Wellposedness of the boundary value formulation of a fixed strike Asian option

Numerical pricing of geometric asian options with barriers

“…The obtained results are then compared with numerical results obtained by two FD methods among the great variety that we can find in literature (resumed, eg, in the work of Hugger). The application of FD methods is not straightforward since explicit boundary conditions have to be derived from financial conditions in such a way to ensure wellposedness of the starting differential problem and to avoid oscillations.…”

A fixed strike Asian option and comments on its numerical solution

“…In [2] the differential operator in (1) is studied. It is found to be hypoelliptic (for smooth data), which guarantees smooth solutions.…”

“…• oscillations of Type 2, extending around the tilted curve A 150 − S where V 0 (see (2)) has a discontinuity in the first derivative, or rather in an area starting at the line and going down towards (0, 0). Table 2: Results for the 18 cases without an artificial boundary condition in A = A min and with h S = h A = 10 , h τ = 0.01…”

“…We consider the Black-Scholes model of the reversed time formulation of a zero dividend, fixed strike Asian average value call option, where the terminal payoff depends on the path, that is, the past history of the risky asset, through the continuous arithmetic running sum (integral of the risky See [1] and [2] for the derivation. The last boundary condition is exact only in the limit S max → ∞ .…”

An Alternating-Direction Implicit Difference Scheme for Pricing Asian Options

“…Let V be the solution of the problem (19)- (20) and the solution of the problem (48); then one has the error estimates…”