Generic Forward Curve Dynamics for Commodity Derivatives

This article presents a generic framework for modeling the dynamics of forward curves in commodity market as commodity derivatives are typically traded by futures or forwards. We have theoretically demonstrated that commodity prices are driven by multiple components. As such, the model can better capture the forward price and volatility dynamics. Empirical study shows that the model prices are very close to the market prices, indicating prima facie that the model performs quite well

The CTMC-Heston model: calibration and exotic option pricing with SWIFT

This work presents an efficient computational framework for pricing a general class of exotic and vanilla options under a versatile stochastic volatility model. In particular, we propose the use of a finite state continuous time Markov chain (CTMC) model, which closely approximates the classic Heston model but enables a simplified approach for consistently pricing a wide variety of financial derivatives (...

Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Efficient valuation of exotic derivatives with path-dependence and early exercise features

The main objective of this thesis is to provide effective means for the valuation of popular financial derivative contracts with path-dependence and/or early-exercisable provisions. Starting from the risk-neutral valuation formula, the approach we propose is to sequentially compute convolutions of the value function of the contract at a monitoring date with the transition density between two dates, to provide the value function at the previous monitoring date, until the present date. A rigorous computational algorithm for the convolutions is then developed based on transformations to the Fourier domain. In the first part of the thesis, we deal with arithmetic Asian options, which, due to the growing popularity they enjoy in the financial marketplace, have been researched signicantly over the last two decades. Although few remarkable approaches have been proposed so far, these are restricted to the market assumptions imposed by the standard Black-Scholes-Merton paradigm. Others, although in theory applicable to Lévy models, are shown to suffer a non-monotone convergence when implemented numerically. To solve the Asian option pricing problem, we initially propose a flexible framework for independently distributed log-returns on the underlying asset. This allows us to generalize firstly in calculating the price sensitivities. Secondly, we consider an extension to non-Lévy stochastic volatility models. We highlight the benefits of the new scheme and, where relevant, benchmark its performance against an analytical approximation, control variate Monte Carlo strategies and existing forward convolution algorithms for the recovery of the density of the underlying average price. In the second part of the thesis, we carry out an analysis on the rapidly growing market of convertible bonds (CBs). Despite the vast amount of research which has been undertaken yet. This is due to the need for proper modelling of the CBs composite payout structure and the multi factor modelling arising in the CB valuation. Given the dimensional capacity of the convolution algorithm, we are now able to introduce a new jump diffusion structural approach in the CB literature, towards more realistic modelling of the default risk, and further include correlated stochastic interest rates. This aims at fixing dimensionality and convergence limitations which previously have been restricting the range of applicability of popular grid- based, lattice and Monte Carlo methods. The convolution scheme further permits flexible handling of real-world CB specications; this allows us to properly model the call policy and investigate its impact on the computed CB prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper

Interest-rate models: an extension to the usage in the energy market and pricing exotic energy derivatives.

In this thesis, we review various popular pricing models in the interest-rate market. Among these pricing models, we choose the LIBOR Market model (LMM) as the benchmark model. Based on market practice experience, we also develop a pricing model named the “Market volatility model”. By pricing vanilla interest-rate options such as interest-rate caps and swaptions, we compare the performance of our Market volatility model to that of the LMM. It is proved that the Market Volatility model produce comparable results to the LMM, while its computing efficiency largely exceeds that of the LMM. Following the recent rapid development in the commodity market, in particular the energy market, we attempt to extend the use of our proposed Market volatility model from the interest-rate market to the energy market. We prove that the Market Volatility model is capable of pricing various energy derivative under the assumption of absence of the convenience yield. In addition, we propose a new type of exotic energy derivative which has a flexible option structure. This energy derivative is named as the Flex-Asian spread options (FASO). We give examples of different option structures within the FASO framework and use the Market volatility model to generate option prices and greeks for each structure. Although the Market volatility model can be used to price various energy derivatives based on oil/gas contracts, it is not compatible with the structure of one of the most advanced derivatives in the energy market, the storage option. We modify the existing pricing model for storage options and use our own 3D-binomial tree approach to price gas storage contracts. By doing these, we improve the performance of the traditional storage model

Turbo Warrants under Hybrid Stochastic and Local Volatility

This paper considers the pricing of turbo warrants under a hybrid stochastic and local volatility model. The model consists of the constant elasticity of variance model incorporated by a fast fluctuating Ornstein-Uhlenbeck process for stochastic volatility. The sensitive structure of the turbo warrant price is revealed by asymptotic analysis and numerical computation based on the observation that the elasticity of variance controls leverage effects and plays an important role in characterizing various phases of volatile markets