scholarly journals Modelando Opcões de Conversão com Movimento de Reversão à Média

2007 ◽  
Vol 5 (2) ◽  
pp. 97 ◽  
Author(s):  
Carlos L. Bastian-Pinto ◽  
Luiz E. T. Brandão
Keyword(s):  
Brownian Motion ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Commodity Prices ◽  
Geometric Brownian Motion ◽  
Base Case ◽  
Option Value ◽  
Uncertain Variables ◽  
Mean Reverting Process

Commodity prices are generally better modeled by a long-term Mean Reverting Process, than by a Geometric Brownian Motion stochastic diffusion process, which is more generally used to value real options, since it is simpler to use. In this article we model two correlated uncertain variables using a mean reversing process bivariate lattice to value the switch option between outputs available to ethanol and sugar producers, using the same source: sugarcane. The model results show that the switch option adds a significant value for the producer income. The article also shows that when modeled by a geometric brownian motion, the switch option yields significantly higher values than with a mean reverting model, for the option itself as much as for the base case without flexibility. This confirms that the stochastic model chosen can influence significantly the option value.

scholarly journals The Randomized American Option as a Classical Solution to the Penalized Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Guillaume Leduc
Keyword(s):  
Cauchy Problem ◽  
Brownian Motion ◽  
Classical Solution ◽  
Penalty Method ◽  
Infinitesimal Generator ◽  
American Option ◽  
Geometric Brownian Motion ◽  
Uniform Bound ◽  
Option Value ◽  
The Cauchy Problem

We connect the exercisability randomized American option to the penalty method by showing that the randomized American option valueuis the uniqueclassicalsolution to the Cauchy problem corresponding to thecanonicalpenalty problem for American options. We also establish a uniform bound forAu, whereAis the infinitesimal generator of a geometric Brownian motion.

Stochastic Modelling of Particle Segregation in a Horizontal Drum Mixer

1992 ◽  
Vol 57 (10) ◽  
pp. 2100-2112 ◽  
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Andrzej Rochowiecki
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Stochastic Modelling ◽  
Solid Particles ◽  
Kolmogorov Equation ◽  
Particle Segregation ◽  
Drum Mixer ◽  
Horizontal Drum

A process of segregation of two distinct fractions of solid particles in a rotating horizontal drum mixer was described by stochastic model assuming the segregation to be a diffusion process with varying diffusion coefficient. The model is based on description of motion of particles inside the mixer by means of a stochastic differential equation. Results of stochastic modelling were compared to the solution of the corresponding Kolmogorov equation and to results of earlier carried out experiments.

The Economics of Commodities and Commodity Markets

2018 ◽  
Author(s):  
Florian Ielpo
Keyword(s):  
Raw Materials ◽  
Commodity Prices ◽  
Essential Element ◽  
Commodity Markets ◽  
Production Costs ◽  
Demand And Supply ◽  
Spot Prices ◽  
Supply Shocks ◽  
The Business Cycle

This chapter covers the economic fundamentals of commodity markets (i.e., what shapes the evolution of the price of raw materials) in three steps. First, it covers the theories explaining why the futures curve can be upward or downward sloping, an essential element for commodity producing companies. The evolution of inventories and hedging pressures are the two dominant sources of explanation. Second, the chapter reviews the fundamentals of commodity spot prices: technologies, supply, demand, and speculation. Production costs draw the long-term evolution of prices, but demand and supply shocks can trigger substantial variations in commodity prices. Third, the chapter presents how commodity prices interact with the business cycle. Commodities are influenced by the world activity but can also have a material impact on it.

scholarly journals Geometric Brownian motion with affine drift and its time-integral

2021 ◽  
Vol 395 ◽  
pp. 125874
Author(s):  
Runhuan Feng ◽  
Pingping Jiang ◽  
Hans Volkmer
Keyword(s):  
Brownian Motion ◽  
Geometric Brownian Motion ◽  
Time Integral

scholarly journals HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

2015 ◽  
Vol 56 (4) ◽  
pp. 359-372 ◽  
Author(s):  
PAVEL V. SHEVCHENKO
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Real Life ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Fixed Amount ◽  
Underlying Asset ◽  
Closed Form Solutions ◽  
Pricing Options ◽  
Interest Rate Volatility

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

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