A Simple Approach to Option Valuation and Hedging in the Black-Scholes Model

1994 ◽  
Vol 50 (2) ◽  
pp. 25-28 ◽  
Author(s):  
Menachem Brenner ◽  
Marti G. Subrahmanyam
Keyword(s):  
Simple Approach ◽  
Option Valuation ◽  
Black Scholes Model ◽  
Black Scholes

Exchange option valuation using Liu process

2021 ◽  
pp. 2150018
Author(s):  
Seema Uday Purohit ◽  
Prasad Narahar Lalit
Keyword(s):  
Financial Mathematics ◽  
Option Valuation ◽  
Normal Distributions ◽  
Black Scholes Model ◽  
Liu Process ◽  
Proposed Model ◽  
Black Scholes ◽  
The Difference ◽  
Log Normal ◽  
Exchange Option

Margrabe formula is an extension of the famous Black–Scholes model extended to two correlated stocks. In the stochastic financial mathematics approach, the difficulty of addressing this valuation lies in the fact that the difference between two log-normal distributions is not log-normal. We avoided this approach in this work and valued the European type exchange option using the Liu process, a Brownian motion’s fuzzy counterpart. The work compares the proposed model values with the simulated values obtained by the Margrabe formula.

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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