scholarly journals The Pricing and Hedging of an Attainable Claim in a Hybrid Black–Scholes Model under Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Kuanhou Tian ◽  
Yanfang Li ◽  
Guixin Hu
Keyword(s):  
Regime Switching ◽  
The Self ◽  
Black Scholes Model ◽  
Complete Market ◽  
Black Scholes ◽  
Theoretical Results

This article formulates and dissects a Black–Scholes model with regime switching that can be used to describe the performance of a complete market. An explicit integrand formula ϕ t , ω is obtained when the T -claim F ω is given for an attainable claim in this complete market. In addition, some perfect results are presented on how to hedge an attainable claim for this Black–Scholes model, and the price p of the European call and the self-financing portfolio θ t = θ 0 t , θ 1 t are given explicitly. Finally, some concluding remarks are provided to illustrate the theoretical results.

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

scholarly journals Stochastic Analysis of the Effect of Asset Prices to a Single Economic Investor

2016 ◽  
Vol 17 ◽  
pp. 33-39
Author(s):  
Enyinnaya Ekuma-Okereke ◽  
Joseph Thomas Eghwerido ◽  
E. Efe-Eyefia ◽  
Samuel Zelibe
Keyword(s):  
Stochastic Analysis ◽  
Market Value ◽  
Dynamic Programming Principle ◽  
Fair Price ◽  
Brownian Motion Process ◽  
Black Scholes Model ◽  
Complete Market ◽  
Black Scholes ◽  
Motion Process ◽  
Hamilton Jacobi Bellman

In this paper, we propose a single economic investor whose asset follows a geometric Brownian motion process. Our objective therefore is to obtain the fair price and the present market value of the asset with an infinitely horizon expected discounted investment output. We apply dynamic programming principle to derive the Hamilton Jacobi Bellman (HJB)-equation associated with the problem which is found to be equivalent to the famous Black-Scholes Model under no risk neutrality. In addition, for a complete market under equilibrium, we obtained the value of the present asset with risk neutrality and its fair price.

AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING

2021 ◽  
pp. 1-20
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

Abstract 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.

TERM STRUCTURE OF VANILLA OPTIONS

2007 ◽  
Vol 10 (08) ◽  
pp. 1323-1337
Author(s):  
DORJE C. BRODY ◽  
IRENE C. CONSTANTINOU ◽  
BERNHARD K. MEISTER
Keyword(s):  
Term Structure ◽  
Implied Volatility ◽  
Volatility Smile ◽  
Discount Function ◽  
Forward Rates ◽  
Black Scholes Model ◽  
Initial Term ◽  
Complete Market ◽  
Black Scholes ◽  
Structure Density

Every maturity-dependent derivative contract entails a term structure. For example, when the value of the portfolio consisting of a long position in a stock and a short position in a vanilla option is expressed in units of its instantaneous exercise value, the resulting quantity defines a discount function. Thus, the derivative of the discount function with respect to the time left until maturity defines a term structure density function, and the "hazard rate" associated with the discount function determines the forward rates for the vanilla option portfolio. The dynamics associated with these quantities are obtained in the complete market setting. In particular, one can model vanilla options based on the associated forward rates. The formulation based on forward rates for options extends the approach based on modeling the implied volatility process. As an illustrative example, the initial term structure of the Black–Scholes model is considered. It is shown in this example that the implied volatility smile has the effect of making the option forward rates homogeneous across different strikes.

Study of the Effect of Hole Clearance and Thread Fit on the Self-Loosening of Threaded Fasteners

2006 ◽  
Vol 129 (6) ◽  
pp. 586-594 ◽  
Author(s):  
Sayed A. Nassar ◽  
Basil A. Housari
Keyword(s):  
Analytical Investigation ◽  
The Self ◽  
Time Data ◽  
Experimental Procedure ◽  
Test Setup ◽  
Threaded Fasteners ◽  
Service Load ◽  
Real Time Data ◽  
Theoretical Results ◽  
Simplified Mathematical Model

This study provides an experimental and theoretical investigation of the effect of hole clearance and thread fit on the self-loosening of tightened threaded fasteners that are subjected to a cyclic transverse service load. An experimental procedure and test setup are developed in order to collect real-time data on the rate of clamp load loss per cycle as well as the loosening rotation of the bolt head. Three levels of hole clearance are investigated; namely, 3%, 6%, and 10% of the bolt nominal diameter. For the commonly used 2A thread fit for a selected bolt size, three classes of the nut thread fit are considered; namely, 1B, 2B, and 3B. A simplified mathematical model is used for the analytical investigation of the effect of the hole clearance and thread fit on threaded fasteners self-loosening. The experimental and theoretical results are presented and discussed.

Sign in / Sign up

Export Citation Format

Share Document