Related papers: Implied volatility explosions: European calls and …
In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…
This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a H\"older continuous payoff function in a local…
Based on the concept of self-decomposability, we extend some recent multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
In this paper, we solve exit problems for a level-dependent L\'evy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All…
We consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to…
We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant…
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…
Employee stock options (ESOs) are American-style call options that can be terminated early due to employment shock. This paper studies an ESO valuation framework that accounts for job termination risk and jumps in the company stock price.…
The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is…
The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative L\'evy process \xi with unbounded variation.…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional…
A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied…
The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the…
Let $X_t^\sharp$ be a multivariate process of the form $X_t =Y_t - Z_t$, $X_0=x$, killed at some terminal time $T$, where $Y_t$ is a Markov process having only jumps of the length smaller than $\delta$, and $Z_t$ is a compound Poisson…
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…