In this paper, we derive a reflection principle for a random walk with the symmetric double exponential distribution. This allows us to come up with the closed form solution for the joint probability of the running maximum and the terminal value of the random walk. Based on this new theoretical...

We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Itô process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the...

We propose and implement an empirical automatic bias correction (ABC) procedure for correcting the downward bias in the volatility estimators that utilize extreme value of asset prices. The bias originates from the random walk effect. The proposed estimator does not require knowledge of N, the...

Thresholded Realized Power Variations (TPVs) are one of the most popular nonparametric estimators for general continuous-time processes with a wide range of applications. In spite of their popularity, a common drawback lies in the necessity of choosing a suitable threshold for the estimator, an...

We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening, and closing prices to estimate the volatility of the stock price. This novel theoretical approach results in an estimator that is genuinely range-based on daily...

We examine the empirical properties of the theoretical Black–Scholes–Merton (BSM) bankruptcy model. We evaluate the predictive ability of various existing modifications of the BSM model and extend prior studies by estimating volatility directly from market-observable returns on firm value....