American options in nonlinear markets

Kim, Edward; Nie, Tianyang; Rutkowski, Marek

doi:10.1214/21-ejp658

Cited by 7 publications

(6 citation statements)

References 66 publications

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“…More generally, the results obtained in this work can be employed to derive the results of the valuation, hedging and exercising of American and game options in any market model where the price processes of primary assets are governed by stochastic differential equations driven by discontinuous noise processes. Some applications of our results to the American and game options are presented in follow-up works by Kim et al [39,40].…”

Section: Introductionmentioning

confidence: 79%

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Nie,

Rutkowski

2021

Preprint

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We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu [55] and Dumitrescu et al. [13] who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.

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Section: Introductionmentioning

confidence: 79%

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Nie,

Rutkowski

2021

Preprint

Self Cite

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“…By the same token, results from this work can be used to study market models where asset prices are governed by noise processes with jumps. Applications of our results on BSDEs and reflected BSDEs driven by RCLL martingales to the valuation, hedging and exercising of American and game options are presented in the follow-up works by Kim et al [19,20]. Finally, it is also worth mentioning that several classes of BSDEs driven by a Brownian motion and a martingale random measure were studied by, among others, Barles et al [1], El Karoui et al [11], Jeanblanc et al [17,18], Quenez and Sulem [30], Royer [31] and Tang and Li [32].…”

Section: Introductionmentioning

confidence: 80%

“…We stress that Assumption 5.2 is not directly concerned with the dynamics of asset prices, but rather with modeling of underlying sources for various kinds of financial risks. Therefore, it is not restrictive when dealing with practical applications of BSDEs driven by an RCLL martingale to problems arising in financial mathematics (see, in particular, Dumitrescu et al [8] or Kim et al [19,20] for recent studies of American and game options in nonlinear markets).…”

Section: Let Us Denote Nmentioning

confidence: 99%

“…Secondly, and more importantly, we give in Proposition 5.1 an explicit solution to the linear BSDE and subsequently use its form to prove the strict comparison theorem, which is a crucial result for financial applications, most notably, the arbitrage-free pricing of European, American and game options in nonlinear markets (see [2,19,20]). Carbone et al [4] established the comparison theorem under some assumptions which are not easy to verify (see Theorem 2.2 and Lemma 2.2 in [4]) and they studied a BSDE with the generator term involving integration w.r.t.…”

Section: Introductionmentioning

confidence: 99%

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Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales

Nie,

Rutkowski

2021

Preprint

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Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models with jumps, including as particular cases the setups studied by Peng and Xu [27,28] and Dumitrescu et al. [7] who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.

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“…See, for example, [12,Proposition 3.3]. For definitions of hedger-specific arbitrage opportunities, readers can refer to [12,10,6,7,8,41,40].…”

Section: Hedging Portfolio Under Bilateral Contractsmentioning

confidence: 99%

A Risk-Sharing Framework of Bilateral Contracts

Lee¹,

Sturm²,

Zhou³

2020

SIAM J. Finan. Math.

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We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same pricing methodology and parameters. Thus, the two parties should enter the derivative contracts with a negotiated price, and we call the negotiation a risk-sharing problem. This framework defines the negotiation as a problem that maximizes the sum of utilities of the two parties. By the derived optimal price, we provide a theoretical analysis on how the price is determined between the two parties. As well as the price, the risk-sharing framework produces an optimal amount of collateral. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. However, inter-dealers markets are governed by regulations. As recommended in Basel III, it is a convention in inter-dealer contracts to pledge the full amount of a close-out price as collateral. In this case, using the optimal collateral, we interpret conditions for the full margin requirement to be indeed optimal.

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American options in nonlinear markets

Cited by 7 publications

References 66 publications

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales

A Risk-Sharing Framework of Bilateral Contracts

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