Search results for " Option pricing"

showing 4 items of 14 documents

Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations

2008

In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of…

Transaction costAsymptotic analysisMathematical optimizationActuarial scienceValuation of optionsEconomicsPortfolioAsian optionBlack–Scholes modelFinite difference methods for option pricingFutures contractSSRN Electronic Journal
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THE CARMA INTEREST RATE MODEL

2014

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Vasicek modelBond optionInterest rate model short rate forward rate term structure CARMA process bond pricing bond option pricing yield curve volatility curve calibrationImplied volatilityBond valuationShort-rate modelForward rateShort rateForward volatilityEconometricsEconomicsLIBOR market modelYield curveVolatility (finance)General Economics Econometrics and FinanceFinanceAffine term structure modelRendleman–Bartter modelMathematicsInternational Journal of Theoretical and Applied Finance
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Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

2017

Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…

ta113Mathematical optimizationGeneral Computer ScienceStochastic volatilityDifferential equationEuropean optionMonte Carlo methods for option pricingJump diffusion010103 numerical & computational mathematics01 natural sciencesTheoretical Computer Science010101 applied mathematicsValuation of optionsModeling and Simulationlinear complementary problemRange (statistics)Asian optionreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingMathematicsJournal of Computational Science
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Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models

2016

American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed

ta113Mathematical optimizationStochastic volatilityDiscretizationComputer scienceJump diffusionFinite difference method010103 numerical & computational mathematics01 natural sciencesNon-negative matrix factorization010101 applied mathematicsValuation of optionslinear complementary problemRange (statistics)General Earth and Planetary SciencesApplied mathematicsreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingGeneral Environmental ScienceProcedia Computer Science
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