Barrier options and touch-and-out options under regular Lévy processes of exponential type

Boyarchenko, Svetlana; Levendorskiı̌, Sergei

doi:10.1214/aoap/1037125863

Cited by 123 publications

(105 citation statements)

References 22 publications

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“…We want to point out that 8 For recent developments of numerical solution and analytic approximation of Þnite horizon American options within the classical geometric Brownian motion model, see, for example, Broadie and Detemple (1996), Carr (1998), Ju (1998), Geske and Johnson (1984), McMillan (1986), Tilley (1993), Tsitsiklis and van Roy (1999), Sullivan (2000), Broadie and Glasserman (1997), Carriére (1996) Carr 1998, and Ju 1998) for geometric Brownian motion models, and whether these algorithms can be effectively extended to jump diffusion models invites further investigation.…”

Section: Some Notationsmentioning

confidence: 99%

Option Pricing Under A Double Exponential Jump Diffusion Model

2001

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Analytical tractability is one of the challenges faced by many alternative models that try to generalize the Black-Scholes option pricing model to incorporate more empirical features. The aim of this paper is to extend the analytical tractability of the BlackScholes model to alternative models with jumps. We demonstrate a double exponential jump diffusion model can lead to an analytic approximation for Þnite horizon American options (by extending the Barone-Adesi and Whaley method) and analytical solutions for popular path-dependent options (such as lookback, barrier, and perpetual American options). Numerical examples indicate that the formulae are easy to be implemented and accurate.

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Section: Some Notationsmentioning

confidence: 99%

Option Pricing Under A Double Exponential Jump Diffusion Model

2001

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“…These problems can be solved in closed form that is amenable to very fast numerical calculations using the operator form of the WienerHopf factorization method developed in a series of works by Boyarchenko and Levendorskiȋ [30,48,50,51]. The maturity period of the claim is divided into N subintervals, using points 0 = t 0 < t 1 < · · · < t N = T, and each sub-period [t s , t s + 1 ] is replaced with an exponentially distributed random maturity period with mean s = t s + 1 − t s .…”

Section: Carr's Randomization and Backward Induction With Cva And Fvamentioning

confidence: 99%

Efficient Option Pricing Under Levy Processes, with CVA and FVA

2015

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We generalize the Piterbarg [1] model to include (1) bilateral default risk as in Burgard and Kjaer [2], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.

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“…Boyarchenko and Levendorskii (2002) derived explicit formulas for Europeantype barrier options and touch-and-out options assuming that under a chosen equivalent martingale measure the stock returns follow a Lévy process. Petrella and Kou (2004) provided a comprehensive study of discrete single-barrier options in Merton's and Kou's jump-diffusion models in this framework based on Spitzer's identity.…”

Section: Literature Reviewmentioning

confidence: 99%

A Probabilistic Monte Carlo model for pricing discrete barrier and compound real options

Rostan

Rostan²,

Racicot³

2014

J Deriv Hedge Funds

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PhD, is Associate Professor of Finance at the Telfer School of Management, University of Ottawa. His research interests focus on the problems of measurement errors, specification errors and endogeneity in financial models of returns. He is also interested in developing new methods for forecasting financial time series, especially with regard to hedge fund risk. He has published several books and many articles on quantitative finance and financial econometrics.Correspondence: Pierre Rostan, Department of Management, American University in Cairo, AUC Avenue, P.O. Box 74, New Cairo 11835, Egypt E-mail: prostan@aucegypt.edu ABSTRACT We present an original Probabilistic Monte Carlo (PMC) model for pricing European discrete barrier options and compound real options. On the basis of Monte Carlo (MC) simulation, for barrier options the PMC model computes the probability of not crossing the barrier for knock-out options and crossing the barrier for knock-in options. This probability is then multiplied by an average sample discounted payoff of a plain vanilla option that has the same inputs as the barrier option but barrier-free, and to which we have applied a filter. We test the consistency of our model with an analytical solution (Merton, 1973;Reiner and Rubinstein, 1991) adjusted for discretization by Broadie et al (1997) and a naïve numerical model using MC simulation presented by Clewlow and Strickland (2000). Our study shows that the PMC model accurately prices barrier options. Moreover, the idea behind the method is simple and can be applied to the pricing of complex derivatives, easing the valuation step significantly: we illustrate the versatility of the PMC model in pricing

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Barrier options and touch-and-out options under regular Lévy processes of exponential type

Cited by 123 publications

References 22 publications

Option Pricing Under A Double Exponential Jump Diffusion Model

Option Pricing Under A Double Exponential Jump Diffusion Model

Efficient Option Pricing Under Levy Processes, with CVA and FVA

A Probabilistic Monte Carlo model for pricing discrete barrier and compound real options

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