Completeness and Hedging

2019 ◽  
pp. 119-127
Author(s):  
Tomas Björk
Keyword(s):  
Risky Assets ◽  
Market Completeness ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Absence Of Arbitrage

The concept of market completeness is discussed in some detail and we prove that the Black–Scholes model is complete. We also discuss how completeness and absence of arbitrage is related to the number of risky assets and the number of random sources in the model.

scholarly journals Ruin Probability in Compound Poisson Process with Investment

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Yong Wu ◽  
Xiang Hu
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Ruin Probability ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Compound Poisson ◽  
Risky Assets ◽  
Black Scholes Model ◽  
Black Scholes

We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.

FINANCIAL MARKETS WITH NO RISKLESS (SAFE) ASSET

2017 ◽  
Vol 20 (08) ◽  
pp. 1750054
Author(s):  
SVETLOZAR T. RACHEV ◽  
STOYAN V. STOYANOV ◽  
FRANK J. FABOZZI
Keyword(s):  
Option Pricing ◽  
Financial Markets ◽  
Price Dynamics ◽  
Jump Diffusions ◽  
Risky Assets ◽  
No Arbitrage ◽  
Market Completeness ◽  
Black Scholes ◽  
Stochastic Volatilities

We study markets with no riskless (safe) asset. We derive the corresponding Black–Scholes–Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geometric fractional Brownian and Rosenblatt motions. No-arbitrage and market-completeness conditions are derived in all four cases.

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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