Related papers: Dirac Processes and Default Risk
We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
We introduce a class of short-rate models that exhibit a ``higher for longer'' phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
This paper presents an option pricing model that incorporates clustered jumps using a bivariate Hawkes process. The process captures both self- and cross-excitation of positive and negative jumps, enabling the model to generate return…
Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement…
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…
This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive…
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and…
Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The…
The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to compute the price dynamics of traded securities one needs to solve a…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…