertain process • Interest rate ceiling • Interest rate floor • Cox-Ingersoll-Ross (CIR) model Mathematics Subject Classification 91B26 • 91B60 B Farshid Mehrdoust
Soft Computing, 2020
This paper presents an uncertain stock model under the multifactor uncertain volatility framework... more This paper presents an uncertain stock model under the multifactor uncertain volatility framework. Based on the uncertainty theory, some closed-form and analytical formulas presented to value a European call and put option under the multifactor uncertain volatility model. Numerical tests are reported to highlight how the proposed model provides interesting results on pricing a European option. Finally, we summarize the theoretical results and some numerical experiments. Keywords Uncertainty theory Á Liu process Á Multifactor model Á European option Communicated by A. Di Nola.
Sādhanā, 2020
This paper considers the problem of pricing of Bermuda options on zero-coupon bond in which the d... more This paper considers the problem of pricing of Bermuda options on zero-coupon bond in which the dynamics of the interest rate model follows the mixed fractional Vasicek model. The strong convergence of the Euler discretization scheme for the mixed fractional Vasicek model is analysed. Specifically, we find an approximate formula for zero-coupon bond price. Numerical experiments are provided and compared for Bermuda-style call and put options with the Monte Carlo simulation approach.
International Journal of Financial Engineering, 2019
In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the vol... more In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.
Communications in Statistics - Theory and Methods, 2018
In this work, we study the existence and uniqueness of the solution to a fractional version of th... more In this work, we study the existence and uniqueness of the solution to a fractional version of the Cox-Ingersoll-Ross (fCIR) stochastic differential equation. The strong convergence of this equation is analyzed and according to it's framework, we obtain the price of the double barrier option under transaction cost. Finally, we verify the effect of the parameters of the model on the value of the option.
Soft Computing, 2017
Valuation of an option plays an important role in modern finance. As the financial market for der... more Valuation of an option plays an important role in modern finance. As the financial market for derivatives continues to grow, the progress and the power of option pricing models at predicting the value of option premium are under investigations. In this paper, we assume that the volatility of the stock price follows an uncertain differential equation and propose an uncertain counterpart of the Heston model. This study also focuses on deriving a numerical method for pricing a European option under uncertain volatility model, and some numerical experiments are presented. Numerical experiments confirm that the developed methods are very efficient. Keywords Uncertainty theory • Uncertain finance • Uncertain volatility model • European option pricing Communicated by V. Loia.
Journal of Computational and Applied Mathematics, 2018
This paper presents a fractional version of the Heston model in which the volatility Brownian and... more This paper presents a fractional version of the Heston model in which the volatility Brownian and price Brownian are replaced by mixed fractional Brownian motions with Hurst parameter H ∈ (3 4 , 1) so that the model exhibits a long range dependence. Then the existence and uniqueness of solution of mixed fractional Heston model are discussed as well as the error of an Euler scheme applied on this model. Finally, some numerical illustrations are given in the last section by computing American put option prices.
Journal of Computational and Applied Mathematics, 2017
This paper proposes an extended version of the Cox-Ingersoll-Ross (CIR) model with stochastic vol... more This paper proposes an extended version of the Cox-Ingersoll-Ross (CIR) model with stochastic volatility and a pricing method on zero-coupon bond under this model. In this version, we replace the standard Brownian motion process with a semi-martingale process named the mixed fractional Brownian motion (mfBm) process which is a linear combination of a fractional Brownian motion (fBm) and a standard Brownian motion. We assume that the part of the volatility process follows a mixed Wishart process which defines by the square of the matrix-valued mfBm process. In order to evaluate the price of the zero-coupon bond under the proposed model we use Monte Carlo simulation method. The computed values of the zero-coupon bond compare with the other interest rate models.
Optimization and Engineering, 2016
We examine the robust mean-VaR portfolio optimization problem when a parametric approach is used ... more We examine the robust mean-VaR portfolio optimization problem when a parametric approach is used for estimating VaR. A robust optimization formulation is used to accommodate estimation risk, and we obtain an analytic solution when there is a risk-free asset and short-selling is allowed. This renders the model computationally tractable. Further, to avoid the conservatism of robust optimal portfolios, we suggest an adjusted robust optimization approach. Empirically, we evaluate the out-of-sample performance of the new approach, the robustness of obtained solutions and level of conservatism of the resulting portfolios. The empirical results highlight some benefits of our approach.
ANZIAM Journal, 2011
The problem of obtaining the smallest and the largest generalised eigenvalues using quasi Monte C... more The problem of obtaining the smallest and the largest generalised eigenvalues using quasi Monte Carlo algorithm is considered. We first study the results of Dimov and others using three algorithms based on the power method combined with Monte Carlo and quasi Monte Carlo methods for evaluating extremal eigenvalue of real matrices. We present a quasi Monte Carlo algorithm for computing both the smallest and the largest generalised eigenvalues using Sobol, Halton sequences and the rand function in Matlab. We finally compare the efficiency of three employed generators in our algorithm for different pencils.
ISRN Applied Mathematics, 2013
One of the most important problems faced by every investor is asset allocation. An investor durin... more One of the most important problems faced by every investor is asset allocation. An investor during making investment decisions has to search for equilibrium between risk and returns. Risk and return are uncertain parameters in the suggested portfolio optimization models and should be estimated to solve the problem. However, the estimation might lead to large error in the final decision. One of the widely used and effective approaches for optimization with data uncertainty is robust optimization. In this paper, we present a new robust portfolio optimization technique for mean-CVaR portfolio selection problem under the estimation risk in mean return. We additionally use CVaR as risk measure, to measure the estimation risk in mean return. To solve the model efficiently, we use the smoothing technique of Alexander et al. (2006). We compare the performance of the CVaR robust mean-CVaR model with robust mean-CVaR models using interval and ellipsoidal uncertainty sets. It is observed that ...
Matrix balancing may effect the stability of algorithms in matrix computations and the accuracy o... more Matrix balancing may effect the stability of algorithms in matrix computations and the accuracy of computed solutions. In this paper, we first introduce an algorithm for matrix balancing. Then, using Monte Carlo method we propose a robust algorithm to evaluate dominant eigenpair of a given matrix. Finally, several randomly generated examples are presented to show the efficiency of the new method.
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Papers by Farshid Mehrdoust