Related papers: Erratum for: Smile dynamics -- a theory of the imp…
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The…
A common belief is that leveraged ETFs (LETFs) suffer long-term performance decay due to \emph{volatility drag}. We show that this view is incomplete: LETF performance depends fundamentally on return autocorrelation and return dynamics. In…
We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…
Decisions taken in our everyday lives are based on a wide variety of information so it is generally very difficult to assess what are the strategies that guide us. Stock market therefore provides a rich environment to study how people take…
We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows…
We propose a non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated…
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the…
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based…
In this work we present a new family of options (mirror options) specially crafted to satisfy the necessities of aggressive speculators. The main ideas behind mirror options are: 1) A product that can be adjusted by the holder to agree with…
Leveraged Exchange Traded Funds (LETFs), while extremely controversial in the literature, remain stubbornly popular with both institutional and retail investors in practice. While the criticisms of LETFs are certainly valid, we argue that…
In this work, we establish a novel theoretical connection between supervised fine-tuning and offline reinforcement learning under the token-level Markov decision process, revealing that large language models indeed learn an implicit…
In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing…
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and…
In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise…
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous…
Large language models (LLMs), including ChatGPT, can extract profitable trading signals from the sentiment in news text. However, backtesting such strategies poses a challenge because LLMs are trained on many years of data, and backtesting…