Pricing S&P500 barrier put option of American type under Heston–CIR model with regime-switching

2019 ◽  
Vol 06 (02) ◽  
pp. 1950014 ◽  
Author(s):  
Farshid Mehrdoust ◽  
Idin Noorani
Keyword(s):  
Expectation Maximization ◽  
Regime Switching ◽  
Likelihood Estimation ◽  
Least Square ◽  
Hidden Markov Chain ◽  
Cir Model ◽  
Binomial Tree ◽  
Put Option ◽  
Rate Processes ◽  
Tree Method

In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.

scholarly journals PENENTUAN HARGA KONTRAK OPSI KOMODITAS EMAS MENGGUNAKAN METODE POHON BINOMIAL

2017 ◽  
Vol 6 (2) ◽  
pp. 99
Author(s):  
I GEDE RENDIAWAN ADI BRATHA ◽  
KOMANG DHARMAWAN ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Option Prices ◽  
European Option ◽  
Binomial Tree ◽  
Call Options ◽  
Option Contracts ◽  
Put Option ◽  
Black Scholes ◽  
Tree Method

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

scholarly journals Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

scholarly journals Modelling of Fuel- and Energy-Switching Prices by Mean-Reverting Processes and Their Applications to Alberta Energy Markets

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 709
Author(s):  
Weiliang Lu ◽  
Alexis Arrigoni ◽  
Anatoliy Swishchuk ◽  
Stéphane Goutte
Keyword(s):  
Natural Gas ◽  
Expectation Maximization ◽  
Regime Switching ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Uhlenbeck Process ◽  
Switching Model ◽  
Fuel Switching ◽  
Power Switch ◽  
Switching Models

This paper introduces a fuel-switching price to the Alberta market, which is designed for encouraging power plant companies to switch from coal to natural gas when they produce electricity; this has been successfully applied to the European market. Moreover, we consider an energy-switching price which considers power switch from natural gas to wind. We modeled these two prices using five mean reverting processes including a Regime-switching processes, Lévy-driven Ornstein–Uhlenbeck process and Inhomogeneous Geometric Brownian Motion, and estimate them based on multiple procedures such as Maximum likelihood estimation and Expectation-Maximization algorithm. Finally, this paper proves previous results applied to the Albertan Market where the jump modeling technique is needed when modeling fuel-switching data. In addition, it not only gives promising conclusions on the necessity of introducing Regime-switching models to the fuel-switching data, but also shows that the Regime-switching model is better fitted to the data.

scholarly journals Binomial tree method for pricing a regime-switching volatility stock loans

2018 ◽  
Vol 974 ◽  
pp. 012045
Author(s):  
Endah R.M. Putri ◽  
Muhammad S Zamani ◽  
Daryono B Utomo
Keyword(s):  
Regime Switching ◽  
Binomial Tree ◽  
Tree Method

Option Pricing in a Jump-Diffusion Model with Regime Switching

2009 ◽  
Vol 39 (2) ◽  
pp. 515-539 ◽  
Author(s):  
Fei Lung Yuen ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Extended Model ◽  
Exotic Options ◽  
Switching Model ◽  
Jump Diffusion Model ◽  
Trinomial Tree ◽  
Tree Method

AbstractNowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

scholarly journals Joint clock synchronization and position estimation in time of arrival–based passive positioning systems

2018 ◽  
Vol 14 (11) ◽  
pp. 155014771878689 ◽  
Author(s):  
Shenghong Li ◽  
Lingyun Lu ◽  
Mark Hedley ◽  
David Humphrey ◽  
Iain B Collings
Keyword(s):  
Clock Synchronization ◽  
Likelihood Estimation ◽  
Least Square Method ◽  
Position Estimation ◽  
Least Square ◽  
Time Of Arrival ◽  
Positioning Systems ◽  
Reference Node ◽  
Localization Scheme ◽  
Wireless Signal

A widely used scheme for target localization is to measure the time of arrival of a wireless signal emitted by a tag, which requires the clocks of the anchors (receivers at known locations) to be accurately synchronized. Conventional systems rely on transmissions from a timing reference node at a known location for clock synchronization and therefore are susceptible to reference node failure. In this article, we propose a novel localization scheme which jointly estimates anchor clock offsets and target positions. The system does not require timing reference nodes and is completely passive (non-intrusive). The positioning algorithm is formulated as a maximum likelihood estimation problem, which is solved efficiently using an iterative linear least square method. The Cramér–Rao lower bound of positioning error is also analyzed. It is shown that the performance of the proposed scheme improves with the number of targets in the system and approaches that of a system with perfectly synchronized anchors.

A RECOMBINING TREE METHOD FOR OPTION PRICING WITH STATE-DEPENDENT SWITCHING RATES

2016 ◽  
Vol 19 (02) ◽  
pp. 1650012 ◽  
Author(s):  
J. X. JIANG ◽  
R. H. LIU ◽  
D. NGUYEN
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Asset Price ◽  
Numerical Results ◽  
Price Process ◽  
State Dependent ◽  
Switching Models ◽  
Markovian Regime Switching ◽  
Tree Method ◽  
Markovian Regime

This paper develops simple and efficient tree approaches for option pricing in switching jump diffusion models where the rates of switching are assumed to depend on the underlying asset price process. The models generalize many existing models in the literature and in particular, the Markovian regime-switching models with jumps. The proposed trees grow linearly as the number of tree steps increases. Conditions on the choices of key parameters for the tree design are provided that guarantee the positivity of branch probabilities. Numerical results are provided and compared with results reported in the literature for the Markovian regime-switching cases. The reported numerical results for the state-dependent switching models are new and can be used for comparison in the future.

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