2026/05/03 by Elisa Alòs, Òscar Burés · 1 voice
Economics, Econometrics and Finance · #Asset (computer security) #Control variates #Diverse Specialized Academic Research #Economic theories and models #Financial asset #Implied volatility #Monte Carlo method #Stochastic processes and financial applications #Stochastic volatility #Taylor series #Variance (accounting) #Volatility (finance) #q-fin.CP
paper · pdf · doi:10.3390/e28060642
arxiv published 2026/05/03 · arxiv updated 2026/05/08 · openalex publication_date 2026/06/06 · openalex created_date 2026/06/09 · openalex updated_date 2026/07/27
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the at-the-money implied volatility coincides with the fair value of the volatility swap. Using this identity as a starting point and applying classical Itô calculus and Taylor expansions, we write the price for out-of the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (non-integer) powers of the future mean volatility. As an a application, we use it as a control variate to reduce the variance of Monte Carlo option prices in the correlated case.