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Option Pricing (option + pricing)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting80%
Mathematics and Statistics19%

Terms modified by Option Pricing

  • option pricing model
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  • option pricing models
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    Selected Abstracts

    SELF-DECOMPOSABILITY AND OPTION PRICING

    MATHEMATICAL FINANCE, Issue 1 2007
    Peter Carr
    The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and maturities at a point of time. Considerations of parameter stability over time suggest a preference for two of these models. Currently, there are several option pricing models with 6,10 free parameters that deliver a comparable level of performance in synthesizing option prices. The dimension reduction attained here should prove useful in studying the variation over time of option prices. [source]

    APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICING

    MATHEMATICAL FINANCE, Issue 1 2006
    Jin-Chuan Duan
    This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored. [source]

    STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE-DIMENSIONAL FORWARD RATES AND OPTION PRICING

    MATHEMATICAL FINANCE, Issue 1 2005
    Shin Ichi Aihara
    We model the term-structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage-free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results. [source]

    Smiles, Bid-ask Spreads and Option Pricing

    EUROPEAN FINANCIAL MANAGEMENT, Issue 3 2001
    Ignacio Peña
    Given the evidence provided by Longstaff (1995), and Peña, Rubio and Serna (1999) a serious candidate to explain the pronounced pattern of volatility estimates across exercise prices might be related to liquidity costs. Using all calls and puts transacted between 16:00 and 16:45 on the Spanish IBEX-35 index futures from January 1994 to October 1998 we extend previous papers to study the influence of liquidity costs, as proxied by the relative bid-ask spread, on the pricing of options. Surprisingly, alternative parametric option pricing models incorporating the bid-ask spread seem to perform poorly relative to Black-Scholes. [source]

    Randomized Stopping Times and American Option Pricing with Transaction Costs

    MATHEMATICAL FINANCE, Issue 1 2001
    Prasad Chalasani
    In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming. [source]

    Option Pricing with Extreme Events: Using Câmara and Heston(2008),s Model,

    ASIA-PACIFIC JOURNAL OF FINANCIAL STUDIES, Issue 2 2009
    Sol Kim
    Abstract For the KOSPI 200 Index options, we examine the effect of extreme events for pricing options. We compare Black and Scholes (1973) model with Câmara and Heston (2008)'s options pricing model that allows for both big downward and upward jumps. It is found that Câmara and Heston (2008)'s extreme events option pricing model shows better performance than Black and Scholes (1973) model does for both in-sample and out-of-sample pricing. Also downward jumps are a more important factor for pricing stock index options than upward jumps. It is consistent with the empirical evidence that reports the sneers or negative skews in the stock index options market. [source]

    Option pricing under Markov-switching GARCH processes

    THE JOURNAL OF FUTURES MARKETS, Issue 5 2010
    Chao-Chun Chen
    This study proposes an N -state Markov-switching general autoregressive conditionally heteroskedastic (MS-GARCH) option model and develops a new lattice algorithm to price derivatives under this framework. The MS-GARCH option model allows volatility dynamics switching between different GARCH processes with a hidden Markov chain, thus exhibiting high flexibility in capturing the dynamics of financial variables. To measure the pricing performance of the MS-GARCH lattice algorithm, we investigate the convergence of European option prices produced on the new lattice to their true values as conducted by the simulation. These results are very satisfactory. The empirical evidence also suggests that the MS-GARCH model performs well in fitting the data in-sample and one-week-ahead out-of-sample prediction. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:444,464, 2010 [source]

    An explicitly solvable multi-scale stochastic volatility model: Option pricing and calibration problems

    THE JOURNAL OF FUTURES MARKETS, Issue 9 2009
    Lorella Fatone
    We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a one-dimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk-neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus-obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the "observed" option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site http://www.econ.univpm.it/recchioni/finance. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:862,893, 2009 [source]

    Economic significance of risk premiums in the S&P 500 option market

    THE JOURNAL OF FUTURES MARKETS, Issue 12 2002
    R. Brian Balyeat
    Option pricing is complicated by the theoretical existence of risk premiums. This article utilizes a testable methodology to extract the pricing impact resulting from these risk premiums. First, option prices (based on the full dynamics of the underlying) are computed under the assumption that these risk premiums are not priced. The pricing methodology is independent of any particular option-pricing model or distributional assumptions on the return process for the underlying. The difference between the actual market prices and these "no-premium base case" prices reflects the effect of risk premiums. For at-the-money, 13-week S&P 500 options trading from 1989 until 1993, the effect of risk premiums is statistically significant and averages slightly over 20% (in units of Black,Scholes implied volatility). A simple delta-hedging strategy is used to demonstrate the economic significance of risk premiums, as the trading strategy provides enough profit to absorb a crash similar in magnitude to the 1987 crash once every 6.20 years. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1147,1178, 2002 [source]

    Estimating unobservable valuation parameters for illiquid assets

    ACCOUNTING & FINANCE, Issue 3 2009
    Glenn Boyle
    G12; R33 Abstract A problem that often arises in applied finance is one where decision-makers need to choose a value for some parameter that will affect the cash flows between two parties involved in the operation of an illiquid asset. Because the values of the cash flows also depend on various unobservable parameters, identifying the value of the policy parameter that achieves the desired allocation between the parties is no simple task, often resulting in disputes and the invocation of ad hoc approaches. We show how this problem can be solved using an extension of the well-known ,implied volatility' technique from option pricing, and apply it to the determination of equilibrium rental rates on ground leases of commercial land. [source]

    Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest Rates

    INTERNATIONAL REVIEW OF FINANCE, Issue 3-4 2002
    George J. Jiang
    In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous-time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk-neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk-neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk-neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long-term options, random jump tends to price the short-term options better, and option pricing based on multiple risk-neutral distributions significantly outperforms that based on a single risk-neutral distribution. [source]

    The Contributions of Professors Fischer Black, Robert Merton and Myron Scholes to the Financial Services Industry

    INTERNATIONAL REVIEW OF FINANCE, Issue 4 2000
    Terry Marsh
    This paper is written as a tribute to Professors Robert Merton and Myron Scholes, winners of the 1997 Nobel Prize in economics, as well as to their collaborator, the late Professor Fischer Black. We first provide a brief and very selective review of their seminal work in contingent claims pricing. We then provide an overview of some of the recent research on stock price dynamics as it relates to contingent claim pricing. The continuing intensity of this research, some 25 years after the publication of the original Black,Scholes paper, must surely be regarded as the ultimate tribute to their work. We discuss jump-diffusion and stochastic volatility models, subordinated models, fractal models and generalized binomial tree models for stock price dynamics and option pricing. We also address questions as to whether derivatives trading poses a systemic risk in the context of models in which stock price movements are endogenized, and give our views on the ,LTCM crisis' and liquidity risk. [source]

    Time Changes for Lévy Processes

    MATHEMATICAL FINANCE, Issue 1 2001
    Hélyette Geman
    The goal of this paper is to consider pure jump Lévy processes of finite variation with an infinite arrival rate of jumps as models for the logarithm of asset prices. These processes may be written as time-changed Brownian motion. We exhibit the explicit time change for each of a wide class of Lévy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Lévy processes that are analytically tractable, in their characteristic functions and Lévy densities, and hence are relevant for option pricing. [source]

    High order smoothing schemes for inhomogeneous parabolic problems with applications in option pricing

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007
    A.Q.M. Khaliq
    Abstract A new family of numerical schemes for inhomogeneous parabolic partial differential equations is developed utilizing diagonal Padé schemes combined with positivity,preserving Padé schemes as damping devices. We also develop a split version of the algorithm using partial fraction decomposition to address difficulties with accuracy and computational efficiency in solving and to implement the algorithms in parallel. Numerical experiments are presented for several inhomogeneous parabolic problems, including pricing of financial options with nonsmooth payoffs.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]

    Alternative tilts for nonparametric option pricing

    THE JOURNAL OF FUTURES MARKETS, Issue 10 2010
    M. Ryan Haley
    This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie,Read family of divergence measures. Alhough the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black,Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:983,1006, 2010 [source]

    Option pricing for the transformed-binomial class

    THE JOURNAL OF FUTURES MARKETS, Issue 8 2006
    António Câmara
    This article generalizes the seminal Cox-Ross-Rubinstein (1979) binomial option pricing model to all members of the class of transformed-binomial pricing processes. The investigation addresses issues related with asset pricing modeling, hedging strategies, and option pricing. Formulas are derived for (a) replicating or hedging portfolios, (b) risk-neutral transformed-binomial probabilities, (c) limiting transformed-normal distributions, and (d) the value of contingent claims, including limiting analytical option pricing equations. The properties of the transformed-binomial class of asset pricing processes are also studied. The results of the article are illustrated with several examples. © 2006 Wiley Periodicals, Inc. Jrl. Fut Mark 26:759,787, 2006 [source]

    The accuracy and efficiency of alternative option pricing approaches relative to a log-transformed trinomial model

    THE JOURNAL OF FUTURES MARKETS, Issue 6 2002
    Hsuan-Chi Chen
    This article presents a log-transformed trinomial approach to option pricing and finds that various numerical procedures in the option pricing literature are embedded in this approach with choices of different parameters. The unified view also facilitates comparisons of computational efficiency among numerous lattice approaches and explicit finite difference methods. We use the root-mean-squared relative error and the minimum convergence step to evaluate the accuracy and efficiency for alternative option pricing approaches. The numerical results show that the equal-probability trinomial specification of He (12) and Tian (25) and the sharpened trinomial specification of Omberg (21) outperform other lattice approaches and explicit finite difference methods. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:557,577, 2002 [source]

    First passage time for multivariate jump-diffusion processes in finance and other areas of applications

    APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
    Di Zhang
    Abstract The first passage time (FPT) problem is an important problem with a wide range of applications in science, engineering, economics, and industry. Mathematically, such a problem can be reduced to estimating the probability of a stochastic process first to reach a boundary level. In most important applications in the financial industry, the FPT problem does not have an analytical solution and the development of efficient numerical methods becomes the only practical avenue for its solution. Most of our examples in this contribution are centered around the evaluation of default correlations in credit risk analysis, where we are concerned with the joint defaults of several correlated firms, the task that is reducible to a FPT problem. This task represents a great challenge for jump-diffusion processes (JDP). In this contribution, we develop further our previous fast Monte Carlo method in the case of multivariate (and correlated) JDP. This generalization allows us, among other things, to evaluate the default events of several correlated assets based on a set of empirical data. The developed technique is an efficient tool for a number of financial, economic, and business applications, such as credit analysis, barrier option pricing, macroeconomic dynamics, and the evaluation of risk, as well as for a number of other areas of applications in science and engineering, where the FPT problem arises. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Assessment and propagation of input uncertainty in tree-based option pricing models

    APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009
    Henryk Gzyl
    Abstract This paper aims to provide a practical example of assessment and propagation of input uncertainty for option pricing when using tree-based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices are as unknown as the inputs they are based on. Option pricing formulas are tools whose validity is conditional not only on how close the model represents reality, but also on the quality of the inputs they use, and those inputs are usually not observable. We show three different approaches to integrating out the model nuisance parameters and show how this translates into model uncertainty in the tree model space for the theoretical option prices. We compare our method with classical calibration-based results assuming that there is no options market established and no statistical model linking inputs and outputs. These methods can be applied to pricing of instruments for which there is no options market, as well as a methodological tool to account for parameter and model uncertainty in theoretical option pricing. Copyright © 2008 John Wiley & Sons, Ltd. [source]