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We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model uncertainty arises as our only assumption on stock price returns…
We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
In financial terms, an implied volatility surface can be described by its term structure, its skewness and its overall volatility level. We use a PCA variational auto-encoder model to perfectly represent these descriptors into a latent…
The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when…
In this article, we study the problem of pricing defaultable bond with discrete default intensity and barrier under constant risk free short rate using higher order binary options and their integrals. In our credit risk model, the risk free…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…
The paper introduces benchmark-neutral pricing and hedging for long-term contingent claims. It employs the growth optimal portfolio of the stocks as numeraire and the new benchmark-neutral pricing measure for pricing. For a realistic…
This paper proposes a simple technical approach for the analytical derivation of Point-in-Time PD (probability of default) forecasts, with minimal data requirements. The inputs required are the current and future Through-the-Cycle PDs of…
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming…
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…
This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a…
We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of…
We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
We consider a two-factor model for the valuation of a non callable defaultable bond which pays coupons at certain given dates. The model under consideration is the Jump to Default Constant Elasticity of Variance (JDCEV) model. The JDCEV…