ASIAN OPTIONS WITH THE AMERICAN EARLY EXERCISE FEATURE

1999 ◽  
Vol 02 (01) ◽  
pp. 101-111 ◽  
Author(s):  
LIXIN WU ◽  
YUE KUEN KWOK ◽  
HONG YU
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Representation ◽  
Asian Option ◽  
Asian Options ◽  
Partial Differential ◽  
Early Exercise ◽  
Equation Formulation ◽  
Option Model ◽  
Early Exercise Premium

By appropriate scaling of the variables, the reduction in the dimensionality of the partial differential equation formulation of an American-style Asian option model is achieved. The integral representation of the early exercise premium can be obtained in a succinct manner. The exercise policy of Asian options with the early exercise provision can then be examined.

SOLVING THE ASIAN OPTION PDE USING LIE SYMMETRY METHODS

2010 ◽  
Vol 13 (08) ◽  
pp. 1265-1277 ◽  
Author(s):  
NICOLETTE C. CAISTER ◽  
JOHN G. O'HARA ◽  
KESHLAN S. GOVINDER
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Stock Price ◽  
Ad Hoc ◽  
Lie Symmetry ◽  
Asian Option ◽  
Asian Options ◽  
Lie Point Symmetries ◽  
Reduced Order

Asian options incorporate the average stock price in the terminal payoff. Examination of the Asian option partial differential equation (PDE) has resulted in many equations of reduced order that in general can be mapped into each other, although this is not always shown. In the literature these reductions and mappings are typically acquired via inspection or ad hoc methods. In this paper, we evaluate the classical Lie point symmetries of the Asian option PDE. We subsequently use these symmetries with Lie's systematic and algorithmic methods to show that one can obtain the same aforementioned results. In fact we find a familiar analytical solution in terms of a Laplace transform. Thus, when coupled with their methodic virtues, the Lie techniques reduce the amount of intuition usually required when working with differential equations in finance.

SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS

2001 ◽  
Vol 11 (03) ◽  
pp. 475-497 ◽  
Author(s):  
E. BARUCCI ◽  
S. POLIDORO ◽  
V. VESPRI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensions ◽  
Asian Options ◽  
Partial Differential ◽  
No Arbitrage ◽  
Strongly Degenerate ◽  
Degenerate Partial Differential Equations

We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.

scholarly journals Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan Zhang ◽  
Di Pan ◽  
Sheng-Wu Zhou ◽  
Miao Han
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Asian Option ◽  
Partial Differential ◽  
No Arbitrage ◽  
Geometric Average ◽  
Brownian Motion Model

The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. Then by solving the partial differential equation, the pricing formula and call-put parity of the geometric average Asian option with dividend payment and transaction costs are obtained. At last, the influences of Hurst index and maturity on option value are discussed by numerical examples.

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