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…
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48 results for “Asian style option”
New method for pricing SOFR futures options, solving both American and Asian exercise styles.
problem Lack of pricing models for SOFR futures options post-LIBOR transition.
method Developed a new version of the GIT method to solve semi-analytically.
result Obtained option prices, exercise boundaries, and Greeks for American and Asian options.
In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying asset prices over some predetermined time interval. The mathematical model for the …
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.
Develops a framework for valuing Asian options with market impact.
problem Valuation of Asian options under price impact.
method Discrete-time quote-level model, continuous-time limits, Hamilton-Jacobi-Bellman equations, CRR-style tree-based Bellman algorithm.
result Endogenous trading volumes feed into prices and costs, leading to nontrivial bid-ask spreads.
Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within the classical Black and Scholes (BS) model, focusing on the evolution of the pr…
We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear t…
New model values equity-linked securities with guaranteed return.
problem Valuation of equity-linked securities with guaranteed return.
method Replicate security price as sum of guaranteed amount and Asian style option price on basket.
result Analytical formulas derived for security price and hedge ratios.
Robust PDE method for path-dependent Asian-style options using MPDATA.
problem Valuation of path-dependent Asian-style options.
method Non-oscillatory forward-in-time second-order MPDATA finite-difference scheme for solving 2D PDEs.
result MPDATA scheme improves solution over first-order upwind step, highlighting its importance.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
In this paper, we present a new method for calculating the limit of early exercise boundary at expiry. We price American style of general derivative using a formula expressed as a sum of the value of European style of derivative and so called American premium. We use the latter expression to calculate an analytic formu…
There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo Simulation approach, amongst other numerical methods, to estimate the value of these op…
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.
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.
In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The fi…
The evaluation of geometric Asian power options under time changed mixed fractional Brownian motionq-fin.PR
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…
Conditional Asian Optionsq-fin.PR
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…
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.
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.
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.
KANOP uses KANs to efficiently price American options.
problem Efficiently pricing American options with limited data.
method Combines KANs with LSMC to estimate continuation value.
result KANOP provides more accurate option value estimates.
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.
Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumpsq-fin.PR
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.
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…
This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket and options on the volume-weighted average price. We demonstrate that in cases under discussion lower bounds allow for the dimensionality of the problem to …
We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money, in-the-money, and at-the-money cases are derived, considering both fixed strike and float…
We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical approximation for the Asian options prices which has the appropriate short matu…
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.
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…
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.
In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-S…
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.
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
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.
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.
Path Integral and Asian Optionsq-fin.PR
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 …
This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a Hölder continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be …
Asian option as a fixed-pointq-fin.PR
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.
On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisitedmath.CA
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…
We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The expone…
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.
Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.
problem Pricing Asian options with polynomial jump-diffusion processes.
method Uses Hermite polynomials and moments of the underlying process for closed-form computation.
result Explicit computation of Greeks and accurate series expansion for Asian options.
Asians and cash dividends: Exploiting symmetries in pricing theorycond-mat.stat-mech
In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim pricing. This allows us to derive, in a natural way, a simple PDE for the price of …