Bayesian approach for option pricing in markets with unknown dynamics.
problem Arbitrage-free valuation of European options in markets with unknown stochastic dynamics.
method Bayesian approach using historic market observations to set up posterior distributions for future market dynamics.
result Bayesian option prices converge to standard BS-Option prices in the high frequency limit, but not in the Merton market with normally distributed jumps.
Study markets without safe assets, deriving option pricing equations.
problem No riskless asset in financial markets.
method Derive Black-Scholes-Merton equations for various risky asset dynamics.
result Option pricing equations for different risky asset dynamics.
Deep learning improves option pricing in incomplete markets.
problem Optimal pricing and hedging in incomplete jump diffusion markets.
method Stackelberg game approach, deep learning (feedforward and LSTM networks).
result Deep learning algorithm outperforms traditional methods in incomplete markets.
The study reveals traders' risk aversion and a new risk premium from market volumes.
problem Understanding traders' rationality and risk aversion from market volumes.
method Optimal Merton dynamics model to estimate average risk aversion and price of risk.
result Validation of the proposed trading strategy model on real data.
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.
This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…
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.
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.
Study on spontaneous symmetry breaking in financial markets using quantum mechanics.
problem Analyzing spontaneous symmetry breaking in financial markets.
method Using Hamiltonian form of Black-Scholes and Merton-Garman equations, analyzing symmetry breaking and interpreting Nambu-Goldstone bosons.
result Interpretation of Nambu-Goldstone bosons in financial markets.
The paper extends option pricing theory for markets with informed traders.
problem Discontinuity in option pricing for markets with informed traders.
method New models for option pricing in complete markets considering informed traders' information on stock price direction and return mean.
result The discontinuity puzzle in option pricing is resolved using continuous diffusion price processes.
Derives an option-pricing formula for fractional markets with skew and smile.
problem Developing a pricing formula for financial options with skew and smile.
method Employed the Lévy-Khintchine theorem and fractional Gaussian noise to generalize the Black-Scholes-Merton formula.
result An exponentially convergent option-pricing formula for fractional markets.
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
problem Inaccurate option pricing due to Black-Scholes assumptions.
method Monte Carlo simulation, GARCH model, Heston model, Merton jump-diffusion model.
result Heston model produces estimates closer to market prices, Merton model performs well for volatile assets, GARCH model improves volatility forecasts.
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.
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.
This paper extends the Black-Scholes-Merton model to more complex market scenarios.
problem Extending the Black-Scholes-Merton model to more complex market scenarios.
method Develops a new approach using Martingale Optimal Transport to replicate financial derivatives under extreme market models given marginals.
result Demonstrates the existence of a portfolio that replicates the payoff of a path-dependent derivative security under various market models.
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.
Two models incorporate market microstructure noise into asset pricing and option valuation.
problem Effect of market microstructure noise on asset pricing and option valuation.
method Developed two models: a continuous-time Black-Scholes-Merton model and a discrete binomial tree model.
result Extracted coefficients to quantify noise impact on volatility and drift.
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.
The paper confirms a conjecture about optimal expected utility in markets with insider information.
problem Optimal expected utility in markets with insider information.
method An extension of the Black-Scholes-Merton model with a sequence of discrete-time economies.
result Optimal expected utility converges to the classic model when conditions are met.
The paper confirms a conjecture about optimal expected utility in discrete-time markets approaching a continuous-time model.
problem Analyzing the convergence of optimal expected utility in discrete-time markets to a continuous-time model.
method Examined a sequence of discrete-time economies generated by scaled random walks, and compared their optimal expected utilities to the continuous-time Black-Scholes-Merton model.
result The conjecture holds for utility functions with asymptotic elasticity strictly less than one, but fails for elasticity equal to one.
Agent maximizes utility with pathwise constraint on portfolio value.
problem Maximizing utility with a pathwise constraint on portfolio value.
method Max-plus decomposition for supermartingales, Black-Scholes-Merton model.
result Explicit form of optimal terminal wealth and process involved.
Enhances option pricing with fractional order Black-Scholes-Merton model.
problem Improving precision and authenticity of option pricing.
method Integrates fractional order Black-Scholes-Merton with neural networks.
result Improves accuracy in capturing complex diffusion dynamics and memory effects.
Investors' strategic trading affects asset prices, modeled as a game.
problem Investors' trading rates influence asset prices in dynamic markets.
method Model as a non-zero sum singular stochastic differential game, establishing equivalence between best-response and auxiliary control problems.
result Unique Nash equilibrium is deterministic with a closed-form solution.
We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. The novelty is that confidence is here represented using ellipsoidal uncertainty sets for the drift, given a volatility realization. This specification affords a simpl…
Introduces RPU to explain randomization preference in dynamic settings.
problem Explains preference for randomization in dynamic investment problems.
method Introduces recursive perturbed utility (RPU) to incorporate randomization preference.
result Proves RPU-optimal portfolio policy is Gaussian and can be expressed in closed form.
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of stochastic differential equations, the Black-Scholes-Merton model, which can be used to p…
Extends BBSM model to incorporate ESG ratings and path dynamics.
problem Price stock options considering historical market index dynamics and ESG ratings.
method Develops discrete, binary tree option pricing model under BBSM with ESG valuation.
result Model accurately fits stock price changes and European call option prices.
Investigates optimal trading strategies for illiquid assets using a modified market impact model.
problem Optimizing investment behavior in a large unregulated financial institution with illiquid assets.
method Extension of Almgren-Chriss model to account for market illiquidity and expected utility optimization.
result Explicit closed-form solution for optimal trading strategy with interesting properties.
Paper introduces R-conditioning for risk-averse valuation in financial markets.
problem Risk-averse valuation in incomplete financial markets.
method Introduces R-conditioning as a new operator between conditional expectation and sublinear expectation.
result R-conditioning can approximate sublinear expectations and is used to compute risk-averse values.
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.
We derive asset pricing formula for markets with incomplete information and subjective views.
problem Asset pricing in markets with informational imperfections and subjective investor beliefs.
method Closed-form market equilibrium formula based on Merton's model, non-linear system of equations, conditional posterior distribution.
result Derivation of market reference model for excess returns under random shadow-costs.
We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random consumption. The striking result is that we obtain two-fund the…
Investment strategy in uncertain markets improved by learning and risk-ambiguity preferences.
problem Investment in financial markets with unknown drift coefficients.
method Optimization under KMM approach, considering risk and ambiguity preferences.
result Optimal investment strategy can be adjusted based on prior drift distribution.
One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive homogeneity axioms. We call …
Investment and consumption strategy for risk-averse agents with Epstein-Zin utility.
problem Optimal investment and consumption strategy for Epstein-Zin utility.
method Detailed introduction to Epstein-Zin utility, existence and uniqueness proof, verification argument.
result Existence and uniqueness of optimal solution for Epstein-Zin utility under certain parameter restrictions.
The paper extends Merton's model to include log-Heston and affine jump processes for option pricing.
problem Developing a pricing model for options in affine generalized Merton models.
method Generalizing Merton's model to include log-Heston and affine jump processes, proposing an approximation method for the latter.
result An approximation method for affine jump processes allows for the pricing of European options.
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).
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.
We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we explore whether it is possible to adjust the number of shares needed to effectively …
We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optim…
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.
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.
Study evaluates hedging strategies for S&P500 index options.
problem Improving returns and risk management in index option portfolios.
method Compared Black-Scholes-Merton and Variance-Gamma models for hedging strategies.
result Systematic option-writing strategies can yield superior returns compared to buy-and-hold benchmarks.
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton …
This paper solves optimal investment-consumption problems for a risk-averse agent with special utility.
problem Optimal investment-consumption problem for a risk-averse agent with special utility.
method Introduced proper utility process and solved optimal investment-consumption problem.
result Existence and uniqueness of proper utility processes for a wide class of consumption streams.
Extended Jarrow-Rudd model with skewness and kurtosis for option pricing.
problem Valuation of options with non-normal market dynamics.
method Introduced a generalized Jarrow-Rudd (GJR) model with skewness and kurtosis, incorporating transaction costs and market driver influences.
result Demonstrated the GJR pricing model's effectiveness in fitting market data.
Optimal investment strategy with price impact model.
problem Maximizing expected utility from liquidation wealth with price impact.
method Price impact model accounting for market depth, liquidity costs, and convexity. Singular optimal stochastic control problem reduced to deterministic optimal tracking problem.
result Explicit solution constructed, free boundaries described, optimal trading strategy identified.