On discrete time hedging errors in a fractional Black-Scholes model

2017 ◽  
Vol 32 (2) ◽  
pp. 211-224 ◽  
Author(s):  
Wen-sheng Wang
Keyword(s):  
Discrete Time ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Discrete Time Hedging

EFFICIENT HEDGING OF PATH–DEPENDENT OPTIONS

2016 ◽  
Vol 19 (05) ◽  
pp. 1650032 ◽  
Author(s):  
ADAM W. KOLKIEWICZ
Keyword(s):  
Discrete Time ◽  
Loss Function ◽  
Residual Risk ◽  
Asian Options ◽  
European Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Efficient Hedging ◽  
Novel Method ◽  
Path Dependent

In this paper, we propose a novel method of hedging path-dependent options in a discrete-time setup. Assuming that prices are given by the Black–Scholes model, we first describe the residual risk when hedging a path-dependent option using only an European option. Then, for a fixed hedging interval, we find the hedging option that minimizes the shortfall risk, which we define as the expectation of the shortfall weighted by some loss function. We illustrate the method using Asian options, but the methodology is applicable to other path-dependent contacts.

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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