Assessment of Contingent Liabilities for Risk Assets Evolutions Built on Brownian Motion

Gonchar, N. S.

doi:10.4236/apm.2020.105016

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…, ω n−1 ) ∈ Ω n−1 , n = 1, N, relative to the measure P n−1 , owing to the inequalities (17) and Foubini Theorem. This proves the inequality (15). The equality ( 16) is also satisfied due to the construction of α n ({ω}…”

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confidence: 53%

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Derivatives Pricing in Non-Arbitrage Market

Gonchar¹

2020

Preprint

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The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent martingale measures to the original measure is a non-empty set. The set of martingale measures is constructed from a set of strictly nonnegative random variables, satisfying certain conditions. The inequalities are obtained for the non-negative random variables satisfying certain conditions. Using these inequalities, a new simple proof of optional decomposition theorem for the nonnegative super-martingale is proposed. The family of spot measures is introduced and the representation is found for them. The conditions are found under which each martingale measure is an integral over the set of spot measures. On the basis of nonlinear processes such as ARCH and GARCH, the parametric family of random processes is introduced for which the interval of non-arbitrage prices are found. The formula is obtained for the fair price of the contract with option of European type for the considered parametric processes. The parameters of the introduced random processes are estimated and the estimate is found at which the fair price of contract with option is the least.

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confidence: 53%

“…In this paper, we generalize the results of the papers [15], [16], [17] and construct the evolution of risky assets for which we completely describe the set of equivalent martingale measures.…”

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confidence: 95%

Derivatives Pricing in Non-Arbitrage Market

Gonchar¹

2020

Preprint

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“…This work is a continuation of the works [1], [19], [20], [21]. In paper [1], a new method for constructing and describing a family of martingale measures was proposed.…”

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confidence: 93%

Non-Arbitrage Models of Financial Markets

Gonchar¹

2021

GJSFR

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In the first part of the paper, we construct the models of the complete non-arbitrage financial markets for a wide class of evolutions of risky assets.This construction is based on the observation that for a certain class of risky as set evolutions the martingale measure is invariant with respect to these evolutions. For such a financial market model the only martingale measure being equivalent to an initial measure is built. On such a financial market,formulas for the fair price of contingent liabilities are presented. A multi-parameter model of the financial market is proposed, the martingale measure of which does not depend on the parameters of the model of the evolution of risky assets and is the only one.

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Assessment of Contingent Liabilities for Risk Assets Evolutions Built on Brownian Motion

Cited by 2 publications

References 13 publications

Derivatives Pricing in Non-Arbitrage Market

Derivatives Pricing in Non-Arbitrage Market

Non-Arbitrage Models of Financial Markets

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