scholarly journals Pricing energy contracts under regime switching time-changed Levy Processes

2021 ◽  
Author(s):  
Konrad Gajewski
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Continuous Time ◽  
Regime Switching ◽  
Switching Time ◽  
Continuous Time Markov Chain ◽  
Energy Data ◽  
Varying Parameters ◽  
Call Options ◽  
Black Scholes

The failures of the popular Black-Scholes-Merton (BSM) model led to an interest in new, robust models which could more accurately model the behavior of historical prices. We consider one such model, the regime switching time-changed Levy process, which builds upon the BSM model by incorporating jumps through a random clock, as well as randomly varying parameters according to a continuous-time Markov chain. We develop the characteristic function as well as two methods for pricing European call options. Finally, we estimate the parameters of the model by incorporating historic energy data and option quotes using a variety of methods.

scholarly journals Pricing energy contracts under regime switching time-changed Levy Processes

2021 ◽  
Author(s):  
Konrad Gajewski
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Continuous Time ◽  
Regime Switching ◽  
Switching Time ◽  
Continuous Time Markov Chain ◽  
Energy Data ◽  
Varying Parameters ◽  
Call Options ◽  
Black Scholes

The failures of the popular Black-Scholes-Merton (BSM) model led to an interest in new, robust models which could more accurately model the behavior of historical prices. We consider one such model, the regime switching time-changed Levy process, which builds upon the BSM model by incorporating jumps through a random clock, as well as randomly varying parameters according to a continuous-time Markov chain. We develop the characteristic function as well as two methods for pricing European call options. Finally, we estimate the parameters of the model by incorporating historic energy data and option quotes using a variety of methods.

scholarly journals Optimal Portfolio and Consumption in a Switching Diffusion Market

2004 ◽  
Vol 24 (2) ◽  
pp. 227 ◽  
Author(s):  
Daniel Oliveira Cajueiro ◽  
Takashi Yoneyama
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Continuous Time ◽  
Optimal Portfolio ◽  
Continuous Time Markov Chain ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Hamilton Jacobi Bellman Equation ◽  
State Of The Economy ◽  
Hamilton Jacobi Bellman

This paper addresses the problem of finding the optimal portfolio and consumption of a small agent in an economy. The novelty of this work is in considering that the financial market, in contrast to the celebrated Black-Scholes model, is composed of two sources of uncertainties: a Brownian motion and a continuous time Markov chain. While the Brownian motion intends to model the normal oscillations of the asset prices, the continuous time Markov chain aims at taking into account the abrupt variations that can occur in the parameters of the asset dynamics due to changes that take place in the state of the economy. The problem is formulated in terms of classical optimal stochastic control and the Hamilton-Jacobi-Bellman equation is solved to yield the solution.

scholarly journals Adaptive Duty Cycling in Sensor Networks With Energy Harvesting Using Continuous-Time Markov Chain and Fluid Models

2015 ◽  
Vol 33 (12) ◽  
pp. 2687-2700 ◽  
Author(s):  
Wai Hong Ronald Chan ◽  
Pengfei Zhang ◽  
Ido Nevat ◽  
Sai Ganesh Nagarajan ◽  
Alvin C. Valera ◽  
...  
Keyword(s):  
Markov Chain ◽  
Sensor Networks ◽  
Energy Harvesting ◽  
Continuous Time ◽  
Fluid Models ◽  
Continuous Time Markov Chain ◽  
Duty Cycling
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