scholarly journals The absence of arbitrage on the complete Black-Scholes-Merton regime-switching Lévy market

Econometrics ◽  
2021 ◽  
Vol 25 (3) ◽  
pp. 72-84
Author(s):  
Anna Sulima
Keyword(s):  
Regime Switching ◽  
Black Scholes ◽  
Absence Of Arbitrage

An analytical approximation formula for the pricing of credit default swaps with regime switching

2021 ◽  
Vol 63 ◽  
pp. 143-162
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

scholarly journals Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Wei-Guo Zhang ◽  
Ping-Kang Liao
Keyword(s):  
Credit Risk ◽  
Regime Switching ◽  
Numerical Solutions ◽  
Dilution Effect ◽  
Convertible Bonds ◽  
Bond Pricing ◽  
Convertible Bond ◽  
Pricing Model ◽  
Black Scholes ◽  
The Impact

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

scholarly journals Regime-Switching Risk: To Price or Not to Price?

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Tak Kuen Siu
Keyword(s):  
Relative Entropy ◽  
Regime Switching ◽  
Martingale Measure ◽  
Martingale Measures ◽  
Equivalent Martingale Measure ◽  
Equivalent Martingale Measures ◽  
Black Scholes ◽  
Normative Issues ◽  
Equivalent Martingale ◽  
Markovian Regime Switching

Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.

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 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 The Pricing and Hedging of an Attainable Claim in a Hybrid Black–Scholes Model under Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Kuanhou Tian ◽  
Yanfang Li ◽  
Guixin Hu
Keyword(s):  
Regime Switching ◽  
The Self ◽  
Black Scholes Model ◽  
Complete Market ◽  
Black Scholes ◽  
Theoretical Results

This article formulates and dissects a Black–Scholes model with regime switching that can be used to describe the performance of a complete market. An explicit integrand formula ϕ t , ω is obtained when the T -claim F ω is given for an attainable claim in this complete market. In addition, some perfect results are presented on how to hedge an attainable claim for this Black–Scholes model, and the price p of the European call and the self-financing portfolio θ t = θ 0 t , θ 1 t are given explicitly. Finally, some concluding remarks are provided to illustrate the theoretical results.

Completeness and Hedging

2019 ◽  
pp. 119-127
Author(s):  
Tomas Björk
Keyword(s):  
Risky Assets ◽  
Market Completeness ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Absence Of Arbitrage

The concept of market completeness is discussed in some detail and we prove that the Black–Scholes model is complete. We also discuss how completeness and absence of arbitrage is related to the number of risky assets and the number of random sources in the model.

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