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Yan Dolinsky

  1. Approximating stochastic volatility by recombinant trees.

    Thu, 05/17/2012 - 15:01 — SomNambul
    Authors: Yan Dolinsky, Erdinc Akyildirim, H.Mete Soner
    Subjects: Computational Finance
    Abstract

    A general method to construct recombinant tree approximations for stochastic
    volatility models is developed and applied to the Heston model for stock price
    dynamics. In this application, the resulting approximation is a four tuple
    Markov process. The ?first two components are related to the stock and
    volatility processes and take values in a two dimensional Binomial tree. The
    other two components of the Markov process are the increments of random walks
    with simple values in {-1; +1}.

  2. Duality and Convergence for Binomial Markets with Friction.

    Mon, 06/13/2011 - 15:01 — SomNambul
    Authors: Yan Dolinsky, Halil Mete Soner
    Subjects: Computational Finance
    Abstract

    We prove limit theorems for the super-replication cost of European options in
    a Binomial model with friction. The examples covered are markets with
    proportional transaction costs and the illiquid markets. The dual
    representation for the super-replication cost in these models are obtained and
    used to prove the limit theorems. In particular, the existence of the liquidity
    premium for the continuous time limit of the model proposed in [6] is proved.
    Hence, this paper extends the previous convergence result of [13] to the
    general non-Markovian case.

  3. Hedging of Game Options With the Presence of Transaction Costs.

    Tue, 03/08/2011 - 16:01 — SomNambul
    Authors: Yan Dolinsky
    Subjects: Portfolio Management
    Abstract

    We study the problem of super-replication for game options under proportional
    transaction costs. We consider a multidimensional model which is an extension
    of the usual Black-Scholes (BS) model, in the sense that the volatility is a
    progressively measurable function of the stock. For this case we show that the
    super-replication price is the cheapest cost of a trivial super-replication
    strategy. This result is an extension of previous papers (see [1], [2], [10]
    and [11]) in which only European options with Markovian structure were
    considered.

  4. Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model.

    Mon, 04/12/2010 - 15:02 — SomNambul
    Authors: Yan Dolinsky
    Subjects: Computational Finance
    Abstract

    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.

  5. Error Estimates for Multinomial Approximations of American Options in Merton's Model.

    Mon, 04/12/2010 - 15:01 — SomNambul
    Authors: Yan Dolinsky
    Subjects: Computational Finance
    Abstract

    We derive error estimates for multinomial approximations of American options
    in a multidimensional jump--diffusion Merton's model. We assume that the
    payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates
    for such type of approximations were not obtained before. Our main tool is the
    strong approximations theorems for i.i.d. random vectors which were obtained
    [14]. For the multidimensional Black--Scholes model our results can be extended
    also to a general path dependent payoffs which satisfy Lipschitz type
    conditions.

  6. Limit Theorems for Partial Hedging Under Transaction Costs.

    Mon, 04/12/2010 - 15:01 — SomNambul
    Authors: Yan Dolinsky
    Subjects: Computational Finance
    Abstract

    We study shortfall risk minimization for American options with path dependent
    payoffs under proportional transaction costs in the Black--Scholes (BS) model.
    We show that for this case the shortfall risk is a limit of similar terms in an
    appropriate sequence of binomial models. We also prove that in the continuous
    time BS model for a given initial capital there exists a portfolio strategy
    which minimizes the shortfall risk. In the absence of transactions costs
    (complete markets) similar limit theorems were obtained in Dolinsky and Kifer
    (2008, 2010) for game options.

  7. Applications of Weak Convergence for Hedging of American and Game Options.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: Yan Dolinsky
    Subjects: Probability
    Abstract

    This paper studies stability of Dynkin's games value under weak convergence.
    We use these results to approximate game options prices with path dependent
    payoffs in continuous time models by sequence of game options prices in
    discrete time models which can be calculated by dynamical programming
    algorithms. We also show that shortfall risks of American options in a sequence
    of multinomial approximations of the multidimensional BS market converge to the
    corresponding quantities for similar American options in the multidimensional
    BS market with path dependent payoffs.

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