论文信息 - European Option Pricing with Ambiguous Return Rate and Volatility

European Option Pricing with Ambiguous Return Rate and Volatility

In this paper, we consider the problem of option pricing when return rate and volatility are ambiguous. Firstly we illustrate how to describe this ambiguous option pricing model by using set-valued differential inclusion and how to change the discussion of pricing bound problems of options into that of maximal and minimal conditional expectations. Secondly we discuss the properties of maximal and minimal conditional expectations, especially the representation theorem of maximal and minimal expectations. Finally we give the bounds of the European option pricing by using above theorems.

Shoumei Li | Junfei Zhang

[1] Reg Kulperger,et al. Minimax pricing and Choquet pricing , 2006 .

[2] J. Kim,et al. On Set-Valued Stochastic Integrals , 2003 .

[3] N. Ahmed. Nonlinear stochastic differential inclusions on balance space , 1994 .

[4] Michał Kisielewicz. Set-valued stochastic intergrals and stochastic inclutions 1 , 1997 .

[5] S. Shreve. Stochastic calculus for finance , 2004 .

[6] Shoumei Li,et al. ON THE SOLUTIONS OF SET-VALUED STOCHASTIC DIFFERENTIAL EQUATIONS IN M-TYPE 2 BANACH SPACES , 2009 .

[7] S. Peng,et al. Backward Stochastic Differential Equations in Finance , 1997 .

[8] F. Black,et al. The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[9] Shoumei Li,et al. Strong solution of Itô type set-valued stochastic differential equation , 2010 .

[10] Jean-Pierre Aubin,et al. The viability theorem for stochastic differential inclusions 2 , 1998 .

[11] Shoumei Li,et al. On set-valued stochastic integrals in an M-type 2 Banach space , 2009 .

[12] M. Kisielewicz,et al. Weak Compactness of Solution Sets to Stochastic Differential Inclusions with Non-Convex Right-Hand Sides , 2005 .

[13] Reg Kulperger,et al. A comonotonic theorem for BSDEs , 2005 .