scholarly journals Malliavin sensitivity analysis with polynomial growth payoff functions under the Black-Scholes model

JSIAM Letters ◽  
2017 ◽  
Vol 9 (0) ◽  
pp. 1-4
Author(s):  
Kazuya Yamamura ◽  
Kazuhiro Yasuda
Keyword(s):  
Sensitivity Analysis ◽  
Polynomial Growth ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Payoff Functions

scholarly journals A EUROPEAN OPTION GENERAL FIRST-ORDER ERROR FORMULA

2013 ◽  
Vol 54 (4) ◽  
pp. 248-272 ◽  
Author(s):  
GUILLAUME LEDUC
Keyword(s):  
Random Walks ◽  
European Security ◽  
European Option ◽  
Order Error ◽  
First Order ◽  
Error Formula ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Values ◽  
Payoff Functions

AbstractWe study the value of European security derivatives in the Black–Scholes model when the underlying asset $\xi $ is approximated by random walks ${\xi }^{(n)} $. We obtain an explicit error formula, up to a term of order $ \mathcal{O} ({n}^{- 3/ 2} )$, which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks ${\xi }^{(n)} $ for which option values converge at a speed of $ \mathcal{O} ({n}^{- 3/ 2} )$.

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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