Daniel Wei-Chung Miao

Sample-path analysis of general arrival queueing systems with constant amount of work for all customers

We consider a discrete-time queueing system where the arrival process is general and each arriving customer brings in a constant amount of work which is processed at a deterministic rate. We carry out a sample-path analysis to derive an exact relation between the set of system size values and the set of waiting time values over a busy period of a given sample path. This sample-path relation is then applied to a discrete-time

A note on the never-early-exercise region of American power exchange options

G/D/c

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

queue with constant service times of one slot, yielding a sample-path version of the steady-state distributional relation between system size and waiting time as derived earlier in the literature. The sample-path analysis of the discrete-time system is further extended to the continuous-time counterpart, resulting in a similar sample-path relation in continuous time.

Using forward Monte-Carlo simulation for the valuation of American barrier options

Abstract We propose a jump-diffusion model where the bivariate jumps are serially correlated with a mean-reverting structure. Mathematical analysis of the jump accumulation process is given, and the European call option price is derived in analytical form. The model and analysis are further extended to allow for more general jump sizes. Numerical examples are provided to investigate the effects of mean-reversion in jumps on the risk-neutral return distributions, option prices, hedging parameters, and implied volatility smiles.

Corrected Discrete Approximations for the Conditional and Unconditional Distributions of the Continuous Scan Statistic

This note discusses how the never-early-exercise region of American power exchange options is influenced by the nonlinearity from its power coefficients. We consider a class of models which satisfy the power invariant property and show that early exercise depends crucially on the quantities termed effective dividend yields. Our mathematical analysis extends an existing model-free result and indicates how early exercise should depend on parameters. A numerical analysis is conducted to complement the analytical results and provide further observations.

Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

In the queueing literature, an arrival process with random arrival rate is usually modeled by a Markov-modulated Poisson process (MMPP). Such a process has discrete states in its intensity and is able to capture the abrupt changes among different regimes of the traffic source. However, it may not be suitable for modeling traffic sources with smoothly (or continuously) changing intensity. Moreover, it is less parsimonious in that many parameters are involved but some are lack of interpretation. To cope with these issues, this paper proposes to model traffic intensity by a geometric mean-reverting (GMR) diffusion process and provides an analysis for the Markovian queueing system fed by this source. In our treatment, the discrete counterpart of the GMR arrival process is used as an approximation such that the matrix geometric method is applicable. A conjecture on the error of this approximation is developed out of a recent theoretical result, and is subsequently validated in our numerical analysis. This enables us to calculate the performance measures with high efficiency and precision. With these numerical techniques, the effects from the GMR parameters on the queueing performance are studied and shown to have significant influences. HighlightsA new traffic source is proposed to accommodate continuously changing intensity.This model is parsimonious with two key parameters having clear physical meanings.A conjecture relating continuous and discrete systems is established and validated.Matrix geometric method and extrapolation are jointly applied for queueing analysis.The effects of the two key traffic parameters on queueing systems are investigated.

A Standardized Normal-Laplace Mixture Distribution Fitted to Symmetric Implied Volatility Smiles

ABSTRACT This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.

A Markov-Switching Range-Based Volatility Model with Applications in Volatility Adjusted VAR Estimation

This paper extends the forward Monte-Carlo methods, which have been developed for the basic types of American options, to the valuation of American barrier options. The main advantage of these methods is that they do not require backward induction, the most time-consuming and memory-intensive step in the simulation approach to American options pricing. For these methods to work, we need to define the so-called pseudo critical prices which are used to determine whether early exercise should happen. In this study, we define a new and more flexible version of the pseudo critical prices which can be conveniently extended to all fourteen types of American barrier options. These pseudo critical prices are shown to satisfy the criteria of a sufficient indicator which guarantees the effectiveness of the proposed methods. A series of numerical experiments are provided to compare the performance between the forward and backward Monte-Carlo methods and demonstrate the computational advantages of the forward methods.