Pricing Asian options in a semimartingale model

In this paper we studyy arithmetic Asian options when the underlying stock is driven by special semimartingale processes. We show that the inherently path dependent problem of pricing Asian options can be transformed into a problem without path dependence in the payoff function. We also show that the price is driven by a process with independent increments, Levy processes being a special case. This approach applies for both discretely or continuously options.

[1]  E. Eberlein,et al.  Equivalence of floating and fixed strike Asian and lookback options , 2005 .

[2]  Pricing via Multiplicative Price Decomposition , 2000 .

[3]  L. Rogers,et al.  The value of an Asian option , 1995, Journal of Applied Probability.

[4]  J. Vecer.  A new PDE approach for pricing arithmetic average Asian options , 2001 .

[5]  Marco Frittelli,et al.  On the Existence of Minimax Martingale Measures , 2002 .

[6]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[7]  Jostein Paulsen.  Sharp conditions for certain ruin in a risk process with stochastic return on investments , 1998 .

[8]  M. Yor,et al.  The Fine Structure of Asset Retums : An Empirical Investigation ' , 2006 .

[9]  Yoshio Miyahara,et al.  [Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems , 2001 .

[10]  M. Fu,et al.  Pricing Continuous Asian Options: A Comparison of Monte Carlo and Laplace Transform Inversion Methods , 1998 .

[11]  Jean-Pierre Fouque,et al.  Pricing Asian options with stochastic volatility , 2003 .

[12]  Jean-Charles Rochet,et al.  Changes of numéraire, changes of probability measure and option pricing , 1995, Journal of Applied Probability.

[13]  J. Hoogland,et al.  Asians and Cash Dividends: Exploiting Symmetries in Pricing Theory , 2000, cond-mat/0006133.

[14]  Hans U. Gerber,et al.  Option pricing by Esscher transforms. , 1995 .

[15]  M. Frittelli.  The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets , 2000 .

[16]  M. Yor,et al.  Exponential functionals of Levy processes , 2005, math/0511265.

[17]  Local scale invariance and contingent claim pricing , 2001 .

[18]  E. Eberlein,et al.  The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures , 2002 .

[19]  M. Yor,et al.  BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES , 1993 .

[20]  M. Yor,et al.  On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options. , 2001 .

[21]  J. Andreasen.  The pricing of discretely sampled Asian and lookback options: a change of numeraire approach , 1998 .

[22]  G. Thompson.  Fast narrow bounds on the value of Asian options , 2002 .

[23]  Ludger Rüschendorf,et al.  Minimax and minimal distance martingale measures and their relationship to portfolio optimization , 2001, Finance Stochastics.

[24]  T. Chan.  Pricing contingent claims on stocks driven by Lévy processes , 1999 .

[25]  D. Madan,et al.  Pricing American options under variance gamma , 2003 .