| 1. |
|
|
| 2. |
- Bordag, Ljudmila A.
(författare)
-
On Option-Valuation in Illiquid Markets : Invariant Solutions to a Nonlinear Model
- 2008
-
Ingår i: Mathematical control theory and finance. - Berlin : Springer Berlin/Heidelberg. - 9783540695318 - 3540695311 - 9783540695325 ; , s. 71-94
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The present model describes a perfect hedging strategy for a large trader. In this case the hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of the Black-Scholes partial differential equation. Using Lie group theory we reduce in special cases the partial differential equation to some ordinary differential equations. The Lie group found for the model equation gives rise to invariant solutions. Families of exact invariant solutions for special values of parameters are described. © 2008 Springer-Verlag Berlin Heidelberg.
|
|
| 3. |
- Bordag, Ljudmila A., 1952-, et al.
(författare)
-
Pricing options in illiquid markets : Symmetry reductions and exact solutions
- 2008
-
Ingår i: Nonlinear Models in Mathematical Finance. - New York : Nova Science Publishers, Inc.. - 9781604569315 ; , s. 103-129
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The present paper is concerned with nonlinear Black Scholes equations arising in certain option pricing models with a large trader and/or transaction costs. In the first part we give an overview of existing option pricing models with frictions. While the financial setup differs between models, it turns out that in many of these models derivative prices can be characterized by fully nonlinear versions of the standard parabolic Black-ScholesPDE. In the second part of the paper we study a typical nonlinear Black-Scholes equation using methods from Lie group analysis. The equation possesses a rich symmetry group. By introducing invariant variables, invariant solutions can therefore be characterized in terms of solutions to ordinary differential equations. Finally we discuss properties and applications of these solutions.
|
|
| 4. |
|
|
