A Black-Scholes user's guide to the Bachelier model
To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges temporarily switched the option model from Black--Scholes to Bachelier in 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical results on volatility conversion, risk management, stochastic volatility, and barrier options pricing to facilitate the model transition. In particular, using the displaced Black-Scholes model as a model family with the Black-Scholes and Bachelier models as special cases, we not only connect the two models but also present a continuous spectrum of model choices.
Code (2)
Tasks
ManagementSimilar Papers 제목 키워드 기반
Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model
We present a unified, market-complete model that integrates both the Bachelier and Black-Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natu…
On the Bachelier implied volatility at extreme strikes
What kind of implied volatility extrapolation is appropriate? Roger Lee proved that the Black-Scholes implied variance can not grow faster than linearly in log-moneyness. This paper investigates what happens in the Bache…
Smile asymptotic for Bachelier Implied Volatility
We investigate the asymptotic behaviour of the Implied Volatility in the Bachelier setting, extending the framework introduced by Benaim and Friz for the Black-Scholes setting. Exploiting the theory of regular variation,…
Risk-neutral valuation of options under arithmetic Brownian motions
On April 22, 2020, the CME Group switched to Bachelier pricing for a group of oil futures options. The Bachelier model, or more generally the arithmetic Brownian motion (ABM), is not so widely used in finance, though. Th…
Weak approximations and VIX option price expansions in forward variance curve models
We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics…