arXiv research

We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of some continuous index process at which the payoff process is even allowed to have…

We build on the work in Fackler and King 1990, and propose a more general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates through a Bayesian dynamic Beta Markov Random Field. Our approach allows for possible time de…

The study examines collective behavior in banking sectors across mature and emerging markets.

We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by Carr [Review of Financial Studi…

Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…

Paper models non-maturing deposits using a Lévy-driven Ornstein-Uhlenbeck process.

New framework values ESOs with multiple exercises and job termination risk.

We consider the problem of hedging a European interest rate contingent claim with a portfolio of zero-coupon bonds and show that an HJM type Markovian model driven by an infinite number of sources of randomness does not have some of the shortcomings found in the classical finite-factor models. Indeed, under natural con…

Derives explicit investment strategy with random endowment.

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random end…

We present cross and time series analysis of price fluctuations in the U.S. Treasury fixed income market. By means of techniques borrowed from statistical physics we show that the correlation among bonds depends strongly on the maturity and bonds' price increments do not fulfill the random walk hyphoteses.

We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that both primal and dual value functions are finite in the interiors of their domains a…

The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unles…

RandNLA uses randomness for matrix problems in machine learning.

Study uncovers that loan maturity layers in interbank networks are crucial for understanding their structure and functions.

The paper adjusts stock and strike prices for dividends after maturity in stock call pricing.

Improved AMM protocol supports diverse loan maturities in DeFi.

The paper analyzes the mathematics of the relationship between the default risk and yield-to-maturity of a coupon bond. It is shown that the yield-to-maturity is driven not only by the default probability and recovery rate of the bond but also by other contractual characteristics of the bond that are not commonly assoc…

In Business Intelligence, accurate predictive modeling is the key for providing adaptive decisions. We studied predictive modeling problems in this research which was motivated by real-world cases that Microsoft data scientists encountered while dealing with e-commerce transaction fraud control decisions using transact…

The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged inst…

We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…

We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small-and large-time behaviours of the implied volatility, and show that the proposed random…

The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilized risk measures cannot be used…

Flexible model captures commodity skews with maturity effects.

The paper analyzes short maturity Asian options using large deviations theory.

The paper analyzes Asian options in local volatility models at short maturity.

Study short maturity Asian options in jump-diffusion models with local volatility.

This paper proposes a Monte Carlo technique for pricing the forward yield to maturity, when the volatility of the zero-coupon bond is known. We make the assumption of deterministic default intensity (Hazard Rate Function). We make no assumption on the volatility of the yield. We actually calculate the initial value of …

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to opt…

We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it is always overestimated for OEX options, except for the shortest maturities wher…

Study short-maturity VIX and European option prices with jumps.

Improved Heston model produces steeper smile for short maturities.

Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical approximation for the Asian options prices which has the appropriate short matu…

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previ…

Cryptocurrencies show mature market characteristics but vary by size.

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digit…

We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t…

Based on 1-minute price changes recorded since year 2012, the fluctuation properties of the rapidly-emerging Bitcoin (BTC) market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents and multiscaling effects. The findings are compared to the stylized facts …

We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic sh…

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Lévy models. This expansion applies to both small and large maturities and is based solely on the p…

Study short-term behavior of up-and-in barrier options using Malliavin calculus.

Study near-maturity convergence rates of American put prices in Lévy models.

Study short-maturity Asian option pricing in LSV models using large deviations theory.

Study shows non-convergence of short-maturity expansion in SABR model.

In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating a pure jump Markov martingale model to match the market prices of Eu…

We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the m…