We use the Itô Decomposition Formula (see Alòs (2012)) to express certain conditional expectations as exponentials of iterated integrals. As one application, we compute an exact formal expression for the leverage swap for any stochastic volatility model expressed in forward variance form. As...

This paper presents a new formalism to price European options in all asset classes that fits the market data remarkably well. We use a model-independent representation of European Option prices as path integrals over all of the underlying asset price from inception to maturity. The no arbitrage...

We treat the problem of option pricing under the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be meanreverting. Assuming that only discrete past stock information is available, we adapt an...

From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough...

I perform a regression analysis to test two of the most famous heuristic rules existing in the literature about the behavior of the implied volatility surface. These rules are the sticky delta rule and the sticky strike rule. I present a new specification to test the sticky strike rule, which...

In this note we describe and compare two methodologies for calculating implied volatility of commodity prices, given the market prices of options on futures or implied volatilities, and a forward curve. The first methodology is fitting an exponential mean-reversion jump-diffusion model to the...

This paper explores the impact of volatility estimation methods on theoretical option values based upon the Black-Scholes-Merton (BSM) model. Volatility is the only input used in the BSM model that cannot be observed in the market or a priori determined in a contract. Thus, properly calculating...

We overcome a long-standing obstacle in statistics. In doing so, we show that the distribution of the sum of log-normal variables is log-normal. Furthermore, we offer a breakthrough result in finance. In doing so, we introduce a simple, exact and explicit formula for pricing the arithmetic Asian...

We introduce a simple, explicit formula for pricing the Bermudan options. Furthermore, the formula does not require any additional parameter (relative to the European option formula). Moreover, we provide an upper bound for the price

In this paper, we show that the influential Merton jump diffusion model and formula are needlessly cumbersome. In doing so, we provide a simple, explicit formula that doesn't require a computational method. Furthermore, we introduce a new, simple method for solving partial...