Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in...

Recently, there has been a growing interest in the methods addressing volatility in computational finance and econometrics. Peiris et al. [8] have introduced doubly stochastic volatility models with GARCH innovations. Random coefficient autoregressive sequences are special case of doubly stochastic time series. In this paper, we consider some doubly stochastic stationary time series with GARCH ...

Over the past few years, model complexity in quantitative finance has increased substantially in response to earlier approaches that did not capture critical features for risk management. However, given the preponderance of the classical Black–Scholes model, it is still not clear that this increased complexity is matched by additional accuracy in the ultimate result. In particular, the last dec...

We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a perturbation around the complete market constant volatility problem for the value function, which is well-unders...

Stochastic volatility (SV) models play an important role in finance. Under these models, the volatility of an asset follows an individual stochastic process. In contrast to the GARCH model, the volatility process in the SV model is autonomous with no need to refer to the asset price. It is often assumed that the log-volatility process follows a standard ARMA process in an SV model. However, emp...

The multivariate lognormal model is a basic pricing model for derivatives with multiple underlying processes, for example, spread options. However, the market observation of implied correlation skew examplifies how inaccurate the constant correlation assumption in the multivariate lognormal model can be. In this paper, we study alternative modeling approaches that generate implied correlation s...

Han, Chuan-Hsiang. Singular Perturbations on Non-Smooth Boundary Problems in Finance. (Under the direction of Jean-Pierre Fouque.) In this work we apply asymptotic analysis on compound options, American options, Asian options, and variance (or volatility) contracts in the context of stochastic volatility models. Singular perturbation techniques are primarily used. A singular-regular perturbatio...

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today’s return and tomorrow’s volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their condi...

This paper presents a model for asset returns incorporating both stochastic volatility and jump e ects. The return process is driven by two types of randomness: small random shocks and large jumps. The stochastic volatility process is a ected by both types of randomness in returns. Speci cally, in the absence of large jumps, volatility is driven by the small random shocks in returns through a G...