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Multiscale Stochastic Volatility Asymptotics
In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process…
Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under…
Wave Propagation and Time Reversal in Randomly Layered Media
and Overview of the Book.- Waves in Homogeneous Media.- Waves in Layered Media.- Effective Properties of Randomly Layered Media.- Scaling Limits.- Asymptotics for Random Ordinary Differential…
Singular Perturbations in Option Pricing
It is shown that, in the presence of time scales between the main observed process and the volatility driving process, asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas.
A direct imaging algorithm for extended targets
Efficiency and robustness of the algorithm with respect to measurement noise and random medium fluctuations are demonstrated and multiple-frequency information improves both resolution and stability of the algorithms.
Maturity cycles in implied volatility
- J. Fouque, G. Papanicolaou, R. Sircar, K. Sølna
- Economics, MathematicsFinance Stochastics
- 1 November 2004
It is shown that the skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients.
Correction to Black-Scholes Formula Due to Fractional Stochastic Volatility
A rigorous analysis is presented for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations.
Short time-scale in S&P500 volatility
A phase and space coherent direct imaging method.
- Songming Hou, Kai Huang, K. Sølna, Hongkai Zhao
- PhysicsThe Journal of the Acoustical Society of America
- 21 January 2009
A direct imaging algorithm for point and extended targets is presented that is simple and efficient since no forward solver or iteration is needed and robustness of the algorithm with respect to noise is demonstrated via numerical examples.
Computing the SVD of a General Matrix Product/Quotient
A new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form that constructs a bidiagonal form of the sequence as an intermediate result and is more economical than current methods.