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Approximate Option Pricing

P. Chalasani, S. Jha, I. Saias
1999 Algorithmica  
As increasingly large volumes of sophisticated options are traded in world financial markets, determining a "fair" price for these options has become an important and difficult computational problem.  ...  Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk.  ...  Asian options are path-dependent options that are particularly hard to price, and for these we design deterministic polynomial-time approximate algorithms.  ... 
doi:10.1007/pl00009280 fatcat:5iyjqqgj2fhihor7gy5pedtsnu

Option pricing with Padé approximations

KÖROĞLU Canan
2012 Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics  
This paper shows various Padé approximaitons to obtain an e¤ective and accurate solution to the Black-Scholes equation for a European put/call option pricing problem.  ...  In this paper, Padé approximations are applied Black-Scholes model which reduces to heat equation.  ...  Of course, one can get a uniform grid in the asset price by choosing constant step size in the asset price.  ... 
doi:10.1501/commua1_0000000679 fatcat:24yakwhbezbgxdum3alxfd7tn4

Heterogeneous Basket Options Pricing Using Analytical Approximations

Georges Dionne, Genevieve Gauthier, Nadia Ouertani, Nabil Tahani
2011 Multinational Finance Journal  
This paper proposes the use of analytical approximations to price an heterogeneous basket option combining commodity prices, foreign currencies and zero-coupon bonds.  ...  Nous proposons d'utiliser les approximations analytiques pour tarifer une option panier hétérogène qui combine à la fois des denrées, des taux de change et des obligations zéro-coupon.  ...  option prices.  ... 
doi:10.17578/15-1/2-2 fatcat:xwwgk5nd3ncbvbu23cocr5el44

Rate of convergence for discrete approximation of option prices [article]

Lauri Viitasaari
2013 arXiv   pre-print
We also provide a method how explicit error formula for more general options can be obtained if such formula is available for digital option prices.  ...  In this article, we study the rate of convergence of prices when a model is approximated by some simplified model.  ...  [9] , who considered the numerical approximation for a European option pricing model with jump-diffusion.  ... 
arXiv:1207.6756v4 fatcat:cd6u3s2ts5bztj4l2xwuaxkwuq

Pricing Basket Options by Polynomial Approximations

Pablo Olivares, Alexander Alvarez
2016 Journal of Applied Mathematics  
We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model.  ...  basket option price as CH ( , , ) fl 1 Q [exp (− ( − 1 2 2 ) + ( (2) )) ⋅̃C H ( (2) , , , )] . (47) The next theorem provides the Chebyshev approximation for the price of a basket option.  ...  Exchange options are spread options with = 0; see [15] . We start writing the price of the basket option, denoted by , in terms of a conditional price via the following elementary proposition.  ... 
doi:10.1155/2016/9747394 fatcat:t7mmunxvg5ei7pmlhmp26zqkf4

Pricing American options via multi-level approximation methods [article]

Denis Belomestny, Fabian Dickmann, Tigran Nagapetyan
2013 arXiv   pre-print
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options.  ...  The performance of the proposed multilevel algorithm is illustrated by a numerical example of pricing Bermudan max-call options.  ...  Glasserman (2004) ) have high dimensions, and these applications have motivated the development of Monte Carlo methods for pricing American option.  ... 
arXiv:1303.1334v2 fatcat:i66ogopbxfc57kfbxubjqakaky

Approximate Option Pricing in the Lévy Libor Model [article]

Zorana Grbac, David Krief, Peter Tankov
2016 arXiv   pre-print
To obtain explicit approximation for option prices, we propose to treat a given L\'evy Libor model as a suitable perturbation of the log-normal LMM.  ...  The approximate option prices in the L\'evy Libor model are given as the corresponding LMM prices plus correction terms which depend on the characteristics of the underlying L\'evy process and some additional  ...  Introduction The goal of this paper is to develop explicit approximations for option prices in the Lévy Libor model introduced by Eberlein andÖzkan (2005) .  ... 
arXiv:1511.08466v2 fatcat:mllrtuoff5alnekvnmkvzs3mhy

Pricing of Basket Options Using Polynomial Approximations [article]

Pablo Olivares
2014 arXiv   pre-print
In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model.  ...  that arise as a consequence of such approximation.  ...  price of a Call Option written on the underlying asset price S (1) T with strike price K(y), maturity at T > 0, volatility σ, spot price S (1) 0 and strike price given by: K(y) = 1 w 1 e −A Ke − σ 1  ... 
arXiv:1404.3160v1 fatcat:g7m4i5l2fvakpnaq3l65dmvjf4

An Approximate Formula for Pricing American Options

Nengjiu Ju, Rui Zhong
1999 Journal of Derivatives  
An approximate formula for pricing American options along the lines of MacMillan [1986] and Barone-Adesi and Whaley [1987] is presented.  ...  In particular, it yields good results for long maturity options for which the existing analytical ones fare poorly.  ...  Summary and Discussions We have proposed a new approximate analytical formula for pricing American options.  ... 
doi:10.3905/jod.1999.319140 fatcat:nsoqmgxdb5echf3djwbqnwjom4

ANALYTIC APPROXIMATIONS FOR MULTI-ASSET OPTION PRICING

Carol Alexander, Aanand Venkatramanan
2011 Mathematical Finance  
We derive general analytic approximations for pricing European basket and rainbow options on N assets.  ...  More generally, approximate analytic prices for multi-asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price  ...  Section 4 derives approximate basket option prices based on both these conditions.  ... 
doi:10.1111/j.1467-9965.2011.00481.x fatcat:csa7q6dabvde5jqncau23akgrq

Heterogeneous Basket Options Pricing Using Analytical Approximations

Georges Dionne, Genevieve Gauthier, Nadia Ouertani, Nabil Tahani
2006 Social Science Research Network  
This paper proposes the use of analytical approximations to price an heterogeneous basket option combining commodity prices, foreign currencies and zero-coupon bonds.  ...  Nous proposons d'utiliser les approximations analytiques pour tarifer une option panier hétérogène qui combine à la fois des denrées, des taux de change et des obligations zéro-coupon.  ...  option prices.  ... 
doi:10.2139/ssrn.882855 fatcat:al7olcvf5fghjiwa3vxynpzz2u

Error estimates for discrete approximations of game options with multivariate diffusion asset prices [article]

Yuri Kifer
2021 arXiv   pre-print
)+N^-1b(XN(n/N)); where ξ(n); n≥1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with  ...  This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.  ...  In the second step we compare fair prices of options with payoffs based on these discrete approximations with the fair price of the option with the diffusion asset evolution.  ... 
arXiv:2012.01257v3 fatcat:zxzstvn5s5cs5komxnqfeyxlvm

Analytic Approximations for Multi-Asset Option Pricing

Carol Alexander, Aanand Venkatramanan
2009 Social Science Research Network  
We derive general analytic approximations for pricing European basket and rainbow options on N assets.  ...  More generally, approximate analytic prices for multi-asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price  ...  Section 4 derives approximate basket option prices based on both these conditions.  ... 
doi:10.2139/ssrn.1424985 fatcat:funotm22kngkngyfsknagypd2a

Pricing Bermudan Options via Multilevel Approximation Methods

Denis Belomestny, Fabian Dickmann, Tigran Nagapetyan
2015 SIAM Journal on Financial Mathematics  
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American or Bermudan options.  ...  Given a sequence of continuation values estimates corresponding to different levels of spatial approximation, we propose a multilevel low biased estimate for the price of the option.  ...  Such an extension can be useful for much more difficult problem of American option pricing.  ... 
doi:10.1137/130912426 fatcat:g7btnmcctfex3le36oydyji33q

Approximation for Option Prices under Uncertain Volatility

Jean-Pierre Fouque, Bin Ren
2014 SIAM Journal on Financial Mathematics  
an approximation procedure for the worst case scenario prices in a UVM with small volatility interval.  ...  In this paper, we study the asymptotic behavior of the worst case scenario option prices as the volatility interval in an uncertain volatility model (UVM) degenerates to a single point, and then provide  ...  The worst case scenario option price when ε = 0 is the Black-Scholes price at volatility σ.  ... 
doi:10.1137/130908385 fatcat:skgpp6iihzftdgiwjm5mtb72ly
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