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We propose a modification of the classical Black-Derman-Toy (BDT) interest rate tree model, which includes the possibility of a jump with small probability at each step to a practically zero interest rate. The corresponding BDT algorithms…

We price and replicate a variety of claims written on the log price $X$ and quadratic variation $[X]$ of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do…

This paper investigates the impact of Trade Policy Uncertainty (TPU) on stock-bond correlation dynamics in the United States. Using daily data on major U.S. stock indices and the 10-year Treasury bond from 2015 to 2025, we estimate…

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…

This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…

We consider the pricing of variable annuities (VAs) with general fee structures under popular stochastic volatility models such as Heston, Hull-White, Scott, $\alpha$-Hypergeometric, $3/2$, and $4/2$ models. In particular, we analyze the…

This paper addresses a critical inconsistency in models of the term structure of interest rates (TSIR), where zero-coupon bonds are priced under risk-neutral measures distinct from those used in equity markets. We propose a unified TSIR…

We perform a large-scale simulation of an Ising-based financial market model that includes 300 asset time series. The financial system simulated by the model shows a fat-tailed return distribution and volatility clustering and exhibits…

We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…

Technical trading rules and linear regressive models are often used by practitioners to find trends in financial data. However, these models are unsuited to find non-linearly separable patterns. We propose a decision tree forecasting model…

In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…

We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by…

One of the risks derived from selling long term policies that any insurance company has, arises from interest rates. In this paper we consider a general class of stochastic volatility models written in forward variance form. We also deal…

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity…

The purpose of the present paper is to incorporate stochastic interest rates into a matrix-approach to multi-state life insurance, where formulas for reserves, moments of future payments and equivalence premiums can be obtained as explicit…

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that…

We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the…

Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity…

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…