Asymptotic analysis for stochastic volatility: Edgeworth expansion

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model

Efficient discretisation of stochastic differential equations

The aim of this study is to find a generic method for generating a path of the solution of a given stochastic differential equation which is more efficient than the standard Euler-Maruyama scheme with Gaussian increments. First we characterize the asymptotic distribution of pathwise error in the Euler-Maruyama scheme with a general partition of time interval and then, show that the error is reduced by a factor (d+2)/d when using a partition associated with the hitting times of sphere for the driving d-dimensional Brownian motion. This reduction ratio is the best possible in a symmetric class of partitions. Next we show that a reduction which is close to the best possible is achieved by using the hitting time of a moving sphere which is easier to implement

Volatility Derivatives and Model-free Implied Leverage

Electronic version of an article published as International Journal of Theoretical and Applied Finance, 17, 1, 2014, 1450002 https://doi.org/10.1142/S0219024914500022 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijta