Related papers: Second Order Multiscale Stochastic Volatility Asym…
Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…
In this paper, we implement and test two types of market-based models for European-type options, based on the tangent Levy models proposed recently by R. Carmona and S. Nadtochiy. As a result, we obtain a method for generating Monte Carlo…
Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation…
In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…
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…
We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
This paper deals with the filtering problem for a class of discrete time stochastic volatility models in which the disturbances have rational probability density functions. This includes the Cauchy distributions and Student t-distributions…
Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…
In this paper, we analyze the robustness and sensitivity of various continuous-time rough Volterra stochastic volatility models in relation to the process of market calibration. Model robustness is examined from two perspectives: the…
The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present,…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
This paper provides robust, new evidence on the causal drivers of market troughs. We demonstrate that conclusions about these triggers are critically sensitive to model specification, moving beyond restrictive linear models with a flexible…
This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…