Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy

We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.

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“…We now focus on the first expectation in (31). Let us set b α := B 2 (T − α) let us condition internally with respect to λ t,λ α , obtaining…”

Section: Correlation Expansionmentioning

confidence: 99%

CVA and vulnerable options pricing by correlation expansions

2019

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“…In this paper, considering the market prices of common systematic jump risks regardless of individual jump risks, we develop an equivalent martingale measure for two regime-switching jump-diffusion processes with correlated jumps via regimeswitching Esscher transform and consider the differences between the physical jump-diffusion processes and the riskneutral jump-diffusion processes. The dynamics of the risk assets prices in this paper are different from those obtained by considering the market prices of all jump risks in Niu and Wang [17] under the risk-neutral measure. In order to consider the influence of the market prices of jump risks on vulnerable option values, we also study vulnerable options pricing formulae with or without market prices of all jump risks.…”

Section: Introductionmentioning

confidence: 88%

“…Bo et al [15] study the pricing of some currency options based on the Markov-modulated jump-diffusion models for the spot foreign exchange rate. Wang and Wang [16] and Niu and Wang [17] study the pricing problem of vulnerable European options under the Markov regime switching jump-diffusion models. However, they regard all jump risks as systematic risks.…”

Section: Introductionmentioning

confidence: 99%

Pricing Vulnerable Options with Market Prices of Common Jump Risks under Regime-Switching Models

Han

Song

Niu

et al. 2018

Discrete Dynamics in Nature and Society

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This paper investigates the valuation of vulnerable European options considering the market prices of common systematic jump risks under regime-switching jump-diffusion models. The way of regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options. Explicit analytical pricing formulae for vulnerable European options are derived by risk-neutral pricing theory. For comparison, the other two cases are also considered separately. The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks. Numerical examples for the valuation of vulnerable European options are provided to illustrate our results and indicate the influence of the market prices of jump risks on the valuation of vulnerable European options.

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“…The standard option pricing formulas [1,2] do not focus on counterparty risk. Subsequently, some literatures begin to pay attention to the pricing of vulnerable options and consider counterparty risk (see [3][4][5][6][7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

“…Yoon et al [13] use the Double Merlin Transform under constant and random (Hull-White) interest rates to get analytical pricing formulas for each interest rate case so that vulnerable option's value can be accurately and effectively calculated. Through a Markov modulation mechanism switching method to simulate various economic conditions and giving the dynamics of the assets values by two related jump-diffusion processes, Niu et al [4] study the pricing of vulnerable European options. By Laplace transforms, they obtain an analytical solution of the price of vulnerable options.…”

Section: Introductionmentioning

confidence: 99%

Pricing vulnerable options with variable default boundary under jump-diffusion processes

Zhou

Wang

2018

Adv Differ Equ

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For the pricing of vulnerable options, we improve the results of Klein and Inglis [Journal of Banking and Finance] and Tian et al. [The Journal of Futures and Markets], considering the circumstances in which the writers of options face financial crisis. Our pricing model faces the risks of default and the occasional impact experienced by the underlying assets and counterparty's assets. The correlation between the option's underlying assets and the option writer's assets is clearly modeled. Asset prices are driven by the jump-diffusion processes of two related assets. Furthermore, we consider a variable default boundary (VDB) based on the option's potential debt and the option writer's other liabilities. In case financial distress happens, the payout rate is connected to the option writer's assets. Through the Taylor expansion, we derive an approximate explicit valuation for vulnerable options.MSC: 60H10; 60J75; 60H30; 90G20; 90G40

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Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy

Cited by 31 publications

References 39 publications

CVA and vulnerable options pricing by correlation expansions

CVA and vulnerable options pricing by correlation expansions

Pricing Vulnerable Options with Market Prices of Common Jump Risks under Regime-Switching Models

Pricing vulnerable options with variable default boundary under jump-diffusion processes

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