In this note, we consider European options of type \(h(X^1_T, X^2_T,\ldots , X^n_T)\) depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger (J Bus 51:621–651, 1978) on the relation between derivatives of the call price and the risk-neutral density of the underlying asset. The pricing measure is assumed to be absolutely continuous with respect to the Lebesgue measure on the state space.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Bick, A.: Comments on the valuation of derivative assets. J. Financ. Econ. 10, 331–345 (1982)
Breeden, D.T., Litzenberger, R.H.: Prices of state-contingent claims implicit in option prices. J. Bus. 51, 621–651 (1978)
Brown, D.J., Ross, S.A.: Spanning, valuation and options. Econ. Theory 1, 3–12 (1991)
Carr, P., Picron, J.: Static hedging of timing risk. J. Deriv. 3, 57–70 (1999)
Carr, P., Laurence, P.: Multi-asset local stochastic variance. Math. Financ. 21, 21–52 (2010)
Di Nunno, G., Oksendal, B.: Advanced Mathematical Methods in Finance. Springer, Berlin (2011)
Fengler, M.: Semiparametric modeling of Implied Volatility. Springer, Berlin (2005)
Jeanblanc, M., Yor, M., Chesney, M.: Mathematical Methods for Financial Markets. Springer Finance Textbooks, London (2009)
Rights and permissions
About this article
Cite this article
Talponen, J., Viitasaari, L. Note on multidimensional Breeden–Litzenberger representation for state price densities. Math Finan Econ 8, 153–157 (2014). https://doi.org/10.1007/s11579-014-0113-5
- Option valuation
- Options of multidimensional assets
- State price densities
- Rainbow options
- Basket options
- Breeden–Litzenberger representation