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To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other…
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style…
In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the…
We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$,…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…
In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on…
In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in…
We derive the short-maturity asymptotics for option prices in the local volatility model in a new short-maturity limit $T\to 0$ at fixed $\rho = (r-q) T$, where $r$ is the interest rate and $q$ is the dividend yield. In cases of practical…
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…
We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing…
We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…