Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.

Distribution of suprema for generalized risk processes

Abstract: We study a generalized risk process X(t)=Y(t)−C(t),t∈[0,τ], where Y is a Levy process, C an independent subordinator and τ an independent exponential time. Dropping the standard assumptions on the ...

Multiple Subordinated Modeling of Asset Returns: Implications for Option Pricing

Abstract: Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial time-clocks motivated by behavioral finance. To be consistent with dynamic asset pricing theory and option pricing, as suggested by behavioral finance, the investors' view is considered by introducing an intrinsic time process which we refer to as a behavioral subordinator. The process is subordinated to the Brownian motion process in the well-known log-normal model, resulting in a new log-price process. The number of embedded subordinations results in a new parameter that must be estimated and this parameter is as important as the mean and variance of asset returns. We describe new distributions, demonstrating how they can be applied to modeling the tail behavior of stock market returns. We apply the proposed models to modeling S&P 500 returns, treating the CBOE Volatility Index as intrinsic time change and the CBOE Volatility-of-Volatility Index as the volatility subordinator. We find that these volatility indexes are not proper time-change subordinators in modeling the returns of the S&P 500.

A spectral approach to pricing of forward starting options

Abstract: We propose a new class of models for pricing forward starting options. We assume that the asset price is a nonlinear function of a CIR process, time changed by a composition of a Levy subordinator and an absolutely ´ continuous process. The new models introduce the nonlinearity in both drift and diffusion components of the underlying process and can capture jumps and stochastic volatility in a flexible way. By employing the spectral expansion technique, we are able to derive the analytical formulas for the forward starting option prices. We also implement a specific model numerically and test its sensitivity to some of the key parameters of the model.