Algorithm for Determining the Volatility Function in the Black–Scholes Model

2019 ◽  
Vol 59 (10) ◽  
pp. 1753-1758 ◽  
Author(s):  
V. M. Isakov ◽  
S. I. Kabanikhin ◽  
A. A. Shananin ◽  
M. A. Shishlenin ◽  
S. Zhang
Keyword(s):  
Black Scholes Model ◽  
Black Scholes ◽  
Volatility Function

Reconstruction of the local volatility function using the Black–Scholes model

2021 ◽  
Vol 51 ◽  
pp. 101341
Author(s):  
Sangkwon Kim ◽  
Hyunsoo Han ◽  
Hanbyeol Jang ◽  
Darae Jeong ◽  
Chaeyoung Lee ◽  
...  
Keyword(s):  
Local Volatility ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Volatility Function

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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