The paper analyzes short maturity Asian options using large deviations theory.
problem Efficiency of existing methods for small maturities and volatilities.
method Large deviations theory and a local volatility model with a jump term.
result Asymptotics for Asian options are derived, showing rare event behavior for out-of-the-money options and more complex behavior for at-the-money options.
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from conditional Asian options are determined only by average prices above certain t…
The paper analyzes Asian options in local volatility models at short maturity.
problem Short-maturity pricing and hedging of Asian options in local volatility models.
method Approximation of local volatility model by Gaussian process at short maturity, combined with Malliavin calculus.
result Short-maturity Asian option prices and delta values approximate European counterparts with a specific volatility function.
The study examines various methods for pricing Asian options with discrete dividends.
problem Pricing Asian options with discrete dividends.
method Several approaches including analytical approximations and finite difference methods are compared.
result Hybrid methods and randomized quasi-Monte Carlo methods are effective for different scenarios.
Paper develops bounds for pricing Catastrophic Mortality Bonds.
problem Challenging task in valuing Catastrophic Mortality Bonds.
method Expresses bond payoff as an Asian put option and uses comonotonic theory.
result Derives model-independent bounds for bond pricing.
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.
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
The paper suggests using derivatives instead of stocks for better utility and risk management.
problem The use of stocks in portfolio construction is challenged.
method The study uses the Black--Scholes--Merton setting to demonstrate the benefits of derivatives for maximizing utility and minimizing risk.
result Two derivatives are sufficient to maximize utility and minimize risk exposure in a two-asset portfolio.
Space mapping calibrates financial models, shown feasible for Heston model.
problem Calibrating financial models with few observable parameters and non-linear constraints.
method Space mapping approach using a coarse surrogate model and fine model calibration.
result Space mapping approach feasible for Heston model calibration.
Paper evaluates geometric Asian power options using a mixed fractional model.
problem Evaluating geometric Asian power options under specific stochastic processes.
method Mixed fractional subdiffusive Black-Scholes model applied to time changed mixed fractional Brownian motion.
result Derives a pricing formula for geometric Asian options.
New formulas for pricing Asian and basket options using stochastic expansion.
problem Pricing Asian and basket options under time-dependent parameters.
method Stochastic Taylor expansion around a log-normal proxy model.
result Highly accurate approximations for Asian options and vanilla options with discrete dividends.
Study short maturity Asian options in jump-diffusion models with local volatility.
problem Analyzing Asian options pricing in models with jumps and local volatility.
method Asymptotic analysis for short maturity, considering fixed and floating strike options.
result Explicit results for Asian option prices in several models, including Merton, double-exponential, and Variance Gamma models.
Analytical approximations for Asian option sensitivities in Black-Scholes model.
problem Calculating sensitivities of Asian options in the Black-Scholes model.
method Small maturity/volatility approximation and large deviations theory.
result Good agreement with alternative numerical simulation results for practical cases.
Study short maturity Asian options under CEV model, presenting an analytical approximation.
problem Analyzing short maturity behavior of Asian options in CEV model.
method Presented an analytical approximation for Asian options prices under CEV model.
result Good numerical agreement with Monte Carlo simulations and benchmark test cases.
Paper presents a novel nonparametric method to price Asian options.
problem Difficulty in pricing Asian options, especially with arithmetic average price.
method Nonparametric Predictive Inference (NPI) for Asian option pricing.
result NPI method provides a more precise and uncertain prediction of future asset prices.
New approximations for Asian basket spread options using stochastic Taylor expansions.
problem Pricing Asian basket spread options under the Black-Scholes model.
method Stochastic Taylor expansion applied to a log-normal proxy model.
result Highly accurate approximations for Asian and spread options, without numerical integration.
Study Asian option pricing under uncertain volatility, approximating prices with small volatility intervals.
problem Asian option pricing in uncertain volatility conditions.
method Procedure to approximate Asian option prices with small volatility intervals, solving fully nonlinear PDE.
result Approximation method for solving fully nonlinear PDE.
Study short maturity Asian options in local volatility models.
problem Analyzing Asian options with short maturities under local volatility.
method Derive asymptotics for out-of-the-money, in-the-money, and at-the-money cases; solve non-trivial variational problem; present analytical approximation.
result Good numerical agreement with Monte Carlo simulations and Black-Scholes model for practical parameters.
Deep learning models price options using volatility surfaces.
problem Pricing exotic options with high accuracy and efficiency.
method Variational autoencoder for volatility surface compression, multilayer perceptron for option pricing.
result Trained model achieves high accuracy across American and Asian options.
Study finds a small correction to Asian option volatility.
problem Implied volatility of Asian options at short maturity.
method Large deviations property and asymptotic expansion for the Hartman-Watson distribution.
result Subleading correction to Asian option volatility is derived.
The paper provides approximations for pricing Asian options using a mixed fractional Brownian motion with jumps.
problem Pricing Asian options under a mixed fractional Brownian motion with jumps.
method Approximate closed-form solutions for arithmetic Asian options and power options.
result Analytical formulas for pricing arithmetic Asian options and power options are derived.
Introduces a new stochastic volatility model using Jacobi processes.
problem Modeling asset return volatility with improved accuracy and tractability.
method Uses Jacobi processes to model squared volatility, deriving closed-form option pricing formulas.
result Option prices can be accurately approximated using series representations.
The paper offers methods to price complex options using upper and lower bounds.
problem Pricing complex options like Asian and basket options.
method Develops a general framework using lower and upper bounds.
result Lower bounds simplify the problem and provide reasonable approximations.
Study short-maturity Asian option pricing in LSV models using large deviations theory.
problem Derive short-maturity asymptotics for Asian option prices in LSV models.
method Large deviations theory and novel expansion method.
result Explicit series expansions for the solution of the variational problem around the ATM point.
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return process and European option prices. The computation of arithmetic Asian option pr…
Derives pricing formulae for power binary and normal distribution standard options.
problem Developing pricing models for binary and standard options.
method Incorporates Buchen's formulae into power binary options and derives a formula for normal distribution standard options.
result Derives pricing formulae for power binary and normal distribution standard options.
Asymptotic analysis of forward start Asian options in local volatility models.
problem Analyzing the pricing of forward start Asian options with short maturity under local volatility models.
method Large deviations theory and optimization problems for exponential decay rates; closed-form solutions for specific cases.
result Closed-form solutions and asymptotic behaviors of the rate function for various strike conditions.
The paper studies the discrete-time average of geometric Brownian motion and its application to Asian options pricing.
problem Understanding the pricing of Asian options with discrete-time averaging.
method Deriving asymptotics for the discrete-time average of geometric Brownian motion and analyzing its impact on Asian options pricing.
result Derives the asymptotics for the price of Asian options with discrete-time averaging in the Black-Scholes model.
The paper introduces new methods for Asian option pricing using Laguerre quadrature.
problem Developing accurate pricing models for Asian options.
method Utilizes Laguerre quadrature and diffusion kernel approach.
result Demonstrates new techniques to solve complex Asian option pricing equations.
An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in "A Modern Theory of Random Variation", by Patrick Muldowney, 2012.
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processe…
The paper addresses hedging Asian options with transaction costs using asymptotic hedging.
problem Hedging Asian options in markets with transaction costs.
method Asymptotic hedging approach.
result Probability convergence of investment portfolio value to payment function as revision count approaches infinity.
The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.
problem Pricing geometric Asian options in the Volterra-Heston model.
method Derives semi-closed formulas using Fourier transforms and Riccati-Volterra equations.
result Derives formulas for pricing geometric Asian options with fixed and floating strikes.
New methods estimate Asian option prices more efficiently.
problem Estimating the price of discretely monitored Asian options.
method General multilevel Monte Carlo methods.
result Estimates with standard deviation O(ε) in O(m+(1/ε)2) expected time. The paper provides a series expansion for Asian option pricing using orthogonal polynomials.
problem Deriving a series expansion for the price of Asian options in the Black-Scholes model.
method The approach uses orthogonal polynomials that are orthogonal with respect to the log-normal distribution.
result The series expansion is fully explicit and converges under certain conditions, with negligible asymptotic bias in practice.
The article calculates the most-likely path for Asian option pricing in local volatility models.
problem Approximating the price of Asian options in local volatility models.
method Path-integral approach using Brownian bridge and Laplace asymptotic formula.
result The most-likely path (MLP) is found to approximate the option price in the limit of small sampling time.
Extends unbiased simulation method to Asian options.
problem Simulating path-dependent dynamics for Asian options.
method Extension of unbiased simulation method for SDEs to path-dependent dynamics.
result Extension applies to numerical resolution of path-dependent PDEs.
In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral …
Study Asian option pricing in NIG and VG Levy markets.
problem Value of Asian options in incomplete Levy markets.
method Two methods of constructing risk-neutral measures.
result Both methods generally produce similar prices.
We prove existence, regularity and a Feynman-Kač representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian option with arithmetic average.
This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy described…
The paper compares machine learning methods with traditional techniques for pricing and sensitivities of financial products with path-dependent structures.
problem Evaluating financial products with early-termination clauses, especially those with path-dependent structures.
method The paper compares regression methods including randomized recurrent and feed-forward neural networks, and a novel approach using signatures of the underlying price process, with traditional polynomial basis functions for pricing and sensitivities.
result Machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates.
We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sud…
Study on implied volatility of Asian options with stochastic volatility.
problem Understanding the implied volatility of Asian options under stochastic volatility models.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for the implied volatility and skew.
result Developed short-maturity asymptotic formulas for the skew of the implied volatility, which depends on the roughness of the volatility model.
New method for pricing discrete Asian and Lookback options under Heston model.
problem Efficient pricing of discrete Asian and Lookback options under Heston model.
method Data-driven approach using artificial neural networks and stochastic collocation points.
result High accuracy and significant computational time reduction compared to classical methods.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Lap…
Tensor networks improve exotic option pricing efficiency.
problem Challenges in pricing exotic financial derivatives using standard methods.
method Combining binomial pricing with tensor network techniques (Matrix Product States).
result Linear scaling with parameters and reduced computational complexity.