相关论文: Time-Changed Bessel Processes and Credit Risk

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…

Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…

We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the…

We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…

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…

We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the…

Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely…

This paper examines the valuation and hedging of standard equity protection swap (EPS) products proposed by Xu et al.. To account for financial crises and counterparty default risk, we develop pricing frameworks based on Merton's…

In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy…

This paper introduces an analytical formula for the fractional-order conditional moments of nonlinear drift constant elasticity of variance (NLD-CEV) processes under regime switching, governed by continuous-time finite-state irreducible…

We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as exp(-c|y|), where c is a positive…

Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…

We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the…

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…

We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\--Scholes\--type equation whose spatial domain for the logarithmic stock price $x\in \RR$ and the variance $v\in (0,\infty)$ is the…

We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…

We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump L\'evy processes; this setup provides a natural extension to usual default metrics…

It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…