We propose two main applications of Gyöngy (1986)’s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)’s result. We then present Bessel-based stochastic volatility models in which this relation is used to compute analytical formulas for the loc...

Partially observed microstructure models, containing stochastic volatility, dynamic trading noise, and short-term inertia, are introduced to address the following questions: (1) Do the observed prices exhibit statistically significant inertia? (2) Is stochastic volatility (SV) still evident in the presence of dynamical trading noise? (3) If stochastic volatility and trading noise are present, w...

Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations. However such models lack the ability to take into account long term and fundamental economic factors e.g. credit crunch. Regime switching models with mean r...

We address the problems of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. We show that when volatility is stochastic but fast mean reverting Black-Scholes pricing theory can be corrected. The correction accounts for the effect of stochastic volatility and the associated market price of risk. For European derivatives it is given by explic...

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This...

! ! The daily return and the realized volatility are simultaneously modeled in the stochastic volatility model with leverage and long memory. In addition to the stochastic volatility model with leverage for the daily returns, ARFIMA process is jointly considered for the realized volatilities. Using a state space representation of the model, we estimate parameters by Markov chain Monte Carlo met...

The aim of this paper is to price European options for underlying assets with stochastic volatility (SV) in Heston model in 1993 using fuzzy set theory. The main idea is to transform the probability distribution of stochastic volatility to its possibility distribution (from ‘volatility smile to volatility frown’) and reduce the problem to a fuzzy stochastic process for underlying asset with a n...

We consider the problem of pricing inflation-linked caplets in a BlackScholes-type framework as well as in the presence of stochastic volatility. By using results on the pricing of forward starting options in Heston’s Model on stochastic volatility, we derive closed-form solutions for inflations caps which aim to receive smile-consistent option prices. Additionally we price options on the infla...

Estimation of the volatility of time series has taken off since the introduction of the GARCH and stochastic volatility models. While variants of the GARCH model are applied in scores of articles, use of the stochastic volatility model is less widespread. In this article it is argued that one reason for this difference is the relative difficulty of estimating the unobserved stochastic volatilit...

We model elasticity of volatility as a stochastic process with an eye to merge popular constant elasticity of variance (CEV) and stochastic volatility (SV) models in order to understand when it is appropriate to use absolute or relative changes or some intermediate transformation as well as to compare with more traditional autoregressive exponential stochastic volatility formulations. We descri...