26,197 research outputs found

    Executive stock option exercise with full and partial information on a drift change point

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    We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration F^\widehat{\mathbb{F}} in which the stock drift becomes a diffusion driven by the innovations process, an F^\widehat{\mathbb{F}}-Brownian motion also driving the stock under F^\widehat{\mathbb{F}}, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.Comment: 48 pages, final version, accepted for publication in SIAM Journal on Financial Mathematic

    Real options with priced regime-switching risk

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    We develop a model of regime-switching risk premia as well as regimedependent factor risk premia to price real options. The model incorporates the observation that the underlying risky income streams of real options are subject to discrete shifts over time as well as random changes. The presence of discrete shifts is due to systematic and unsystematic risk associated with changes in business cycles or in economic policy regimes or events such as takeovers, major changes in business plans. We analyze the impact of regime switching behavior on the valuation of projects and investment opportunities. We find that accounting for Markov switching risk results in a delay in the expected timing of the investment while the regime-specific factor risk premia make the possibility of a regime shift more pronounced

    Efficient pricing options under regime switching

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    In the paper, we propose two new efficient methods for pricing barrier option in wide classes of LĆ©vy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.LĆ©vy processes; barrier options;regime switching models; Wiener-Hopf factorization; Laplace transform; numerical methods; numerical transform inversion

    Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

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    This paper investigates a regime switching model of stochastic lumber prices in the context of an optimal tree harvesting problem. Using lumber derivatives prices, two lumber price models are calibrated: a regime switching model and a single regime model. In the regime switching model, the lumber price can be in one of two regimes in which different mean reverting price processes prevail. An optimal tree harvesting problem is specified in terms of a linear complementarity problem which is solved using a fully implicit finite difference, fully-coupled, numerical approach. The land value and critical harvesting prices are found to be significantly different depending on which price model is used. The regime switching model shows promise as a parsimonious model of timber prices that can be incorporated into forestry investment problems.optimal tree harvesting, regime switching, calibration, lumber derivatives prices, fully implicit finite difference approach
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