Pricing Of Asian Options Research Articles

Asian Options Pricing and Parameter Estimation of Uncertain Mean‐Reverting Currency Model With Exponential Ornstein–Uhlenbeck Exchange Rate

This paper introduces an uncertain mean‐reverting currency model that incorporates floating domestic and foreign interest rates along with an exponential Ornstein–Uhlenbeck exchange rate process, all grounded in uncertainty theory. Pricing formulas for both Asian call and put options are derived within this framework. The parameters of the model are estimated using real financial data from Canada and the United States, including the Canadian Overnight Repo Rate Average (CORRA), the American Federal Funds Effective Rate (AFFER), and the monthly average exchange rate of the US Dollar to the Canadian Dollar (USDCAD). The method of moments is applied to estimate the unknown parameters, and goodness‐of‐fit tests are conducted to validate the parameter estimates. Numerical experiments demonstrate that Asian option prices decrease as domestic and foreign initial interest rates increase. The prices of call and put options show divergent behaviors with respect to the initial exchange rate and the fixed strike price. Additionally, the paper investigates the nonlinear relationship between option prices and expiration time. In the appendix, the uncertain currency model is transformed into a stochastic currency model, and statistical tests confirm its inapplicability to the selected data, thereby substantiating the choice of the uncertain currency model.

Pricing Asian Options in Uncertain Stochastic Markets With Jumps

Pricing Asian Options in Uncertain Stochastic Markets With Jumps

Research on Asian Option Pricing Based on Uncertain Volatility

Research on Asian Option Pricing Based on Uncertain Volatility

Pricing of discretely sampled arithmetic Asian options, under the Hull–White interest rate model

This paper studies the pricing of discrete arithmetic Asian options (AAOs) with fixed strikes under the Hull–White interest rate model. For the pricing of AAOs, we first investigate the stochastic dynamics of the price of the underlying asset under the T-forward measure, and then study the distribution of the discrete arithmetic average of the underlying asset price. Specifically, we provide the first three moments of the discrete arithmetic average under the T-forward measure. Then, we derive approximate pricing formulas for AAOs using the three-moment matching method. Furthermore, we calculate the first three conditional moments of the discrete arithmetic average, given the final value of the underlying asset, under the T-forward measure. These conditional moments can be used to improve the accuracy of the approximation of the AAO prices. The numerical results show that our three-moment matching approximations are very accurate. Additionally, the accuracy can be further improved by combining the conditioning approach with the three-moment matching method. Our procedure is also applied to the computation of deltas of AAOs.

Pricing of geometric average Asian option under the sub-diffusion Merton interest rate model

. Asian option is an essentially new type of option. In existing option pricing models, the Brownian motion is generally the stochastic driving source of changes in the underlying asset price. This article explores the pricing problem of geometric average Asian option under the sub-diffusive Merton interest rate model. The results obtained the partial differential equations satisfied by the geometric average Asian option via constructing portfolios and utilizing the delta hedging technique. Finally, the findings provide display expressions for the geometric average Asian option under the sub-diffusive Merton interest rate model, combined with boundary conditions and variable substitutions.

A Stochastically Correlated Bivariate Square-Root Model

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we analytically obtain the corresponding solutions for the conditional moment-generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case which encompasses a range of processes similar to those produced by a bivariate square-root process in which entries are correlated in the standard way, that is, via a constant correlation coefficient. Note that closed-form solutions for the conditional characteristic and moment-generating functions are not available for the latter. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices using a Fourier cosine series method.

Continuous-time Markov chain approximation for pricing Asian options under rough stochastic local volatility models

We propose a general framework for pricing both discretely and continuously monitored arithmetic average Asian options whose underlying asset price satisfies the rough stochastic local volatility model. We use a semimartingale approximation approach for the rough stochastic local volatility model to obtain its Markovian representation. For each type of Asian options, we use the double-layer continuous-time Markov chain to approximate the transformed underlying asset price, and derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. We invert the analytical double transforms of Asian option prices under the approximate continuous-time Markov chain numerically to obtain the approximations for Asian option prices. Monte Carlo simulation demonstrates the accuracy and efficiency of the proposed method for Asian option pricing.

Asymptotics for short maturity Asian options in jump-diffusion models with local volatility

We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with Lévy jumps, including the exponential Lévy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity.

Locally risk minimizing pricing of Asian option in a semi-Markov modulated market

We consider a regime-switching model where the stock volatility dynamics is a semi-Markov process. Under this model assumption, we find the locally risk-minimizing price of some Asian options with European-style exercise. The price function is shown to satisfy a non-local degenerate system of parabolic PDEs in dimension two with a terminal condition. We show this by deriving the F-S decomposition of the discounted contingent claim. The related Cauchy problem involving the PDE is shown to be equivalent to an integral equation (IE). The existence and uniqueness of the classical solution to the PDE are determined by studying the IE and using semigroup theory. To be more precise, we first obtain the mild solution of the PDE and then we show that the mild solution has sufficient regularity. The locally risk-minimizing hedging for the option has also been identified in this work. Finally, the computational aspects of Asian option prices have been discussed by solving the equation numerically.

Asian option pricing under negative asset price in commodity market

Asian option pricing under negative asset price in commodity market

Asian option pricing under negative asset price in commodity market

Asian option pricing under negative asset price in commodity market

The valuation of arithmetic Asian options with mean reversion and jump clustering

It is known that the prices of many commodities exhibit mean reversion and are subject to jumps. Particularly, there is mounting empirical evidence that suggests the existence of clustered jumps. In this paper, we consider the valuation problem of arithmetic Asian options under a Hawkes jump diffusion model which captures both the mean reversion and jump clustering phenomena. We compute option prices by means of characteristic functions and Fourier-cosine series expansion. Numerical studies justify the validity and efficiency of our pricing method, and demonstrate the nonnegligible effects of mean reversion and jump clustering on Asian option prices.

Compact IMEX scheme for a moving boundary PIDE system of the regime-switching jump-diffusion Asian option pricing

Compact IMEX scheme for a moving boundary PIDE system of the regime-switching jump-diffusion Asian option pricing

Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion

We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion F(θ,T)=E[e−θXT] with XT=∫0TeσWs+(a−12σ2)sds, which is exact in the limit σ2T→0 at fixed σ2θT2 and aT. This asymptotic result is applied to pricing zero coupon bonds in the Dothan model of stochastic interest rates. The asymptotic result provides an approximation for bond prices which is in good agreement with numerical evaluations in a wide range of model parameters. As a side result we obtain the asymptotics for Asian option prices in the Black-Scholes model, taking into account interest rates and dividend yield contributions in the σ2T→0 limit.

Short-Time Behavior in Arithmetic Asian Option Price Under a Stochastic Volatility Model with Jumps

In this paper, we study the short-time behavior of the arithmetic average of Asian option price (AOP) derived from a general class of the stochastic volatility model with jumps. The AOP that rarely has explicit expression can reduce the volatility in the option price because of the average of the underlying asset price over the time interval. We consider the future average process in the model which is a non-adapted process. By using the Malliavin calculus operators, we get a non-adapted Itô formula, and also a decomposition formula of the option price in the model. We apply the decomposition formula to find the short-time limit of the arithmetic AOP and the implied volatility.

L ∞-norm convergence rates of an IMEX scheme for solving a partial integro-differential equation system arising from regime-switching jump-diffusion Asian option pricing

The purpose of this paper is to rigorously prove -norm convergence rates of an implicit-explicit (IMEX) difference method called Crank-Nicolson-Leap-Frog (CN-LF) scheme for solving a partial integro-differential equation (PIDE) system with moving boundaries from the regime-switching jump-diffusion Asian option pricing. The IMEX scheme is employed to discretize the PIDE system. Then the unconditional stability, unique solvability and convergence of second-order rates in both time and space are rigorously proved in the sense of -norm. Finally, several numerical examples are conducted to verify the theory.

Preintegration via Active Subspace

Preintegration is an extension of conditional Monte Carlo to quasi–Monte Carlo and randomized quasi–Monte Carlo. Conditioning can reduce but not increase the variance in Monte Carlo. For quasi–Monte Carlo it can bring about improved regularity of the integrand with potentially greatly improved accuracy. We show theoretically that, just as in Monte Carlo, preintegration can reduce but not increase the variance when one uses scrambled net integration. Preintegration is ordinarily done by integrating out one of the input variables to a function. In the common case of a Gaussian integral one can also preintegrate over any linear combination of variables. For continuous functions that are differentiable almost everywhere, we propose to choose the linear combination by the first principal component in an active subspace decomposition. We show that the lead eigenvector in an active subspace decomposition is closely related to the vector that maximizes a computationally intractable criterion using a Sobol’ index. A numerical example of Asian option pricing finds that this active subspace preintegration strategy is competitive with preintegrating the first principal component of the Brownian motion, which is known to be very effective. The new method outperforms others on some basket and rainbow options where there is no generally accepted counterpart to the principal components construction.

Pricing of Asian Options on Tesla Based on BSM model

Due to the interaction of the changes in the world political situation and the influence of the global epidemic, the world economy has entered a period of instability and turmoil. This can be an opportunity for people who would like to make an investment. However, without adequate research and good preparation, they may face huge losses. Therefore, this research shows how to choose a reasonable investment approach for a particular market. To be more specific, the research topic of this paper is to show how Asian put options work well in Tesla Market, and the methods of this study include the BSM model, sensitivity analysis, and making a comparison of the Asian options with the European options. Then, the results could be seen that the Asian options will be a more affordable and less risky investment strategy for the Tesla market which is a market with high volatility. Thus, to invest in a market in the current society, it is better for investors to make a clear understanding of their target income and then make multifaceted research. As a result, the investor could reduce their unnecessary losses.

Pricing of Asian Options and Barrier Options for The Microsoft Corporation Based on Monte-Carlo Simulation

In the current unstable financial market, option is a popular financial tool to hedge the risk of the underlying asset. Compared with the vanilla options, the exotic options can deal with the more complex requirements of investors. This paper focus on evaluating the Asian options and barrier options based on the data simulated from the Microsoft Corporation. This paper has three main research findings: the first is that it prices the Asian options and four types of the barrier options; the second is that it illustrates the reason for the price difference among the European options, the Asian options and barrier options with the help of payoff diagrams; the third is that it is explain the relationship between these two exotic options and the parameters used in the simulation. This paper would help investors better understanding the difference between the Asian options and barrier options from the perspective of the price and the sensitivity to the parameters.

Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method

Financial derivatives have developed rapidly over the past few decades due to their risk-averse nature, with options being the preferred financial derivatives due to their flexible contractual mechanisms, particularly Asian options. The Black–Scholes stock option pricing model is often used in conjunction with Monte Carlo simulations for option pricing. However, the Black–Scholes model assumes that the volatility of asset returns is constant, which does not square with practical financial markets. Additionally, Monte Carlo simulation suffers from slow error convergence. To address these issues, we first correct the asset volatility in the Black–Scholes model using a GARCH model. Then, the low error convergence rate of the Monte Carlo method is improved using variance reduction techniques. Meanwhile, the quasi-Monte Carlo approach based on low discrepancy sequences is used to refine the error convergence rate. We also provide a simulation experiment and result analysis to validate the effectiveness of our proposed method.