Estimating option implied risk‐neutral densities using spline and hypergeometric functions

Abstract

Summary We examine the ability of two recent methods – the smoothed implied volatility smile method (SML) and the density functionals based on confluent hypergeometric functions (DFCH) – for estimating implied risk‐neutral densities (RNDs) from European‐style options. Two complementary Monte Carlo experiments are conducted and the performance of the two RND estimators is evaluated by the root mean integrated squared error (RMISE) criterion. Results from both experiments show that the DFCH method outperforms the SML method for the overall quality of the estimated RNDs concerning both accuracy and stability. An application of the two methods to the OTC currency options market is also presented.

Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

“…Regarding the DFCH method, the results of Table 2 and the plots of Fig. 1 indicate that, despite the fact that this method provides more accurate estimates than the SPL one (see, also Bu and Hadri, 2007), it is outperformed by the MED-RNM method even when the latter is estimated based on a small data set, e.g. N 2 = 7.…”

“…1997) and the A-type Gram-Charlier series expansion (see Corrado and Su, 1996). 8 Bu and Hadri (2007) indicate that it also outperforms the SPL method, too. In our simulation study, we assume that option prices are generated from the stochastic volatility with jumps (SVJ) model suggested by Bates (1996).…”

“…However, it must be noted that the RND estimates retrieved by the SPL method are robust to alternative weighting schemes (see also Kang and Kim, 2006), for similar evidence). Equal weights are also used for the estimation of the RND based on the DFCH method, given that alternative weighting schemes have little impact on the estimation procedure (see Bu and Hadri, 2007). 11 We have also tried for a larger number of option prices as constraints (that is N 2 N 7), but we have found that the problem of ill-conditioned Hessian matrix appears.…”

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

“…Such a treatment is a matter of convenience. We therefore stick to (10) and (11) according to the range of γ for the rest of the paper. It is easily verified that ∂U (r t , γ) /∂r t = r −γ t .…”

A Simple and Reliable Way to Compute Option-Based Risk-Neutral Distributions

“…The conversion to deltas may be done using the same at-the-money volatility for all strikes (so-called "point conversion") or using each strike's volatility ("smile conversion") to avoid cases in which segments of the volatility smile are so steep that an option may have a lower call delta than another with a higher exercise price. Bu and Hadri (2007) discuss the phenomenon, which intuitively seems likely to be due to no-arbitrage violations in the data. The issue doesn't arise with our technique because we are going from input data sets in (δ, σ)-space to (δ, X)-space rather than vice versa.…”