1,721,385 research outputs found
Special Issue in Honour of Prof. Carl Chiarella
No full textDawid H, He T, Semmler W, eds. Special Issue in Honour of Prof. Carl Chiarella. Journal of Economic Dynamics and Control. 2018;91
Pricing range notes within Wishart affine models
No full textWe provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor
Wishart affine framework which extends significantly the standard affine model. Using estimates for three
short rate models, two of which are based on the Wishart process whilst the third one belongs to the
standard affine framework, we price these structured products using the FFT methodology. Thanks to the
Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same
dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions)
between models translate in terms of derivatives pricing errors, and we show that the models can produce
different price evolutions for the Range Accrual Notes. The differences can be substantial and underline
the importance of model risk both from a static and a dynamic perspective. These results are confirmed
by an analysis performed at the hedge ratios level
A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models
Full text linkThe aim of this work is to develop a simulation approach to the yield curve evolution in the Heath, Jarrow and Morton [Econometrica 60 (1) (1992) 77] framework. The stochastic quantities considered as affecting the forward rate volatility function are the spot rate and the forward rate. A decomposition of the volatility function into a Hull and White [Rev. Financial Stud. 3 (1990) 573] volatility and a remainder allows us to develop an efficient Control Variate Method that makes use of the closed form solution of the Hull and White call option. This technique considerably speeds up the simulation algorithm to approximate call option values with Monte Carlo simulation. © 2003 Elsevier B.V. All rights reserved
American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach
Full text linkThis paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given by the solution to an inhomogeneous integro-partial differential equation in an unbounded domain, and subsequently derive the solution using Fourier transforms. We also extend McKean’s incomplete Fourier transform approach to solve the free boundary problem under Merton’s framework, for a general jump size distribution. We show how the two methods are related to each other, and also to the Geske-Johnson compound option approach used by Gukhal (2001). The paper also derives results concerning the limit for the free boundary at expiry, and presents a numerical algorithm for solving the linked integral equation system for the American call price, delta and early exercise boundary. This scheme is applied to Merton’s jump-diffusion model, where the jumps are log-normally distributed.American options; jump-diffusion; Volterra integral equation; free boundary problem
Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions
Full text linkThis paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both European and American call options, and algorithms are presented for calculating the option price in each case. Since the series expansions only require discretisation in time to be implemented, the resulting price approximations require no asset price interpolation, and for certain maturities are demonstrated to produce both accurate and efficient solutions when compared with alternative methods, such as numerical integration, the method of lines and finite difference schemes.American options; jump-diusion; Fourier-Hermite series expansions; free boundary problem
Modelling and Estimating the Forward Price Curve in the Energy Market
Full text linkThe stochastic or random nature of commodity prices plays a central role in models for valuing financial contingent claims on commodities. In this paper, by enhancing a multifactor framework which is consistent not only with the market observable forward price curve but also the volatilities and correlations of forward prices, we propose a two factor stochastic volatility model for the evolution of the gas forward curve. The volatility is stochastic due to a hidden Markov Chain that causes it to switch between "on peak" and "off peak" states. Based on the structure functional forms for the volatility, we propose and implement the Markov Chain Monte Carlo (MCMC) method to estimate the parameters of the forward curve model. Applications to simulated data indicate that the proposed algorithm is able to accommodate more general features, such as regime switching and seasonality. Applications to the market gas forward data shows that the MCMC approach provides stable estimates.
Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model
Full text linkIn this paper, a class of forward rate dependent Markovian transformations of the Heth-Jarrow-Morton [HJM92] term structure model are obtained by considering volatility processes that are solutions of linear ordinary differential equations. These transformations generalise the Markovian system obtained by Carverhill [Car94], Ritchken and Sankarasubramanian [RS95], Bhar and Chiarella [BC97], and Inui and Kijima [IK98], and also generalise the bond price formulae obtained therin.
Preface
No full textThe MDEF Workshop has been held at the University of Urbino since 2000. The 2014 Workshop is particularly dedicated to Carl Chiarella for his 70th birthday. As the second home (along with the University of Bielefeld, another second home), Carl visited Urbino in 1998 for the first time and the visit has become an almost annual event since then. In order to commemorate the occasion, a number of Carl’s colleagues from around the world gladly agreed to contribute chapters to a special book dedicated to this event. The book is the outcome of this process. It contains the latest developments in nonlinear economic dynamics, financial market modeling, and quantitative finance, the three most active research areas Carl has been involved in
Dynamics of Beliefs and Learning Under aL Processes - The Heterogeneous Case
Full text linkThis paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.heterogeneous beliefs; recursive L-process; general aL-process; stability; instability; bifucation; cobweb model
Macroeconomic prospects and policies for the European Community. Economic Papers No. 12, April 1983
Full text link- …
