Analytical Approximation Formula for Barrier Option Prices under the Regime-Switching Model

2019 ◽  
Vol 27 (2) ◽  
pp. 108-119
Author(s):  
Xin-Jiang He ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Option Prices ◽  
Barrier Option ◽  
Regime Switching Model ◽  
Switching Model

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.

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

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