We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit...

We introduce a novel semi-parametric estimator of the price of American options in a discrete time, Markovian framework. The estimator is based on a parametric specification of the stochasticdiscount factor and is non-parametric w.r.t. the historical dynamics of the state variables. The...

We study the nonparametric calibration of exponential, self-decomposable Lévy models whose jump density can be characterized by the k-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, the activity measure a := k(0+) + k(0-) and analog parameters for...

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy...

A number of studies on the S&P 500 index options market claim that the no arbitrage assumption cannot be rejected for this market because either the martingale restriction defined in Longstaff (1995) cannot be rejected by the data, or, even when it is rejected, a large proportion of the...

Haley and Walker (2010) present the Euclidean and Empirical Likelihood nonparametric option pricing models as alternative tilts to Stutzer's (1996) Canonical pricing method. We empirically test the comparative strengths of each of these methods using a large sample of traded options on the...

This paper studies the use of noisy high-frequency data to estimate the time-varying state-price density implicit in European option prices. A dynamic kernel estimator of the conditional pricing function and its derivatives is proposed that can be used for model-free risk measurement. Infi ll...

In order to better capture empirical phenomena, research on option price and implied volatility modeling increasingly advocates the use of nonparametric methods over simple functional forms. This, however, comes at a price, since these methods require dense observations to yield sensible...

We suggest a semi-nonparametric estimator for the entire call price surface based on a tensor-product B-spline. To enforce no-arbitrage constraints in strike and calendar dimensions we establish sufficient no-arbitrage conditions on the control net of the tensor product (TP) B-spline. Since...