scholarly journals Option pricing in a regime-switching model using the fast Fourier transform

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
R. H. Liu ◽  
Q. Zhang ◽  
G. Yin
Keyword(s):  
Fourier Transform ◽  
Markov Chain ◽  
Fast Fourier Transform ◽  
Regime Switching ◽  
Asset Price ◽  
Sample Path ◽  
Regime Switching Model ◽  
Switching Model ◽  
Large State Space ◽  
Black Scholes

This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black-Scholes formula. Finally, numerical results are reported.

scholarly journals A CONDITIONAL MARKOV REGIME SWITCHING MODEL TO STUDY MARGINS: APPLICATION TO THE FRENCH FUEL RETAIL MARKETS

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
RAPHAËL HOMAYOUN BOROUMAND ◽  
STÉPHANE GOUTTE ◽  
SIMON PORCHER ◽  
THOMAS PORCHER
Keyword(s):  
Markov Chain ◽  
Market Structure ◽  
Regime Switching ◽  
Markov Regime Switching ◽  
Regime Switching Model ◽  
Switching Model ◽  
The Standard Model ◽  
High Volatility ◽  
Volatility Regimes ◽  
Markov Regime Switching Model

<p class="ESRBODY">This paper uses a regime-switching model that is built on mean-reverting and local volatility processes combined with two Markov regime-switching processes to understand the market structure of the French fuel retail market over the period 1990-2013. The volatility structure of these models depends on a first exogenous Markov chain, whereas the drift structure depends on a conditional Markov chain with respect to the first one. Our model allows us to identify mean reverting and switches in the volatility regimes of the margins. In the standard model of cartel coordination, volatility can increase competition. We find that cartelization is even stronger in phases of high volatility. Our best explanation is that consumers consider volatility in prices to be a change in market structure and are therefore less likely to search for lower-priced retailers, thus increasing the market power of the oligopoly. Our findings provide a better understanding of the behavior of oligopolies.</p>

REGIME-SWITCHING RECOMBINING TREE FOR OPTION PRICING

2010 ◽  
Vol 13 (03) ◽  
pp. 479-499 ◽  
Author(s):  
R. H. LIU
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Asset Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Regime Switching Model ◽  
Switching Model ◽  
Tree Construction ◽  
Volatility Model ◽  
Tree Approach

In this paper we develop an efficient tree approach for option pricing when the underlying asset price follows a regime-switching model. The tree grows only linearly as the number of time steps increases. Thus it enables us to use large number of time steps to compute accurate prices for both European and American options. We present conditions that guarantee the positivity of branch probabilities. We numerically test the sensitivity of option prices to the choice of a key parameter for tree construction. As an interesting application, we develop a regime-switching model to approximate the Heston's stochastic volatility model and then employ the tree approach to approximate the option prices. Numerical results are provided and compared.

A new method for option pricing via time-fractional PDE

2018 ◽  
Vol 11 (05) ◽  
pp. 1850074 ◽  
Author(s):  
Elaheh Saberi ◽  
S. Reza Hejazi ◽  
Elham Dastranj
Keyword(s):  
Continuous Time ◽  
Regime Switching ◽  
Asset Price ◽  
Options Pricing ◽  
Chain Process ◽  
Hidden Markov Chain ◽  
Underlying Asset ◽  
Regime Switching Model ◽  
Switching Model ◽  
Fractional Pde

In this paper, power options pricing is driven via time-fractional PDE when the dynamic of underlying asset price follows a regime switching model in which the risky underlying asset depends on a continuous-time hidden Markov chain process. An exact solution for power options pricing is driven under our considered model.

scholarly journals A Markov Regime-Switching Model with Time-Varying Transition Probabilities for Identifying Asset Price Bubbles

2018 ◽  
Vol 10 (4) ◽  
pp. 1 ◽  
Author(s):  
Matthew L. Higgins ◽  
Frank Ofori-Acheampong
Keyword(s):  
Regime Switching ◽  
Transition Probabilities ◽  
Asset Price ◽  
Time Varying ◽  
Markov Regime Switching ◽  
Regime Switching Model ◽  
Switching Model ◽  
Asset Price Bubbles ◽  
Price Bubbles ◽  
Markov Regime Switching Model

In this paper, a Markov regime-switching model with time-varying transition probabilities is developed to identify asset price bubbles in the S&P 500 index. The model nests two different methodologies; a state-dependent regime-switching model and a Markov regime-switching model. Three bubble regimes are identified; dormant, explosive, and collapsing. Time-varying transition probabilities are specified for each of the nine possible transitions in the Markov regime-switching model. Estimation of the model is done using conditional maximum likelihood with the Hamilton filter. Results show that transition probabilities depend significantly on trading volume and relative size of the bubble. Overall, the model works well in detecting multiple bubbles in the S&P 500 between January 1888 and May 2010. Explosive bubbles tend to immediately precede recession periods, while collapsing bubbles tend to coincide with recession periods.

DIVIDEND OPTIMIZATION FOR A REGIME-SWITCHING DIFFUSION MODEL WITH RESTRICTED DIVIDEND RATES

2014 ◽  
Vol 44 (2) ◽  
pp. 459-494 ◽  
Author(s):  
Jinxia Zhu
Keyword(s):  
Markov Chain ◽  
Regime Switching ◽  
Critical Level ◽  
Sufficient Conditions ◽  
Insurance Company ◽  
Threshold Strategy ◽  
Regime Switching Model ◽  
Switching Model ◽  
Switching Diffusion ◽  
Optimal Dividend

AbstractWe consider the optimal dividend control problem to find an optimal strategy under the constraint that dividend rates is restricted such that the expected total discounted dividends are maximized for an insurance company. The evolution of the reserve is modeled by a diffusion process with drift and volatility coefficients modulated by an observable Markov chain. We consider the regime-switching threshold strategy which pays out dividends at the maximal possible rate when the current reserve is above some critical level dependent on the regime of the Markov chain at the time, and pays nothing when the reserve is below that level. We give sufficient conditions under which such type of strategy is optimal for the regime-switching model.

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