Direct Nonparametric Estimation of State Price Density with Regularized Mixture

Jeon, Yong-Ho

  • Received : 20110500
  • Accepted : 20110700
  • Published : 2011.08.31


We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.


State price density;European call option;shape constraints;gamma mixture density


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