Complete-market Models of Stochastic Volatility
نویسنده
چکیده
In the Black-Scholes option pricing theory, asset prices are modelled as geometric Brownian motion with a fixed volatility parameter σ, and option prices are determined as functions of the underlying asset price. Options are in principle redundant in that their exercise values can be replicated by trading in the underlying. However, it is an empirical fact that the prices of exchange-traded options do not correspond to a fixed value of σ as the theory requires. This paper proposes a modelling framework in which certain options are non-redundant: these options and the underlying are modelled as autonomous financial assets, linked only by the boundary condition at exercise. A geometric condition is given, under which a complete market is obtained in this way, giving a consistent theory under which traded options as well as the underlying asset are used as hedging instruments.
منابع مشابه
Modeling Stock Return Volatility Using Symmetric and Asymmetric Nonlinear State Space Models: Case of Tehran Stock Market
Volatility is a measure of uncertainty that plays a central role in financial theory, risk management, and pricing authority. Turbulence is the conditional variance of changes in asset prices that is not directly observable and is considered a hidden variable that is indirectly calculated using some approximations. To do this, two general approaches are presented in the literature of financial ...
متن کاملComparing the performance of GARCH (p,q) models with different methods of estimation for forecasting crude oil market volatility
The use of GARCH models to characterize crude oil price volatility is widely observed in the empirical literature. In this paper the efficiency of six univariate GARCH models and two methods of estimation the parameters for forecasting oil price volatility are examined and the best method for forecasting crude oil price volatility of Brent market is determined. All the examined models in this p...
متن کاملModeling Stock Market Volatility Using Univariate GARCH Models: Evidence from Bangladesh
This paper investigates the nature of volatility characteristics of stock returns in the Bangladesh stock markets employing daily all share price index return data of Dhaka Stock Exchange (DSE) and Chittagong Stock Exchange (CSE) from 02 January 1993 to 27 January 2013 and 01 January 2004 to 20 August 2015 respectively. Furthermore, the study explores the adequate volatility model for the stoc...
متن کاملDeterministic volatility models and dynamics of option returns
In this research, we revamp the approach of Buraschi and Jackwerth (2001), especially, in the derivation of the pricing-kernel and the data-handling technique and then empirically analyze the consistency of the DVMs introduced in Mawaribuchi, Miyazaki and Okamoto (2009) to the dynamics of the cross-sectional option returns. The implication attained from our quantitative analyses is that even in...
متن کاملSimulating Exchange Rate Volatility in Iran Using Stochastic Differential Equations
The main purpose of this paper is to analyze the exchange rate volatility in Iran in the time period between 2011/11/27 and 2017/02/25 on a daily basis. As a tradable asset and as an important and effective economic variable, exchange rate plays a decisive role in the economy of a country. In a successful economic management, the modeling and prediction of the exchange rate volatility is esse...
متن کاملAn Infinite Dimensional Stochastic Analysis Approach to Local Volatility Dynamic Models
The difficult problem of the characterization of arbitrage free dynamic stochastic models for the equity markets was recently given a new life by the introduction of market models based on the dynamics of the local volatility. Typically, market models are based on Itô stochastic differential equations modeling the dynamics of a set of basic instruments including, but not limited to, the option ...
متن کامل