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We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from Gosper's algorithm.
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This paper develops a model for volatility sensitivity to the underlying asset price. It has applications to option pricing and dynamic delta hedging under stochastic volatility. The model allows at-the-money volatility sensitivity to change continuously with S and this corresponds to a quadratic parameterization to the volatility surface. The extension to fixed strike volatility sensitivities is achieved using a principal component analysis on the deviation of fixed strike volatilities from at-the-money volatility.

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In an economy in which investors with different time preferences have heterogeneous beliefs about a dividend
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by Kristina Andersson
In the original Black-Scholes model, the risk is quantied by a constant volatility parameter. It has been proposed by many authors that the volatilities should be modeled by a stochastic process to obtain a more realistic model. The volatility that corresponds to actual market data for option prices in Black-Scholes model is called the implied volatility. This volatility is in general dependent on the strike price, in contrast to the underlying assumption of Black-Scholes model. As a function of strike it forms a curve called "volatility smile". To explain this smile it has been proposed to study models allowing for a volatility driven by a stochastic process. In the present paper a review of stochastic volatility is presented and three stochastic volatility models are studied in some detail. We study the volatility smile of these models and show that in some cases we can reproduce a smile similar to the curves occuring in reality. We also study a corrected Black-Scholes pricing formula

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A presentation by Andrew Ledvina

Covers SABR,Heston, and others
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In this article we discuss the Heston model with stochastic interest rates driven by Hull-White (HW) or Cox-Ingersoll-Ross (CIR) processes. We define a so-called volatility compensator which guarantees that the Heston hybrid model with a non-zero correlation between the equity and interest rate processes is properly defined. Moreover, we propose an approximation for the characteristic function, so that pricing of basic derivative products can be efficiently done using Fourier techniquesWe also discuss the effect of the approximations on the instantaneous correlations, and check the influence of the correlation between stock and interest rate on the implied volatilities.

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Heston-Hull-White, Heston-Cox-Ingersoll-Ross, equity-interest rate hybrid products, affine jump diffusion processes


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nice thesis by Linghao Yi
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