Stochastic Behavior of Commodity Prices: The Valuation of Derivative-Linked Securities

2009 ◽  
Vol 17 (1) ◽  
pp. 51-75
Author(s):  
Bong-Gyu Jang ◽  
Sang-Gyu Lim ◽  
Ho-Seok Lee
Keyword(s):  
Stochastic Process ◽  
Term Structure ◽  
Commodity Prices ◽  
Theoretical Models ◽  
Foreign Exchange Rate ◽  
Constant Ratio ◽  
Convenience Yield ◽  
Underlying Asset ◽  
Model Combining ◽  
Key Characteristics

We investigated term structure models for commodity prices to value derivative-linked securities (DLS) traded in Korea. We especially highlighted geometric Brownian motion (GBM) model considering a convenience yield and Schwartz model reflecting mean-reverting property. One of key characteristics of the paper is that this paper provides theoretical models for multi underlying assets and the model combining GBM model and Schwartz model. Furthermore, it gives us an analysis for quanto adjustment which occurs in the valuation of DLS. In case of GBM model, quanto adjustment seems to be relatively simple by adjusting a constant ratio to risk-free interest rate. Unlike GBM model, we find out that, in case of Schwartz model, such adjustment can be achieved only when the stochastic process of foreign exchange rate is considered. After having valuation, both models show stable results for DLS prices using WTI index as an underlying asset. However, they results in outcomes, which are relatively not stable, on valuing DLS written on multi underlying assets including nickel.

Irreversible Decisions and Record-Setting News Principles

2004 ◽  
Vol 94 (3) ◽  
pp. 557-568 ◽  
Author(s):  
Svetlana Boyarchenko
Keyword(s):  
Probability Distributions ◽  
Commodity Prices ◽  
Fat Tails ◽  
Explicit Formulas ◽  
Underlying Asset ◽  
Real Options Theory ◽  
Gaussian Case ◽  
Geometric Levy Process ◽  
Options Theory ◽  
Irreversible Decisions

In the now-classical real options theory, the price of an underlying asset is modeled as a geometric Brownian motion, and optimal exercise strategies are described by simple explicit formulas. This paper extends the classical theory to allow any geometric Lévy process to model prices. Such processes may account for fat tails and skewness of probability distributions of commodity prices. The optimal exercise strategies are specified in the paper in terms of statistics of record-setting low or high prices. The formulas derived extend those observed in the Gaussian case, but the form of the result is novel even for that case.

Studies in dialogue and discourse; an exponential law of successive questioning

1975 ◽  
Vol 4 (1) ◽  
pp. 31-51 ◽  
Author(s):  
Elliot G. Mishler
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Exponential Function ◽  
First Grade ◽  
Finite Markov Chain ◽  
Constant Ratio ◽  
Conversational Analysis ◽  
Exponential Law ◽  
Simple Exponential Function ◽  
Temporal Location

ABSTRACTThe structure of natural conversations in first-grade classrooms is the focus of this inquiry. Analyses of a particular type of discourse, namely, connected conversations initiated and sustained by questioning, suggest that the probability that a conversation will be continued may be expressed as a simple exponential function. The formula, pi = ari−1, generates a curve of theoretically-expected rates of successive questions in a series that closely matches observed rates. The formula is based on the application of a constant ratio, that is, the ratio of rates within each pair of adjacent questions is the same throughout the series: p2:p1=p3:p2 = p4:p3. … Thus, it appears that the probability of a ‘next’ question following an exchange that contains a previous question remains constant through the length of the discourse series. In other words, the probability of a question is independent of the temporal location of an utterance in this type of connected conversation. The analyses suggest further that the model of a finite Markov chain, that is, of a particular type of stochastic process, may be applicable to certain features of a discourse. (Conversational analysis, sequencing in exchanges, U.S. English in first-grade classrooms.)

VARIANCE TERM STRUCTURE AND VIX FUTURES PRICING

2007 ◽  
Vol 10 (01) ◽  
pp. 111-127 ◽  
Author(s):  
YINGZI ZHU ◽  
JIN E. ZHANG
Keyword(s):  
Term Structure ◽  
Futures Market ◽  
Options Market ◽  
Pricing Model ◽  
No Arbitrage ◽  
Drift Term ◽  
Model Combining ◽  
Vix Futures ◽  
Volatility Derivatives ◽  
Futures Pricing

Using no arbitrage principle, we derive a relation between the drift term of risk-neutral dynamics for instantaneous variance and the term structure of forward variance. We show that the forward variance curve can be derived from options market. Based on the variance term structure, we derive a no arbitrage pricing model for VIX futures pricing. The model is the first no arbitrage model combining options market and VIX futures market. The model can be easily generalized to price other volatility derivatives.

scholarly journals A stochastic control approach to managed futures portfolios

2019 ◽  
Vol 06 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Tim Leung ◽  
Raphael Yan
Keyword(s):  
Stochastic Control ◽  
Utility Maximization ◽  
Commodity Prices ◽  
Trading Strategies ◽  
Maximization Problem ◽  
Convenience Yield ◽  
Yield Model ◽  
Managed Futures ◽  
Control Approach ◽  
Utility Maximization Problem

We study a stochastic control approach to managed futures portfolios. Building on the (Schwartz, 1997) stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or multiple futures contracts over a finite horizon. By analyzing the associated Hamilton–Jacobi–Bellman (HJB) equation, we solve the investor’s utility maximization problem explicitly and derive the optimal dynamic trading strategies in closed form. We provide numerical examples and illustrate the optimal trading strategies using WTI crude oil futures data.

A GENERAL SUBORDINATED STOCHASTIC PROCESS FOR DERIVATIVES PRICING

2001 ◽  
Vol 04 (01) ◽  
pp. 121-146 ◽  
Author(s):  
J. L. LESNE ◽  
J. L. PRIGENT
Keyword(s):  
Stochastic Process ◽  
Discrete Time ◽  
Contingent Claims ◽  
Option Valuation ◽  
Derivatives Pricing ◽  
Underlying Asset ◽  
Discrete Time Models

A general subordinated stochastic process is proposed to model the dynamics of the underlying asset of an option. We prove that this class of models can be considered generically as the limit of discrete time models in which the number of transactions is random. We also derive several results for the valuation of contingent claims in this framework. In particular, we compare the impacts of different choices of subordinator processes on the option valuation.

IT Progress Indicators

2014 ◽  
Vol 10 (3) ◽  
pp. 58-71 ◽  
Author(s):  
T. S. Amer ◽  
Todd L. Johnson
Keyword(s):  
Information Technology ◽  
User Experience ◽  
Theoretical Models ◽  
Psychological Research ◽  
User Experiences ◽  
Process Duration ◽  
Key Characteristics ◽  
Sense Of Time

Users of information technology (IT) often encounter “progress indicators” during their interactions. These graphics (e.g., progress bars) appear on computing screens as users wait for a task to complete. The purpose of progress indicators is to inform users of the progress being made to complete a task. This study employs two theoretical models from psychological research on human waiting to develop specific hypotheses related to the design of progress indicators: the sense-of-progress and the subjective-sense-of-time frameworks. The results of three experiments indicate that progress indicators exhibiting key characteristics from these frameworks influence user experiences. Experiment 1 revealed that participants preferred a linear progress bar to a cycling progress bar. Experiment 2 revealed that participants preferred a video progress indicator to a cycling progress bar, and judged the process duration to be shorter with the video progress indicator. Experiment 3 revealed that the video progress indicator yielded the best user experience.

Term Structure Models of Commodity Prices: A Review

CFA Digest ◽  
2006 ◽  
Vol 36 (1) ◽  
pp. 14-15
Author(s):  
Edgar J. Sullivan
Keyword(s):  
Term Structure ◽  
Commodity Prices ◽  
Term Structure Models
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