Download or read book Commodity Asian Option Pricing and Simulation in a 4 Factor Model with Jump Clusters written by Riccardo Brignone and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean reversion, stochastic volatility, convenience yield and presence of jump clustering are well documented salient features of commodity markets, where Asian options are very popular. We propose a model which takes into account all these stylized features. We first state our model under the historical measure, then, after introducing a structure preserving change of measure, we provide a risk-neutral version of the same model and we show how to price geometric and arithmetic Asian options. To this end, we derive semi-closed formulas for the geometric Asian options price and develop a computationally efficient simulation scheme for the price process, allowing to price the arithmetic counterparts using control variate technique. Finally, we propose a simple econometric experiment to document presence of jump clusters in commodity prices and evaluate the performances of the proposed simulation scheme on some parameter sets calibrated on real data.
Download or read book Quantitative Energy Finance written by Fred Espen Benth and published by Springer Nature. This book was released on with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asian Options with Jumps written by Marina Marena and published by . This book was released on 2015 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a closed-form formula for the fair value of call and put options written on the arithmetic average of security prices driven by jump diffusion processes displaying (possibly periodical) trend, time varying volatility, and mean reversion. The model allows one for jointly fitting quoted futures curve and the time structure of spot price volatility. Our result extends the no-jump case put forward in [Fusai, G., Marena, M., Roncoroni, A. 2008. Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets. Journal of Banking and Finance 32 (10), 2033-2045]. A few tests based on commodity price data assess the importance of introducing a jump component on the resulting option prices.
Download or read book Commodity Option Pricing written by Iain J. Clark and published by John Wiley & Sons. This book was released on 2014-03-05 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commodity Option Pricing: A Practitioner’s Guide covers commodity option pricing for quantitative analysts, traders or structurers in banks, hedge funds and commodity trading companies. Based on the author’s industry experience with commodity derivatives, this book provides a thorough and mathematical introduction to the various market conventions and models used in commodity option pricing. It introduces the various derivative products typically traded for commodities and describes how these models can be calibrated and used for pricing and risk management. This book has been developed with input from traders and features examples using real-world data, together with relevant up-to-date academic research. This book includes practical descriptions of market conventions and quote codes used in commodity markets alongside typical products seen in broker quotes and used in calibration. Also discussed are commodity models and their mathematical derivation and volatility surface modelling for traded commodity derivatives. Gold, silver and other precious metals are addressed, including gold forward and gold lease rates, as well as copper, aluminium and other base metals, crude oil and natural gas, refined energy and electricity. There are also sections on the products encountered in commodities such as crack spread and spark spread options and alternative commodities such as carbon emissions, weather derivatives, bandwidth and telecommunications trading, plastics and freight. Commodity Option Pricing is ideal for anyone working in commodities or aiming to make the transition into the area, as well as academics needing to familiarize themselves with the industry conventions of the commodity markets.
Download or read book Efficient Asian Option Pricing Under Regime Switching Jump Diffusions and Stochastic Volatility Models written by Justin Kirkby and published by . This book was released on 2020 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines Continuous-Time Markov Chain (CTMC) approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, alpha-Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a unified approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.
Download or read book Commodity Asian Options written by Gianluca Fusai and published by . This book was released on 2008 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan (1999) [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61-73] allows us to derive a closed-form formula for the fair value of discretely-monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.
Download or read book On the Performance of the Comonotonicity Approach for Pricing Asian Option in Some Benchmark Models from Equities and Commodities written by Jilong Chen and published by . This book was released on 2014 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we investigate the applicability of the Albrecher et. al. (2005) comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Levy models as in Albrecher et. al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz' 1997 stochastic convenience yield model. We show that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by product delivers super-hedging strategies which can be easily implemented.
Download or read book American Asian Option Pricing Based on Monte Carlo Simulation Method written by Shiguang Han and published by . This book was released on 2012 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Pricing Of Asian Options In High Volatile Markets written by Nabil Kamal Riziq Farra and published by . This book was released on 2015 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial derivatives are very important tools in risk management since they decrease uncertainty. Moreover, if used effectively, they can grow the income and save the cost. There are many types of financial derivatives, for instance: futures/forwards, options, and swaps. The present thesis deals with the pricing problem for Asian options. The main aim of the thesis is to generalize the Asian option pricing Partial Differential Equation (PDE) in order to handle post-crash markets where the volatility is high. In other words, we seek to extend the work on the Asian option pricing PDE under the well-known Black-Scholes model to a high volatility model. To this end, we first set up a model that accounts for high volatile situations and we solve the Stochastic Differential Equation (SDE) of the underlying asset price. Our illustrations confirm the high volatile behavior of the model. We then derive the Asian option PDE for the suggested model. The resulting PDE is reduced from two-dimensional space to one-dimensional space using a change of variable. Moreover, we derive a relationship between the Asian options prices of the Black-Scholes model and our high volatility model where the increase in volatility is a deterministic function of the interest rate.
Download or read book Affine Structure Models and the Pricing of Energy Commodity Derivatives written by Ioannis Kyriakou and published by . This book was released on 2019 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a seasonal mean-reverting model for energy commodity prices with jumps and Heston-type stochastic volatility, as well as three nested models for comparison. By exploiting the affine form of the log-spot models, we develop a general valuation framework for futures and discrete arithmetic Asian options. We investigate five major petroleum commodities from the European market (Brent crude oil, gasoil) and US market (light sweet crude oil, gasoline, heating oil) and analyze the effects of the competing fitted stochastic spot models in futures pricing, Asian options pricing and hedging. We find evidence that price jumps and stochastic volatility are important features of the petroleum price dynamics.
Download or read book Exploring the Commodity Market written by Yuexiang Wu and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing Asian Options written by Akos Horvath and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The derivation of Asian option value has posed a challenge to financial mathematicians for the last two decades. Fu, Madan and Wang (1999) made a comparison between the Laplace transform approach and the Monte Carlo approach, and found that the numerical inversion method encountered severe numerical instabilities when volatility was low or maturity was short.In this paper, we seek to answer the question whether it is possible to improve on the efficiency of the inversion, implementing and comparing different numerical algorithms, so that the Laplace transform could be used in real-life situations. We also look into whether today's superior computer environment has changed the relative strength of numerical and simulation approaches with regards to Asian option pricing.Based on an detailed comparison of methods, we find that the speed and reliability of the Laplace transform inversion could be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and calculation time from 20-30 seconds to 3-4 seconds. Also, as a conclusion of our research we suggest that the simulation approach be used when sigma^2*T
Download or read book Pricing of Geometric Asian Options in General Affine Stochastic Volatility Models written by Johannes Ruppert and published by . This book was released on 2016 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this thesis, we look at the general affine pricing model introduced in [11]. This model allows to price geometric Asian options, which are of big interest due to their lower volatility in comparison to, for example, European options. Because of their structure and in order to be able to price these options, we look at the basic theory of Lévy processes and stochastic calculus. Furthermore, we provide the detailed description of the parameters of the pricing formulas for some popular specific single-factor stochastic volatility models with jumps and generalize the approach of [11] to multi-factor models"--Abstract, page iii.
Download or read book Numerical Schemes for Pricing Asian Options Under State Dependent Regime Switching Jump Diffusion Models written by Duy-Minh Dang and published by . This book was released on 2018 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose numerical schemes for pricing Asian options when the underlying asset price follows a very general state-dependent regime-switching jump-diffusion process. Under this model, the price of the option can be obtained by solving a highly complex system of coupled two-dimensional parabolic partial integro-differential equations (PIDEs) via iterative techniques. One of the proposed schemes is provably convergent to the solution of the system of PIDEs. In addition, by treating the coupling and integral terms explicitly, over each iteration of the scheme, the pricing problem under this scheme can be partitioned into independent pricing sub-problem, with communication at the end of the iteration. Hence, this method allows for a very natural and easy-to-implement, yet efficient, parallelization of the solution process on multi-core architectures. We illustrate the accuracy and efficiency of the proposed methods by several numerical examples.
Download or read book Pricing Commodity Futures Options in the Schwartz Multi Factor Model with Stochastic Volatility written by Jilong Chen and published by . This book was released on 2016 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we investigate the applicability of the asymptotic approach developed in Fouque et al. (2000) for pricing commodity futures options in a Schwartz (1997) multi factor model, featuring both stochastic convenience yield and stochastic volatility. We show that the zero order term in the expansion coincides with the Schwartz (1997) two factor term, with expected long-term volatility replacing the constant volatility term, and provide an explicit expression for the first order correction term. Using empirical data from the natural gas futures market, we demonstrate that a significantly better calibration can be achieved by involving the correction term as compared to the standard Schwartz (1997) two factor expression. This improvement comes at virtually no extra effort.
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Download or read book Handbook of Differential Equations written by Daniel Zwillinger and published by Gulf Professional Publishing. This book was released on 1998 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. For nearly every technique, the book provides: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
