We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no-arbitr…
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48 results for “Merton's no-arbitrage”
We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geome…
Cross-Ownership as a Structural Explanation for Over- and Underestimation of Default Probabilityq-fin.RM
Based on the work of Suzuki (2002), we consider a generalization of Merton's asset valuation approach (Merton, 1974) in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous asset values. In contrast …
Two studies explain high margin loan rates by brokers.
problem High margin loan rates charged by stock brokers.
method Two approaches: finite revisions and monopolistic pricing.
result Small differences in revision frequency or monopoly pricing can explain loan rates.
Revisiting the Black-Scholes equationcond-mat.stat-mech
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships …
Entropic framework models stock and option dynamics.
problem Modeling stock and option dynamics with incomplete information.
method Entropic inference framework, scale invariance, Fokker-Planck equation, risk-neutral measure.
result Derives dynamics of stock and option prices using entropic inference.
This paper uses entropy to derive stock price dynamics and option valuation.
problem Deriving stock price dynamics and option valuation from information constraints.
method Develops an entropic inference framework to derive stochastic processes from information constraints, representing price changes through two channels: continuous and jump.
result The derived dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit.
The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
problem The role of asset return in the Black-Scholes-Merton model.
method Refutation of the claim through simplified stochastic calculus approach.
result The expected rate of return of the underlying asset does affect the Black-Scholes-Merton model.
New method for pricing financial products without no-arbitrage condition.
problem Pricing financial products without relying on no-arbitrage conditions.
method Convex duality and Fenchel conjugate for estimating super-replication cost.
result Endogenous weak no-arbitrage condition (AIP) leads to finite prices.
We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation…
No-Arbitrage Symmetriesq-fin.MF
The paper defines symmetries in no-arbitrage markets.
problem Characterizing transformations preserving no-arbitrage.
method Geometric formalization in discrete time models.
result Local characterization of no-arbitrage symmetries.
Paper presents an analytical solution to Merton Garman model using symmetries.
problem Developing an analytical solution to the Merton Garman model.
method Perturbation theory around an exact solution with Galilean symmetry.
result Perturbative solution performs well compared to Monte Carlo simulations.
Solves the Merton investment-consumption problem using a new approach.
problem Infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market.
method Simple and elegant argument involving a stochastic perturbation of the utility function.
result Overcomes complications in existing primal verification proofs.
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).
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
Developed Merton's model for public companies using observed liabilities.
problem Estimating default risk for public companies.
method Campbell and Shiller's approximation method for risk-neutral values and default probabilities.
result Formulas and ML estimators for public companies' default probabilities.
Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costsq-fin.MF
In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Ka…
Solves Merton's investment-consumption problem with certainty equivalent approach.
problem Maximizing CRRA utility of consumption over time and investment mix.
method Identifies a certainty equivalent problem for the Merton problem, reformulates it as an SOCP, and applies it to model predictive control.
result The certainty equivalent problem can be solved as an SOCP, facilitating model predictive control.
In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and …
Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features …
Investigates how trading boundaries change with transaction costs in portfolio selection.
problem Investigates how trading boundaries vary with transaction costs in portfolio selection.
method Analyzes Merton's problem with proportional transaction costs, showing monotonicity of trading boundaries.
result Cost-adjusted trading boundaries are monotone in transaction costs, with implications for the Merton line.
Paper develops a continuous-time framework for financial markets without stochastic calculus.
problem Developing continuous-time financial models without stochastic calculus.
method A general framework using conditional topologies and pseudo-distance topologies.
result No-arbitrage conditions hold in continuous time if and only if they hold in discrete time.
Gauge symmetries explain the emergence of Merton-Garman equation from Black-Scholes in finance.
problem Understanding the emergence of Merton-Garman equation from Black-Scholes in financial markets.
method Using Hamiltonian formulation and gauge symmetry to derive the Merton-Garman equation from Black-Scholes, analyzing the role of stochastic volatility.
result Gauge symmetry explains the appearance of stochastic volatility and its massivation via the Higgs mechanism.
Develops Merton's model for private companies using DDM.
problem Lack of observable asset values for private companies.
method Uses dividend discount model (DDM) to develop structural model.
result Obtains closed-form formulas for equity and liability values, default probability.
In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generali…
Abstract framework for no-arbitrage concepts in topological vector lattices.
problem Generalization of no-arbitrage concepts in topological vector lattices.
method Imposing a structural condition on trading strategies and deriving abstract FTAP.
result NUPBR, NAA, and NA may not be equivalent in general setting.
No arbitrage holds if a Pareto solution exists for vector-valued utility maximization.
problem Existence of no arbitrage in markets with transaction costs and multiple assets.
method Prove no arbitrage condition equivalent to Pareto solution for vector-valued utility maximization.
result A consistent price process can be constructed from the Pareto maximizer.
Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
problem Merton's portfolio optimization in a fake stationary Volterra-Heston model.
method Stochastic factor solution to a Riccati BSDE, combined with martingale optimality principle.
result Derives semi-closed form optimal strategies and value function.
In frictionless financial markets, no-arbitrage is a local property in time. This means that a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage. With capital gains taxes, this equivalence fails. For a model with a linear tax and one non-shortable risky stock, we introduce…
Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Treesq-fin.RM
The study models credit risk using Merton's framework and binomial trees.
problem Credit risk pricing and implied volatility estimation.
method Calibrated using Merton's structural model, with asset volatility derived from Black-Scholes-Merton. Implied mean return and probability surfaces constructed using a recombining binomial tree.
result Established a practical method for constructing implied credit surfaces.
The paper sets criteria for no arbitrage in complex financial models.
problem Determining conditions for the absence of arbitrage in financial markets.
method Established deterministic conditions for no arbitrage, NUPBR, and NFLVR in diffusion market models.
result Provided criteria in terms of scale function and speed measure.
Unified model integrates Bachelier and Black-Scholes-Merton for asset pricing.
problem Study of asset pricing in a natural world with negative prices or riskless rates.
method Unified framework combining Bachelier and Black-Scholes-Merton models.
result Unified model shows different option pricing depending on riskless instruments used.
Paper analyzes U.S. broker call rate laws of motion and their implications.
problem Understanding the dynamics and pricing of margin loans in the U.S. market.
method Analysis of monthly observations, derivation of stochastic differential equations, application of arbitrage theory.
result Margin loan interest rate follows mean-reverting behavior, with total call loan volume constituting over 70% of leveraged portfolios.
Optimizes dynamic investment portfolios with correlated jumps.
problem Maximizing expected terminal wealth in a multivariate Merton model with dependent jumps.
method Approximating CVaR with comonotonic bounds and maximizing expected terminal wealth.
result Improved optimization of dynamic investment portfolios.
Local equivalence found between Black-Scholes and Merton-Garman equations.
problem Restoring local symmetry in stock prices under stochastic volatility.
method Exploring gauge field theory to show local equivalence.
result Black-Scholes and Merton-Garman equations are locally equivalent.
Deep learning models reconstruct volatility surfaces from noisy data under no-arbitrage constraints.
problem Reconstructing implied volatility surfaces from sparse and noisy option quotes.
method Compared multiple neural architectures including Transformers, U-Nets, and variational autoencoders.
result Transformer and U-Net architectures achieve strong reconstruction accuracy, especially under sparse observation regimes.
Investigates optimal investment strategies in financial markets with jumps.
problem Optimal portfolio selection for investors in multi-asset financial markets with jumps.
method Uses martingale optimality principle and Riccati backward stochastic differential equations with jumps.
result Derives semi-closed form optimal strategies and value function for Merton's problem.
We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of gene…
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
Pricing defaultable debt: some exact resultscond-mat.stat-mech
In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky debt's price.
The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved via higher-dimensional operators. The stochastic nature of the secur…
Bayesian approach to portfolio selection reduces pessimism in frequent trading.
problem Tackling the challenge of estimating drift in Merton's portfolio selection model.
method Bayesian distributionally robust control with nonlinear Wasserstein projections.
result Reduced pessimism and improved performance in frequent rebalancing compared to existing methods.
Derives a dual equation for various option types, leading to new pricing and hedging insights.
problem Pricing and hedging of various option types.
method Derives a dual equation with the same form as the Black-Scholes-Merton equation, applicable to homogeneous degree one payoffs.
result Provides simple analytic formulas for delta and gamma, and reveals put-call equality for various options.
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Data-driven RL solves Merton's expected utility problem via policy randomization.
problem Maximizing expected utility in an incomplete market with unknown primitives.
method Policy randomization in continuous-time reinforcement learning.
result RL algorithms solve Merton's problem without estimating model primitives.
Unified approach to Merton's portfolio problem using Pontryagin's principles.
problem Optimizing consumption and investment strategies in financial portfolios.
method PG-DPO framework combining neural networks with Pontryagin's maximum principle.
result Locally optimal policies closely tied to classical stochastic control.
Solves wealth maximization problem using variational analysis.
problem Maximizing expected utility of terminal wealth.
method Variational analysis, forward-backward stochastic differential equation (FBSDE).
result Characterization and solutions for various utility functions.
The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906-925] from diffusion processes to arbitrary continuous semimartin…