In this paper, we consider joint estimation of objective and risk-neutral parameters for stochastic volatility option pricing models using both stock and option prices. A common strategy simplifies the task by limiting the analysis to just one option per date. We first discuss its drawbacks on the basis of model interpretation, estimation results and pricing exercises. We then turn the attention to a more flexible approach, that successfully exploits the wealth of information contained in large heterogeneous panels of options, and we apply it to actual S&P 500 index and index call options data. Our approach breaks the stochastic singularity between contemporaneous option prices by assuming that every observation is affected by measurement error, essentially recasting the problem as a non-linear filtering one. The resulting likelihood function is evaluated using a Monte Carlo Importance Sampling (MCIS) strategy, combined with a Particle Filter algorithm. The results provide useful intuitions on the directions that should be followed to extend the model, in particular by allowing jumps or regime switching in the volatility process.
Estimating and testing non-affine option pricing models with a large unbalanced panel of options
PASTORELLO, SERGIO
2012
Abstract
In this paper, we consider joint estimation of objective and risk-neutral parameters for stochastic volatility option pricing models using both stock and option prices. A common strategy simplifies the task by limiting the analysis to just one option per date. We first discuss its drawbacks on the basis of model interpretation, estimation results and pricing exercises. We then turn the attention to a more flexible approach, that successfully exploits the wealth of information contained in large heterogeneous panels of options, and we apply it to actual S&P 500 index and index call options data. Our approach breaks the stochastic singularity between contemporaneous option prices by assuming that every observation is affected by measurement error, essentially recasting the problem as a non-linear filtering one. The resulting likelihood function is evaluated using a Monte Carlo Importance Sampling (MCIS) strategy, combined with a Particle Filter algorithm. The results provide useful intuitions on the directions that should be followed to extend the model, in particular by allowing jumps or regime switching in the volatility process.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
