Displaying similar documents to “On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications.”

The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics. I

Josef Štěpán, Petr Dostál (2003)

Kybernetika

Similarity:

The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients b and σ being generally C ( ℝ + ) -progressive processes. Any weak solution X is called a ( b , σ ) -stock price and Girsanov Theorem jointly with the DDS Theorem on time changed martingales are applied to establish the probability distribution μ σ of X in C ( ℝ + ) in the special case of a diffusion volatility σ ( X , t ) = σ ˜ ( X ( t ) ) . A martingale option pricing method is presented.

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

Similarity:

A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving...