Illustrates a new self-financing equation's impact.
problem Traditional financial models' limitations.
method Introduces and analyzes a new self-financing condition.
result Enhanced hedging and market maker behavior.
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48 results for “Self-financing”
We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2…
The objective of the note is to remind readers on how self-financing works in Quantitative Finance. The authors have observed continuing uncertainty on this issue which may be because it lies exactly at the intersection of stochastic calculus and finance. The concept of a self-financing trading strategy was originally,…
Derives portfolio dynamics using retarded action principle.
problem Modeling self-financing portfolio dynamics with causality.
method Retarded action principle for differential representation.
result Consistent representation of portfolio dynamics.
Hedging The Risk In The Continuous Time Option Pricing Model With Stochastic Stock Volatilitycond-mat.stat-mech
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order for the theory to be self-consistent. The replicating methods in existing finance …
Proves existence of a strategy to minimize shortfall for game options.
problem Minimizing shortfall for game options in discrete time.
method Proves existence of a self-financing strategy.
result Existence of a self-financing strategy to minimize shortfall for game options in discrete time.
New automated market makers for multi-asset trading.
problem Liquidity management in multi-asset trading.
method Derived from self-financing transactions and rebalancing principles.
result Constant product market maker as a special case.
Trader can make money without borrowing or short selling if they predict future prices perfectly.
problem Trading without borrowing or short selling is theoretically possible with perfect foresight.
method Constructs a self-financing process of finite variation using a semimartingale.
result Shows it's possible to make money without conventional arbitrage constraints.
A new method in finance without probabilities or integrals.
problem Creating a model-free approach to continuous-time finance.
method Pathwise approach using causal functional calculus and transition principle of Isaacs.
result A fully non-linear path-dependent equation characterizes optimal solutions.
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model parameters that correspond to the market price of the option being hedged. The second …
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomi…
Self-Financing, Replicating Hedging Strategies, an incomplete thermodynamic analogycond-mat.stat-mech
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge and the option pricing partial differential equation. Approximately reversible tr…
Researchers find a timing error in Black-Scholes-Merton option pricing model.
problem Timing error in Black-Scholes-Merton option pricing model.
method Discovered a timing mistake in Merton's 1971 model and showed misspecification in continuous and discrete time.
result Invalidates seminal contributions to the literature including Black-Scholes (1973) and Merton (1971).
We study the general model of self-financing trading strategies in illiquid markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(alpha). This function is deep connected to an utili…
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic …
Optimizes risk management in incomplete markets using convex risk measures.
problem Risk management in financial markets with incomplete information.
method Dynamic optimization problem split into static and representation problems; convex duality methods used.
result Optimal strategy involves superhedging a modified claim with a randomized test.
Stochastic relaxational dynamics applied to finance: towards non-equilibrium option pricing theorycond-mat.stat-mech
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 al.) considers fluctuations around this equilibrium state by introducing a relaxati…
A new method for portfolio allocation in continuous-time markets.
problem Path-dependent portfolio allocation in continuous-time markets.
method Path-by-path framework, self-financing concept, partial differential equation, continuous-time algorithms.
result General explicit solution for wealth evolution in generic markets.
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…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid p…
We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partia…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that…
The paper prices European options with transaction costs using a fractional Merton model.
problem Discrete-time option pricing with transaction costs.
method Mixed fractional Merton model with delta hedging.
result Formula for European call option pricing derived.
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class of admiss…
No arbitrage in financial markets with special semimartingales.
problem Proving the absence of arbitrage in non-numéraire financial markets.
method Proving the absence of arbitrage using a multiplicative special semimartingale deflator.
result The market is free of arbitrage if and only if there exists a multiplicative special semimartingale deflator.
The paper analyzes how stock market dimensionality changes impact portfolio performance.
problem Impact of dimensional changes on portfolio performance in a changing market.
method Development of self-financing stock portfolios in a stochastic portfolio theory framework with dimensional jumps.
result Quantification of how listing or delisting events and market shocks affect portfolio return.
We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading strategies and a sufficient condi…
Proves continuity of financial strategies in specific topologies for large investors.
problem Modeling price impact of large investors in illiquid markets.
method Proves continuity of SDE solutions in Skorokhod's M1 and J1 topologies.
result Ensures that proceeds and wealth processes are continuous extensions of continuous strategies.
Neural FGP learns portfolio generating functions from data.
problem Portfolio optimisation challenges in estimating drifts and covariances.
method Neural network approach to learn from market data.
result Neural FGP outperforms classical benchmarks.
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is efficient, in the following sense: we do not expect a prespecified self-financing tradin…
Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costsq-fin.PR
Develops a new framework for currency option pricing with transaction costs.
problem Pricing currency options under transaction costs and fractional Brownian motion.
method Analytic formula derived using mean self-financing delta-hedging in a discrete time setting.
result Minimal price formula for currency options under transaction costs.
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…
Defines risk-free portfolios and risk-free rate using gauge symmetries.
problem Identifying a consistent definition of risk-free rate in economics.
method Introduces three gauge invariant differential operators to define risk-free portfolios and identifies the risk-free rate as the return of an infinitely diversified portfolio.
result Identifies the risk-free rate as the return of an infinitely diversified portfolio and connects it to global price rescaling as a gauge symmetry.
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
Develops a new method for risk diversification using dynamic risk measures.
problem Dynamic risk diversification in investment portfolios.
method Introduces dynamic risk contributions and a recursive optimization approach for coherent dynamic distortion risk measures.
result Dynamic risk budgeting strategies can be solved using deep learning.
Consider an equity market with stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function th…
This paper analyzes the dynamic incentives for technology adoption under a transferable permits system, which allows for strategic trading on the permit market. Initially, firms can invest both in low-emitting production technologies and trade permits. In the model, technology adoption and allowance price are generated…
Relativistic extension of Brownian motion explains volatility smiles.
problem Understanding volatility smiles in financial markets.
method Relativistic extension of Brownian motion to model financial processes.
result The model predicts volatility smiles due to relativistic effects.
Botswana's agricultural credit scheme is unsustainable and needs reform.
problem The current scheme is unsustainable and based on flawed actuarial principles.
method Proposes a new subsidy and premium rate setting method considering non-drought years.
result A sustainable agricultural credit guarantee scheme is recommended.
Study cash-flow forecasting for derivatives, aligning with replication strategy and addressing timing frictions.
problem Inconsistencies in cash-flow forecasting under different measures and stochastic payment times.
method Use discounting sensitivities (funding-curve hedge ratios) for replication and propose a liquidity valuation adjustment.
result Aligns forecasting with replication strategy and avoids measure-mixing issues.
Optimal investment with insurable background risk and nonlinear portfolio allocation frictionsq-fin.MF
Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.
problem Investment and insurance decisions under a model with nonlinear portfolio frictions and background risk.
method Dynamic programming approach to find optimality conditions.
result Agent can choose to assume, partially assume, or purchase total insurance against adverse jumps in wealth.
The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Holdmath.OC
Study compares high-frequency trading vs. buy and hold in stock markets with and without execution delay.
problem Impact of trade execution delay on Kelly-based stock trading strategies.
method Comparison of high-frequency trading and buy and hold strategies using Kelly's criterion and simulation.
result Buy and hold can outperform high-frequency trading with execution delay, contrary to intuition.
Paper optimizes DC pension fund management with VaR and relative performance constraints.
problem Optimizing DC pension fund performance under VaR and relative performance constraints.
method Introduced an auxiliary process to transform the problem into a self-financing problem, combined linearization, Lagrange dual, martingale, and concavification methods.
result Explicit investment strategies obtained for certain penalty and reward functions.
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…
Study optimal investment strategy for pension schemes to hedge longevity risk.
problem Hedging longevity risk in defined contribution pension schemes.
method Transformed optimal investment problem into an unconstrained problem using dynamic programming and numerical studies.
result Longevity risk significantly impacts investment strategies, supporting the use of mortality-linked securities.
Agent-based model predicts microfinance risk shifts in poor economies.
problem Mapping sustainable microfinance credit risk in poor economies.
method Agent-based model using network theory.
result Deteriorating economy and adverse selection cause loan repayment probability shifts.
Unified models for asset prices with transaction costs and infinite variation strategies.
problem Models with transaction costs and infinite variation strategies.
method Unified models using semimartingale price systems.
result Existence of a semimartingale price system consistent with transaction costs.