Hedging with risk for game options in discrete time

Dolinsky, Yan; Kifer, Yuri

doi:10.1080/17442500601097784

Cited by 24 publications

(42 citation statements)

References 14 publications

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“…For the CRR markets we have an analogous definitions. In the next section we will follow [6] and construct optimal hedges (π n , σ n ) ∈ A ξ ,n (x) × T ξ 0n for double barrier options in the n-step CRR markets with barriers L n , R n . By embedding this hedges into the BS model we obtain a simple representation of ε-optimal hedges for the the BS model.…”

Section: Theorem 23 Let I = (L R) Be An Open Interval For Any N Letmentioning

confidence: 99%

Binomial Approximations for Barrier Options of Israeli Style

Dolinsky

Kifer

2010

Annals of the International Society of Dynamic Games

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We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black-Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and the speed of convergence is estimated, as well. The results are new also for usual American style options and they are interesting from the computational point of view, as well, since in binomial markets these quantities can be obtained via dynamical programming algorithms. The paper continues the study of [11] and [7] but requires substantial additional arguments in view of pecularities of barrier options which, in particular, destroy the regularity of payoffs needed in the above papers.

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Section: Theorem 23 Let I = (L R) Be An Open Interval For Any N Letmentioning

confidence: 99%

Binomial Approximations for Barrier Options of Israeli Style

Dolinsky

Kifer

2010

Annals of the International Society of Dynamic Games

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“…Here, E Q denotes the expectation under the unique martingale probability measure Q of the market model. Further research on the pricing of game options and on more sophisticated gametype financial contracts includes in particular papers by Dolinsky and Kifer (2007) [12] and Dolinsky and al. (2011) [11] in the discrete time case, and by Hamadène (2006) [18] in a continuous time perfect market model with continuous payoffs ξ and ζ.…”

Section: Introductionmentioning

confidence: 99%

Game Options in an Imperfect Market with Default

Dumitrescu¹,

Quenez²,

Sulem³

2017

SIAM J. Finan. Math.

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We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in [23] in the case of a perfect market model to the case of an imperfect market with default, when the imperfections are taken into account via the nonlinearity of the wealth dynamics. We introduce the seller's price of the game option as the infimum of the initial wealths which allow the seller to be superhedged. We prove that this price coincides with the value function of an associated generalized Dynkin game, recently introduced in [14], expressed with a nonlinear expectation induced by a nonlinear BSDE with default jump. We moreover study the existence of superhedging strategies. We then address the case of ambiguity on the model, -for example ambiguity on the default probability -and characterize the robust seller's price of a game option as the value function of a mixed generalized Dynkin game. We study the existence of a cancellation time and a trading strategy which allow the seller to be super-hedged, whatever the model is.

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“…Observe that the process H (n) (kT /n) M (n) (kT /n) , 0 ≤ k ≤ n is a martingale with respect toP ξ n and the filtration {F ξ k } n k=0 , thus (since the multinomial markets are complete) there exists π ′ n ∈ A ξ,n (x) such that V π ′ n (k) = H (n) (kT /n) M (n) (kT /n) , k ≤ n. We obtain that for any n there exists a stopping time σ n ∈ T ξ n which satisfies Finally, by using (4.13) for the process Φ(t) := (Y W (t) − H(t) M(t) ) + , (4.9) and (4.11)-(4.12) we obtain H ξ,n (k, l) = G( kT n , S ξ,n )I k<l + F ( lT n , S ξ,n )I l≤k , n ∈ N, 0 ≤ k, l ≤ n. The terms H W (t, s) and H ξ,n (k, l) are the payoff functions for the BS model and the n-step multinomial model, respectively. For game options the shortfall risk is defined by (see [5])…”

Section: Proof Of Main Resultsmentioning

confidence: 99%

Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model

Dolinsky

2010

J. Appl. Probab.

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We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we consider the multi assets case for which we use the weak convergence approach.Date: November 5, 2018. 2000 Mathematics Subject Classification. Primary: 91B28 Secondary: 60F15, 91B30.

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Hedging with risk for game options in discrete time

Cited by 24 publications

References 14 publications

Binomial Approximations for Barrier Options of Israeli Style

Binomial Approximations for Barrier Options of Israeli Style

Game Options in an Imperfect Market with Default

Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model

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