5,565 research outputs found

    Barrier Option Pricing under SABR Model Using Monte Carlo Methods

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    The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models

    Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models

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    Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European options, up-and-out options, double-barrier knock-out options, and options which pay a rebate upon hitting a boundary. For European options, our method is shown to produce option price approximations which are equivalent to those developed in [5]. [5] Jean-Pierre Fouque, George Papanicolaou, and Sircar Ronnie. Derivatives in Financial Markets with Stochas- tic Volatility. Cambridge University Press, 2000

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

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    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.

    A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection

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    We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted as the canonical extension of local volatility for barrier options. Alternatively, a forward partial-integro differential equation (PIDE) is introduced which provides up-and-out call prices, under a Brunick-Shreve model, for the complete set of strikes, barriers and maturities in one solution step. Similar to the vanilla forward PDE, the above-named forward PIDE can serve as a building block for an efficient calibration routine including barrier option quotes. We provide a discretisation scheme for the PIDE as well as a numerical validation.Comment: 20 pages, Quantitative Finance Volume 16, 2016 - Issue

    Delay geometric Brownian motion in financial option valuation

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    Motivated by influential work on complete stochastic volatility models, such as Hobson and Rogers [11], we introduce a model driven by a delay geometric Brownian motion (DGBM) which is described by the stochastic delay differential equation dSðtÞ ¼ mðSðt 2tÞÞSðtÞdt þ VðSðt 2tÞÞSðtÞdWðtÞ. We show that the equation has a unique positive solution under a very general condition, namely that the volatility function V is a continuous mapping from Rþ to itself. Moreover, we show that the delay effect is not too sensitive to time lag changes. The desirable robustness of the delay effect is demonstrated on several important financial derivatives as well as on the value process of the underlying asset. Finally, we introduce an Euler–Maruyama numerical scheme for our proposed model and show that this numerical method approximates option prices very well. All these features show that the proposedDGBMserves as a rich alternative in modelling financial instruments in a complete market framework
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