Pricing Of Geometric Asian Options Research Articles

Pricing of the geometric Asian options under a multifactor stochastic volatility model

This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a new multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is approximated by a quadratic arc. The asymptotic expansion of the price function is assumed, and the first order price approximation is derived using the perturbation techniques for both floating and fixed strike GAOs. Much simplified pricing formulae for the GAOs are obtained in this multifactor stochastic volatility framework. The zeroth order term in the price approximation is the modified Black–Scholes price for the GAOs. This modified price is expressed in terms of the Black–Scholes price for the GAOs. The accuracy of the approximate option pricing formulae is established, and also verified numerically by comparing the model prices with the Monte Carlo simulation prices and the Black–Scholes prices for the GAOs. The model parameter is estimated by capturing the volatility smiles. The sensitivity analysis is also performed to investigate the effect of underlying parameters on the approximated prices.

Option pricing of geometric Asian options in a subdiffusive Brownian motion regime

In this paper, pricing problem of the geometric Asian option in a subdiffusive Brownian motion regime is discussed. The subdiffusive property is manifested by the random periods of time, during which the asset price does not change. Subdiffusive partial differential equations for geometric Asian option are derived by using delta-hedging strategy. Explicit formula for geometric Asian option is obtained by using partial differential equation method. Furthermore, numerical studies are performed to illustrate the performance of our proposed pricing model.

Asian options pricing in Hawkes-type jump-diffusion models

In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple $$ (\lambda (t), X(t) ) $$ is affine, this property allows to extend the general methodology introduced by Hubalek et al. (Quant Finance 17:873–888, 2017) for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method.

Asian Options Pricing in Hawkes-Type Jump-Diffusion Models

In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple (λ(t), X(t)) is affine, this property allows to extend the general methodology introduced by Hubalek, Keller-Ressel and Sgarra for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method.

Numerical pricing of geometric asian options with barriers

In this article, a semianalytical method for pricing of barrier options is described and applied in the context of Asian options with geometric mean. The efficiency of the method is tested and compared with two finite difference methods.

Collocation Boundary Element Method for the pricing of Geometric Asian Options

The Semi-Analytical method for pricing of Barrier Options (SABO) already applied in the context of European options is here extended to the evaluation of geometric Asian options with barriers. The validity of this approximation method, based on the use of collocation Boundary Element Method, is illustrated by numerical examples, where accuracy and stability of the presented approach are analyzed.

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.

Asymptotic approach to the pricing of geometric asian options under the CEV model

This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.

Pricing Geometric Asian Options Under Fuzzy Stochastic Environment

Due to the uncertainty in reality consists of randomness and fuzziness, we employ stochastic analysis and fuzzy set theory to explore the pricing of geometric Asian options. In the fuzzy stochastic world, the price of the underlying asset is assumed to follow a fuzzy stochastic process of which the classic pricing model is a special case. We derive the analytic fuzzy prices of geometric Asian options and their crisp values based on possibilistic mean. Numerical analysis shows that the degree of the fuzziness of the option prices is a increasing function in the degree of the fuzziness of the underlying price. Moreover, from the perspective of the possibilistic means of option prices, the investors are aversive to fuzziness and they ask compensation for fuzziness.

Fuzzy pricing of geometric Asian options and its algorithm

Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.

Pricing of geometric Asian options under Heston's stochastic volatility model

In this work, it is assumed that the underlying asset price follows Heston's stochastic volatility model and explicit solutions for the prices of geometric Asian options with fixed and floating strikes are derived. This approach has to deal with the derivation of the generalized joint Fourier transform of a square-root process and of three different weighted integrals of the square-root process with constant, linear and quadratic weights. Numerical implementation results for the complicated expressions are presented, together with the computational stability and efficiency of the method.

Pricing Geometric Asian Options under the CEV Process

This paper discusses the pricing of geometric Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price geometric Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of geometric Asian options when the stock price follows the CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in the CEV process.