Related papers: Erratum for: Smile dynamics -- a theory of the imp…
We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which…
In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term…
We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…
While the estimation of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…
The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and…
Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address…
In real data, missing values occur frequently, which affects the interpretation with interpretable machine learning (IML) methods. Recent work considers bias and shows that model explanations may differ between imputation methods, while…
There are some statistical anomalies in the Chinese stock market, i.e., positive return skewness, anti-leverage effect (positive returns induce higher volatility than negative returns); and reverse volatility asymmetry (contemporaneous…
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the…
Comment on [R.L. Ingraham, Phys. Rev. A 50, 4502 (1994)]. Ingraham suggested ``a delayed-choice experiment with partial, controllable memory erasing''. It is shown that he cannot be right since his predictions contradict relativistic…
Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands requires that everyone has some chance of receiving any level of the…
While the {estimation} of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…
While Indices, Index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems inherent in Index calculation methodologies and the legal/economic structure of ETFs. These problems raise…
The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity…
After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. We discuss the advantages and drawbacks of each method, the interpretation of their…
In this paper, we introduce a new time series model having a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. The model captures the stochastic…
It is well know that, in the short maturity limit, the implied volatility approaches the integral harmonic mean of the local volatility with respect to log-strike, see [Berestycki et al., Asymptotics and calibration of local volatility…
Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the…
Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An…