The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed...

The common practice of using different volatilities for options of different strikes in the Black-Scholes (1973) model imposes inconsistent assumptions on underlying securities. The phenomenon is referred to as the volatility smile. This paper addresses this problem by replacing the Brownian...

We show that a structural model of firm decisions can produce very flexible implied volatility surfaces: upward and downward sloping, u-shaped. A calibrated version of the model is able to match many unconditional financial characteristics of the average option-able stock, and can help explain...

We present a computationally tractable method for simulating arbitrage free implied volatility surfaces. We illustrate how our method may be combined with a factor model for the implied volatility surface to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach...

There is an inaccurate formula in Huang et al. (1996) [Huang J., M. Subrahmanyam, and G. Yu (1996) Pricing and Hedging American Options: A Recursive Integration Method. Review of Financial Studies 9 (1):277–300]. In fact, a substantial term is missing in their equation (14) for computing the...

Hedging at-the-money digital options near maturity, remains a challenge in quantitative finance. In the present work, we carry out a hedging strategy by means of a bull spread. We study the probability of super- and sub-hedge the digital option and minimize the probability of a sub-hedge...

Chen and Shen (2003) argue that it is possible to improve the Least Squares Monte Carlo Method (LSMC) of Longstaff and Schwartz (2001) to value American options by removing the least squares regression module. This would make not only faster but also more accurate. We demonstrate, using a large...