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Approximate Option Pricing
1999
Algorithmica
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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
2012
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
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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
2011
Multinational Finance Journal
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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]
2013
arXiv
pre-print
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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
2016
Journal of Applied Mathematics
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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]
2013
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
1999
Journal of Derivatives
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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
2011
Mathematical Finance
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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
2006
Social Science Research Network
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:2012.01257v2 fatcat:3clzd3x6anegvirhvuh4loxt5mOther Versions
)+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
2009
Social Science Research Network
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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
2015
SIAM Journal on Financial Mathematics
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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
2014
SIAM Journal on Financial Mathematics
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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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