相关论文: Do your volatility smiles take care of extreme eve…

We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales…

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution…

We investigate the asymptotic behaviour of the implied volatility in the Bachelier setting, extending the large-strike results established for the Black-Scholes framework. Exploiting the theory of regular variation, we derive explicit…

We present a theory of option pricing and hedging, designed to address non-perfect arbitrage, market friction and the presence of `fat' tails. An implied volatility `smile' is predicted. We give precise estimates of the residual risk…

In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but…

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…

We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…

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…

We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention…

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…

It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…

We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function…

Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…

A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…

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…

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of…

We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of…

Classical (It\^o diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential L\'evy and affine models, which exhibit small-maturity exploding…

We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…

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…