Subordinator

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

A recursive pricing method for autocallables under multivariate subordination

Abstract: In this paper we develop a new class of models for pricing autocallables based on multivariate subordinate Orstein Uhlenbeck (OU) processes. Starting from d independent OU processes and an independent d-dimensional Levy subordinator, we construct a new process by time changing each of the OU processes with a coordinate of the Levy subordinator. The prices of underlying assets are then modeled as an exponential function of the subordinate processes. The new models introduce state-dependent jumps in the asset prices and the dependence among jumps is governed by the Levy measure of the d-dimensional subordinator. By employing the eigenfunction expansion technique, we are able to derive the analytical formulas for the worst-of autocallable prices. We also numerically implement a specific model and test its sensitivity to some of the key parameters of the model.

Multiple Subordinated Modeling of Asset Returns

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.

Variance Swaps on Defaultable Assets and Market Implied Time-Changes

Abstract: We compute the value of a variance swap when the underlying is modeled as a Markov diffusion process time changed by a Levy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Levy measure and local stochastic volatility and have a local stochastic default intensity. Moreover, the Levy subordinator that drives the underlying can be obtained directly by observing European call/put prices. To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the underlying is modeled as a Levy subordinated jump-to-default constant elasticity of variance process (see [Carr and V. Linetsky, Finance Stoch., 10, pp. 303--330, 2005]). In this example, we extend the results of [Mendoza-Arriaga, Carr, and Linetsky, Math. Finance, 20, pp. 527--569, 2010], by allowing for joint valuation of credit and equity derivatives as well as variance swaps.

Multiple Subordinated Modeling of Asset Returns

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 Proof from `First Principles' of Kesten's Result for the Probabilities with which a Subordinator Hits Points.

Abstract: We give a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points.