Arithmetic Average Asian Call Option

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Singular Perturbations on Non-Smooth Boundary Problems in Finance

Singular Perturbations on Non-Smooth Boundary Problems in Finance

cently, Fouque-Papanicolaou-Sircar observed a fast time scale volatility factor in S&P 500 high frequency data. They use asymptotic analysis to approximate option pricing and hedging problems in finance. This motivates our paper to generalize Vecer’s [48] dimension reduction technique on pricing arithmetic average Asian option (European style) by relaxing the assumption of constant volatility for the case that volatility is fluctuating and is driven by an auxiliary fast mean-reverting process. Based on the results from asymptotic analysis presented in the Appendix 7.7, the approximated price, or so-called corrected price, is derived. As a consequence, there is no need to estimate the current level of the unobservable stock price volatility. All the param- eters we need to compute the approximated price can be easily calibrated from the observed stock price and the implied volatility surface. Thus, this article describes a robust procedure to correct Asian option prices by taking the observed implied volatility skew into account. Numerical computation of the corrected Asian option price is certainly needed.

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An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option

An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option

underlying price at every node to be a rational number of finite precision. It is partitioned into different parts with varying resolution hence reducing the number of averages considered. It is based on the premise that if the underlying asset prices are multiplied by a constant before pricing the option, then option value divided by the same constant gives the originally desired option value. Convergence is ensured by making sure the underlying asset’s price process simulated mirrors to the continuous time lognormal price process of the underlying. Their work shows that this method converges as the time steps used are increased. In the next section the proposed trinomial model is laid out in more detail.

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Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

is arithmetic type, which is the most commonly used, though an exact analytical solution for arithmetic average rate Asian options does not existed. This solution is missing primarily because the arithmetic average of a set of lognormal random variables is not lognormally distributed.

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The distribution of the average of log normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed form Formula

The distribution of the average of log normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed form Formula

where K is the strike price. Clearly, this is the price of a European option with expiry t. ˆ Thus, the price of the arithmetic Asian option (with expiry time T ) is equal to the price of the equivalent European option with expiry time t. ˆ This explains why the Asian option is cheaper than its European counterpart.

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Variance analysis of control variate technique and applications in Asian option ‎pricing‎

Variance analysis of control variate technique and applications in Asian option ‎pricing‎

nancially well to do, it consumes time to simulate a price inside reasonable boundaries of accuracy for sure contracts.for reduce computational time, some variance reduction techniques have been suggested. For example, control variates, anti- thetic variates and importance sampling. Con- trol variate method have been famously used for calculative finance as a method of variance re- duction. Kemna and Vorst [13] employed a dis- counted geometric average Asian option payoff less than its price as a control. This technique is effective because the geometric Asian option has a analytical solution form and the correlation amonge the arithmetic and the geometric aver- age is high. This study focus on the analysis of control variates, that is one of the most popular and eicient methods used. This method takes ad- vantage of random variables with positively cor- related with the variable under consideration and known expected value.

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Efficient valuation of exotic derivatives with path-dependence and early exercise features

Efficient valuation of exotic derivatives with path-dependence and early exercise features

Even in the simple Black-Scholes-Merton model, arithmetic Asian options do not admit an ex- act formula in closed form. This is because the sum of correlated lognormal asset prices is not lognormal anymore. With the focus on the continuous arithmetic average asset price, Geman and Yor (1993) are the …rst to write the price of the Asian option as the inverse of its Laplace transform which they derive in analytical form. Thereafter several authors have attempted to compute the inverse transform using standard numerical approaches, including Fourier se- ries expansion, Laguerre series expansion, sequence of Gaver functionals, and deformation of Bromwich contour (for a thorough review of these techniques, see Davies (2002), Chapter 19), and all have encountered signi…cant numerical instabilities for short maturities and low volatil- ities (see Dufresne (2000), Linetsky (2004)). These limitations have been attributed to the slow convergence of the inversion algorithms and computational di¢ culties related to the Kummer con‡uent hypergeometric function appearing in the Laplace transform. Instead, Fusai (2004) and Cai and Kou (2010) obtain analytical expressions for the double Laplace transform of the option price, which they invert numerically using a two-sided Euler inversion algorithm. Although the two methods share similarities, Cai and Kou’s inversion technique is faster, for given accuracy, for low asset volatility, e.g., smaller than 0.1, and performs better under jump di¤usion model assumptions.

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Pricing Asian Options: A Comparison of Numerical and Simulation Approaches Twenty Years Later

Pricing Asian Options: A Comparison of Numerical and Simulation Approaches Twenty Years Later

Kemna and Vorst [9] show that in the case of the arithmetic-average Asian option price, the use of the geometric-average Asian option price can be used as an effective control variate. In a succeeding research, Fu and Madan [5] compare the discrete and the continuous geometric-average Asian option price’s performance as control variate with interesting results. They find that even though the appropriate formula for a dis- crete estimator would be the discrete average formula, by using the continuous average formula a greater variance reduction can be achieved. In other words, by using a “bi- ased” ( i.e . non-zero expectation) control variate, we not only reduce the variance of our original estimator, but also add an appropriate bias to it, which compensates for the above mentioned discretization error inherent in the basic simulation method. For this

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What Do You Do If You’ve Been at the Poker Table for Twenty Minutes and Still Can’t Spot the Sucker?  Implications for Individual Investors

What Do You Do If You’ve Been at the Poker Table for Twenty Minutes and Still Can’t Spot the Sucker? Implications for Individual Investors

Part of the conceptual justification for the variation on a traditional covered call writing strategy described here pertains to how the option premium in question should best be interpreted. For longer-dated options a significant portion of the premium represents disagreement about future earnings, a discussion about which we have argued the individual investor shouldn’t enter. On the other hand, the premiums for very short-term options almost entirely represent speculation about upcoming near-term events which are unlikely to affect the long-term value of the company, short-term price patterns as anticipated through technical analysis, etc. These short-term price fluctuations shouldn’t be of interest to an individual investor (especially if unfavorable fluctuations are likely to be eventually reversed by RTM), and thus it makes good sense to monetize their expected value.

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The arithmetic recursive average as an instance of the recursive weighted power mean

The arithmetic recursive average as an instance of the recursive weighted power mean

In this paper we proposed a new family of recursive average (RAV) operators (i.e. the recursive weighted power mean), expanding in particular on the arithmetic RAV. The motivation for the new operator family is the desire to provide an intuitive path to aggregating data (evidence) in conjunction with the powerful structure of a fuzzy measure. We showed how the proposed RAV avoids potential challenges, such as the non- symmetry of outputs for symmetrically flipped inputs that can occur when employing a FI in conjunction with a FM, and thus how the arithmetic RAV can provide a useful alternative to FIs. We provided both synthetic and real world data fusion

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The Call for and Role of Asian Lawyers in the Deep South

The Call for and Role of Asian Lawyers in the Deep South

This article is my response to both the White attorney who wanted to know my unique value or calling in the Deep South and to my Black classmate who wanted to know if an Asian lawyer had a place or role here. Thus, this paper explores the call for and role of Asian lawyers in the Deep South. As will be discussed later in this article, categorization of those of Asian heritage is not simple. Some are Asian Americans, born or naturalized in the United States. Other Asians are present in the United States, but are not US citizens. Moreover, as is noted below, those of Asian heritage are quite diverse. Here, I choose to use the term Asians to refer to all of Asian descent, regardless of particular country identity and regardless of American citizenship status.

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Computer assisted language learning (CALL): Asian learners and users going beyond traditional frameworks

Computer assisted language learning (CALL): Asian learners and users going beyond traditional frameworks

worth noting (Jarvis, 2005) that, in language education, we see the technology impacting on the subject matter itself with computer-mediated-communication varieties of English emerging. How   significant   is   this?   It’s   probably   too   early   to   say;;   perhaps   we   need   to   w8nc (wait and see)! There is no novelty value to CALL for these web generation learners who access the internet and other programs all the time in their daily lives. In short, “unconscious   acquisition”   arising   out   of   frequent   access   to   authentic   English   through globally networked environments using any number of C-bMs, frequently in combination, suggests a need to go beyond CALL.

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Pricing And Hedging of Asian Option Under Jumps

Pricing And Hedging of Asian Option Under Jumps

It is also clear that the utility-indifference price tends to the super-replication price, which is the supremum of the expectations of H over all equivalent martingale measures, as the risk-aversion tends to infinity, price converges to the super-hedging price, that is, worst price under the viability assumption. On the other hand, as the absolute risk-aversion decreases to zero, the utility indifference price tends to a risk-neutral valuation under the minimal entropy martingale measure P ∗ which is the lower bound of the interval of arbitrage-free price i.e. infimum of expectation of H over all equivalent martingale measures. Above theorem for Asian put option and arguments portrays that MEMM P ∗ is the appropriate choice for pricing generalized Asian options.

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Stochastic Volatility Jump Diffusion Model for Option Pricing

Stochastic Volatility Jump Diffusion Model for Option Pricing

The rest of the paper is organized as follows. In Sec- tion 2, we briefly discuss the model descriptions for the option pricing. The relationship between stochastic dif- ferential equations and partial differential equations for the jump-diffusion process with jump stochastic volatil- ity is presented in Section 3. Finally, a closed-form for- mula for a European call option in terms of characteristic functions is presented.

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Option Arbitrage and Quantification Realization Based on Time Value

Option Arbitrage and Quantification Realization Based on Time Value

Option value is composed of connotation value and time value. Connotation value refers to the immediate profit obtained from the exercise of the option. The time value of the option is the part of the option value minus the connotation value. The traditional definition of arbitrage refers to the activity of profiting by buying and selling the same subject matter at the same favorable price in different markets at the same time. Options portfolio trading strategies include buy call option to sell the subject matter, buy put option to sell the subject matter.

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ATLAS 800 SERIES DUAL VIDEO MODULE User Manual

ATLAS 800 SERIES DUAL VIDEO MODULE User Manual

The Video Module installs in any available option slot in the ATLAS 800 Series chassis. You can view the status of the module itself, as well as the circuits to which it interfaces. The terminal menus are accessible using a VT100 terminal connection (through the CONTROL port) or a Telnet session (through the Ethernet port). Use the terminal menu to configure the Video Module and to download application soft- ware.

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Semigroup theory applied to basket options

Semigroup theory applied to basket options

A basket option has two or more underlying assets and the holder of the option has the right to purchase a specified amount of these at the expiry date. When determinig the value of such an option using the Black-Scholes model, the dimensionality of the problem grows linearly with the number of underlying assets.

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A Genetic Algorithm with Weighted Average Normally Distributed Arithmetic Crossover and Twinkling

A Genetic Algorithm with Weighted Average Normally Distributed Arithmetic Crossover and Twinkling

The objective of this paper is to explore the possibilities of incorporating twinkling within genetic algorithms. Thiswork is divided as follows. Section 2 explains the twinkling paradigm, anda brief overview of the simple genetic algorithm is presented in Section 3. The weighted average normally-distributed arithmetic crossover (NADX) is introduced in Section 4. Section 5 describes the process of incorporating twinkling in the SGA crossover operation. The steps of the algorithms proposed in this paper are presented in Section 6. A detailed assessment of the influence of the various components of the pro- posed algorithms on the search progression is discussed in Section 7. Evaluation of the proposed algorithms using various benchmark test functions and engineering design problems is included in Section 8. Finally, conclusions and recommendations for future work are provided in Section 9.

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Valuation of Asian American Option Using a Modified Path Simulation Method

Valuation of Asian American Option Using a Modified Path Simulation Method

We propose a modified path simulation model to value an Asian American option under VG process. Several scenarios have been investigated, especially by comparing Asian American option prices with Plain Vanilla and Asian European option prices. It was found that the proposed method gives option prices that inline with the characterization of each option type. Some scenarios have also been developed to confirm the option prices ob- tained using the modified path simulation method for different values of parameters. In general, we can con- clude that the proposed method performs quite well and can be used as an alternative for determining the option prices, especially for Asian American options.

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Delta-gamma-theta Hedging of Crude Oil Asian Options

Delta-gamma-theta Hedging of Crude Oil Asian Options

Eff ects of the commissions on the strategy performance have also been tested. The commis- sions and trading costs varies depending on the broker providing the market access. The average commission for trading plain vanilla options is around 50 cents per contract (according to Bloomberg statistics). Those for Asian options are lower, because even the prices are lower. Gamma- delta-theta hedging strategy is strongly sensitive to the eff ects of spreads and commissions. Even commission such as 1 cent eliminated possibility of any profi t. Theirs eff ect is even stronger during the last month before maturity, when time value of both call and put options is declining faster.

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On the equivalence of floating and fixed strike Asian options

On the equivalence of floating and fixed strike Asian options

Pricing of the fixed-strike Asian has been the subject of much research over the last ten years and academic interest in these options has experienced a revival recently, see Carr and Schr¨ oder [6], Donati-Martin, Ghomrasni and Yor [9]. Early work used the fact that the distribution of the geometric average of a set of lognormal distributions is also lognormal, see Conze and Visvanathan [8] and Turnbull and Wakeman [24]. A second popular line of research is to price the fixed-strike Asian by direct numerical methods, including Monte Carlo simulation (Kemna and Vorst [16], Lapeyre and Teman [18]) or numerically solving the PDE (Rogers and Shi [22], Alziary et al. [1] ).

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