Tahar FERHATI - Research

Research and projects

I am an Applied Mathematician with teaching and research interests in both the mathematical and computational aspects of financial derivatives. In particular, stochastic volatility and jump diffusion models, exotic options, interest rate modelling.

I acheived many projects in the area of :

Pricing and hedging derivatives: Black-Scholes, Local volatility, HJM, BGM, Stochastic volatility.
Numerical Methods: PDEs, Monte-Carlo simulation, C++ for finance, Calibration.
Stochastic calculus, Lévy processes, stochastic control, High frequency trading, Energy Markets,
Risk Management, Econometrics, Basel Reglementation.

Working Papers

FERHATI, Tahar, Robust Calibration For SVI Model Arbitrage Free (February 24, 2020). Available at SSRN: https://ssrn.com/abstract=3543766 or http://dx.doi.org/10.2139/ssrn.3543766
FERHATI, Tahar, SVI Model Free Wings (March 20, 2020). Available at SSRN: https://ssrn.com/abstract=3557646 or http://dx.doi.org/10.2139/ssrn.3557646

Leading indicator for currency crises in emerging market

The purpose of this project is to analyze the event that defines a currency crisis. To do this, a comparative study of two indicators is used: nominal depreciation indicator, and the zscore of speculative attack. We then studied the effect of the estimation period on the variables composing the index. Then we have developed a new indicator of speculative attack KRLm 1998 : Kaminsky et al. (1998) summarise the results of 28 empirical studies on currency crises that have appeared over the last 20 years. This indicator makes it possible to indicate the fluctuations even in the case of a PEG. The predictive power of the index for this scenario is 54.05%.

Curency crisis : Malaysia 1997 , and Argentina 1995

Estimating the Yield Curve Using the Nelson‐Siegel Model

The term structure of interest rates or yield curve is an important tool for businesses and investors; it is an indicator of the economic and financial health of the country. The Nelson-Siegel model is widely used by central banks and other market as a model for the term structure of interest rates (to model the yield curve). In this project, we calibrated this model using the Gauss–Newton algorithm. We implemented and tested an optimization; we estimated the model’s parameters.

Option Pricing Models with Jumps : regularized Calibration of Merton model

An important issue in finance is model calibration. The calibration problem is the inverse of the option-pricing problem. It can be shown that the usual formulation of the inverse problem via Non-linear Least Squares is an ill posed problem. To achieve well posedness of the problem, some regularization is needed. This project consists of two parts. The first one is the study of the Merton model, the simulation of the evolution of underlying asset with jumps. The analytical calculation of the price of the options in the Merton model and its evaluation by Monte-Carlo method is required. The second part is the study a regularization method based on Lavenberg – Marquart regularization and on relative entropy introduced in the article of Rama Cont and Peter Tankov where the authors reformulate the calibration problem into a problem of finding a risk-neutral exponential Levy model that reproduces the observed option prices and has the smallest possible relative entropy with respect to a chosen prior model.

Euro Call under Merton Model ( MJD)

Calibration and hedging of derivatives: simulation of Delta-hedging in the complete and incomplete market

The purpose of this project is to study the delta-hedging strategy in the Black-Scholes model and in the stochastic volatility. In both cases, trading takes place only on discrete dates and the portfolio is rebalanced only in a finite number of time during the life of the option. A self-financing portfolio strategy is used to represent a dynamic strategy of buying or selling shares and loans or borrowing from the bank whose portfolio value is not affected by the addition or withdrawal of the portfolio. Cash.

P & L (Profit and Loss) of the delta-hedge strategy is measured by the difference between the option price at maturity and the terminal value of the hedge portfolio.

Empirical Properties of Financial Data : Testing the Brownian motion Hypothesis

In this project, we will manipulate some financial data (Stocks, Stock Index, Bonds, Gold, Oil, Currency…), to study some proprieties of the brownien motion. Our data come from Bloomberg terminal. For each historical series, we calculate the returns; next, we use some statistics tools to get the probability of large drops, autocorrelation and independence of the returns, and the correlation between volatility and returns. Finally, we conclude if the return’s distribution is Gaussian and how we could to improve our results in the future.

Evaluation of user anomaly behavior From large advertising system using k-means approach

This is a machine learning project for anomaly detection, also called outlier detection, is one of the important practical questions in data mining in many industrial fields such as banks, internet merchants, and many other online sales providers. In this project, we present the analysis of user anomaly behavior from time sequences in large online advertising system. The data sets from online website user are presented and analyzed. We apply k-means clustering technique to extract the general patterns for users’ behaviors from their historical data. The pattern similarity between the evaluated period and general pattern is calculated. The analysis provides a useful technical tool and insights for bidding advertisement system.

Calibration of implied volatility in the Black Scholes Model: Smile volatility

Traders quote prices in terms of implied volatility. The purpose of this project is to calibrate the implied volatility in the Black Scholes model, we look at implied volatility for call options traded on the London Internetional Financial Futures and Option Exchange (LIFFE, as reported in the Financial Times). The data is for the FTSE 100 index, which is an average of 100 shares quoted on the London Stock Exchange. In the model Black Scholes, the underlying asset follows the geometric Brownian motion.

Heston Model and Smile volatility

In this project, we will study the Heston model as a mathematical model describing the evolution of an underlying asset, it is a stochastic volatility model: Such a model assumes that the volatility of the asset is not constant or deterministic, but it follows a stochastic process. We evaluate the different values of volatility given set of Strike values so that the difference between the option prices, which is a binary option in our case, under the black-sholes model and the price of that same option under the Heston model is minimized.

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