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Journal ArticleDOI: 10.1080/14697688.2020.1781235

A Markov chain approximation scheme for option pricing under skew diffusions

04 Mar 2021-Quantitative Finance (Routledge)-Vol. 21, Iss: 3, pp 461-480
Abstract: In this paper, we propose a general valuation framework for option pricing problems related to skew diffusions based on a continuous-time Markov chain approximation to the underlying stochastic pro...

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Topics: Valuation of options (64%), Markov chain (62%), Valuation (logic) (61%) ... read more
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9 results found


Open accessPosted Content
Sara Mazzonetto1Institutions (1)
10 Dec 2019-arXiv: Probability
Abstract: In this paper a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motions is considered. Their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.

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Topics: Skew (54%), Brownian motion (54%), Local time (53%) ... read more

4 Citations


Open accessPosted Content
Abstract: This technical report presents the methodology and the numerical results for 21 stock prices under the assumption they follow a Drifted Geometric Oscillating Brownian motion model. Such a model takes leverage and mean-reversion effects into account. This report completes the article "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data"

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Topics: Mean reversion (65%), Local volatility (59%), Leverage (statistics) (56%) ... read more

4 Citations


Open accessJournal ArticleDOI: 10.1016/J.AMC.2020.125732
Kailin Ding1, Ning Ning2Institutions (2)
Abstract: In this paper, we propose a general time-inhomogeneous continuous-time Markov chain (CTMC) framework for the approximation of the general one-dimensional and two-dimensional time-inhomogeneous diffusion processes. For the approximating CTMC, we can perform a change of measure, choose the minimal relative entropy measure to determine the measure uniquely, and finally establish the convergence. Therefore, the proposed methodology covers the stochastic processes that are hard to perform a change of measure, and is applicable to valuation problems driven by models not only under the risk-neutral probability measure but also under the physical probability measure.

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Topics: Probability measure (66%), Measure (mathematics) (63%), Markov chain (60%) ... read more

3 Citations


Open accessPosted Content
Yaozhong Hu1, Yuejuan Xi2Institutions (2)
Abstract: Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we need to find the explicit form of the invariant measure. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity.

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Topics: Invariant measure (59%), Estimator (58%), Asymptotic distribution (55%) ... read more

2 Citations


Journal ArticleDOI: 10.1007/S00186-020-00735-5
Wensheng Yang1, Jingtang Ma1, Zhenyu Cui2Institutions (2)
Abstract: The continuous-time Markov chain (CTMC) approximation method is a powerful tool that has recently been utilized in the valuation of derivative securities, and it has the advantage of yielding closed-form matrix expressions suitable for efficient implementation. For two types of popular path-dependent derivatives, the arithmetic Asian option and the occupation-time derivative, this paper obtains explicit closed-form matrix expressions for the Laplace transforms of their prices and the Greeks of Asian options, through the novel use of pathwise method and Malliavin calculus techniques. We for the first time establish the exact second-order convergence rates of the CTMC methods when applied to the prices and Greeks of Asian options. We propose a new set of error analysis methods for the CTMC methods applied to these path-dependent derivatives, whose payoffs depend on the average of asset prices. A detailed error and convergence analysis of the algorithms and numerical experiments substantiate the theoretical findings.

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Topics: Asian option (60%), Valuation of options (55%), Markov chain (54%) ... read more

1 Citations


References
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90 results found


Open accessJournal ArticleDOI: 10.2307/2937922
Paul Krugman1Institutions (1)
Abstract: This paper develops a simple model of exchange rate behavior under a target zone regime. It shows that the expectation that monetary policy will be adjusted to limit exchange rate variation affects exchange rate behavior even when the exchange rate lies inside the zone and is thus not being defended actively. Somewhat surprisingly, the analysis of target zones turns out to have a strong formal similarity to problems in option pricing and investment under uncertainty.

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Topics: Exchange rate (62%), Interest rate parity (59%), Currency band (56%) ... read more

1,192 Citations


Open accessJournal ArticleDOI: 10.1093/RFS/9.4.1211
Mark Broadie1, Jerome Detemple2Institutions (2)
Abstract: We develop lower and upper bounds on the prices of American call and put options written on a dividend-paying asset. We provide two option price approximations, one based on the lower bound (termed LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a 1,000-step binomial tree with a computation speed comparable to a 50-step binomial tree. We introduce a modification of the binomial method (termed BBSR) that is very simple to implement and performs remarkable well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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579 Citations


Open accessBook
21 Apr 2000-
Abstract: The Pricing Equations. Analysis of Finite Difference Methods. Special Issues. Coordinate Transformations. Numerical Examples. Index.

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526 Citations


Open accessJournal ArticleDOI: 10.1287/MNSC.47.7.949.9804
Dmitry Davydov1, Vadim Linetsky2Institutions (2)
01 Jul 2001-Management Science
Abstract: Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance CEV diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.

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Topics: Binomial options pricing model (66%), Trinomial tree (65%), Volatility smile (65%) ... read more

327 Citations


Open accessPosted Content
Abstract: Recent contributions emphasize that the presence of exchange-rate target zones has important effects on the within-band behavior of exchange rates when agents are forward-looking. The authors find that the implications of available models are inconsistent with European exchange-rate data, and they suggest that the frequent realignments occurring in the period they consider may be responsible for this. They construct a model in which the likelihood of a realignment in the near future increases as the exchange rate approaches the limits of its fluctuation band and show that its implications are broadly consistent with the evidence. Copyright 1992 by American Economic Association.

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Topics: Exchange rate (56%)

325 Citations