Journal ArticleDOI
A Markov chain approximation scheme for option pricing under skew diffusions
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TLDR
An explicit closed-form approximation of the transition density of a general skew diffusion process is obtained, which facilitates the unified valuation of various financial contracts written on assets with natural boundary behavior, e.g. in the foreign exchange market with target zones and equity markets with psychological barriers.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...read more
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Rates of convergence to the local time of Oscillating and Skew Brownian Motions
TL;DR: In this article, a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motion is considered and their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.
Journal ArticleDOI
Markov chain approximation and measure change for time-inhomogeneous stochastic processes
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TL;DR: 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.
Journal ArticleDOI
Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates
TL;DR: This paper for the first time establishes the exact second-order convergence rates of the CTMC methods when applied to the prices and Greeks of Asian options and proposes a new set of error analysis methods for these path-dependent derivatives, whose payoffs depend on the average of asset prices.
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Data and methods for A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data [Données et méthodes pour "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data"]
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TL;DR: In this paper, the authors presented the methodology and numerical results for 21 stock prices under the assumption they follow a Drifted Geometric Oscillating Brownian motion model, taking leverage and mean-reversion effects into account.
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Parameter estimation for threshold Ornstein-Uhlenbeck processes from discrete observations
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References
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Journal ArticleDOI
Target Zones and Exchange Rate Dynamics
TL;DR: The authors developed a simple model of exchange rate behavior under a target zone regime and showed that the expectation that monetary policy will be adjusted to limit exchange rate variation affects exchange rate behaviour even when the exchange rate lies inside the zone and is thus not being defended actively.
Journal ArticleDOI
American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods
Mark Broadie,Jerome Detemple +1 more
TL;DR: A modification of the binomial method (termed BBSR) is introduced that is very simple to implement and performs remarkable well and a careful large-scale evaluation of many recent methods for computing American option prices is conducted.
Book
Pricing Financial Instruments: The Finite Difference Method
Curt Randall,Domingo Tavella +1 more
TL;DR: The Pricing Equations. as mentioned in this paper and the Finite-difference method are the most commonly used methods for finite difference methods in the literature, and they can be found in:
Journal ArticleDOI
Pricing and Hedging Path-Dependent Options Under the CEV Process
Dmitry Davydov,Vadim Linetsky +1 more
TL;DR: It is demonstrated that the prices of options, which depend on extrema, 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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On Skew Brownian Motion
J. M Harrison,Larry Shepp +1 more
TL;DR: In this article, the authors considered the stochastic equation where W(t) is a standard Wiener process and L^X_0 (cdot) is the local time at zero of the unknown process.
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