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Pricing Formula (pricing + formula)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	83%

Selected Abstracts

PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

MATHEMATICAL FINANCE, Issue 2 2006
Vadim Linetsky
We solve in closed form a parsimonious extension of the Black,Scholes,Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets. [source]

Equilibrium pricing of contingent claims in tradable permit markets

THE JOURNAL OF FUTURES MARKETS, Issue 6 2010
Masaaki Kijima
We advance a model of the tradable permit market and derive a pricing formula for contingent claims traded in the market in a general equilibrium framework. It is shown that prices of such contingent claims exhibit significantly different properties from those in the ordinary financial markets. In particular, if the social cost function kinks at some level of abatement, the forward price, as well as the spot price, can be subject to the so-called price spike. However, this price-spike phenomenon can be weakened if a system of banking and borrowing is properly introduced. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:559,589, 2010 [source]

Pricing and hedging of quanto range accrual notes under Gaussian HJM with cross-currency Levy processes

THE JOURNAL OF FUTURES MARKETS, Issue 10 2009
Szu-Lang Liao
This study analyzes the pricing and hedging problems for quanto range accrual notes (RANs) under the Heath-Jarrow-Morton (HJM) framework with Levy processes for instantaneous domestic and foreign forward interest rates. We consider the effects of jump risk on both interest rates and exchange rates in the pricing of the notes. We first derive the pricing formula for quanto double interest rate digital options and quanto contingent payoff options; then we apply the method proposed by Turnbull (Journal of Derivatives, 1995, 3, 92,101) to replicate the quanto RAN by a combination of the quanto double interest rate digital options and the quanto contingent payoff options. Using the pricing formulas derived in this study, we obtain the hedging position for each issue of quanto RANs. In addition, by simulation and assuming the jump risk to follow a compound Poisson process, we further analyze the effects of jump risk and exchange rate risk on the coupons receivable in holding a RAN. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:973,998, 2009 [source]

Valuation of floating range notes in a LIBOR market model

THE JOURNAL OF FUTURES MARKETS, Issue 7 2008
Ting-Pin Wu
This study derives an approximate pricing formula of floating range notes (FRNs) within the multifactor LIBOR market model (LMM) framework. The LMM features the ease for calibration procedure, and the resulting pricing formula is more tractable. In addition, since the underlying rate of FRNs is usually the LIBOR rate, the pricing of the FRNs under the LMM is more direct and full of intuition. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:697,710, 2008 [source]

Richardson extrapolation techniques for the pricing of American-style options

THE JOURNAL OF FUTURES MARKETS, Issue 8 2007
Chuang-Chang Chang
In this article, the authors reexamine the American-style option pricing formula of R. Geske and H.E. Johnson (1984), and extend the analysis by deriving a modified formula that can overcome the possibility of nonuniform convergence (which is likely to occur for nonstandard American options whose exercise boundary is discontinuous) encountered in the original Geske,Johnson methodology. Furthermore, they propose a numerical method, the Repeated-Richardson extrapolation, which allows the estimation of the interval of true option values and the determination of the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske,Johnson formula is shown to be more accurate than the original Geske,Johnson formula for pricing American options, especially for nonstandard American options. This study also illustrates that the Repeated-Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, the authors investigate the possibility of combining the binomial Black,Scholes method proposed by M. Broadie and J.B. Detemple (1996) with the Repeated-Richardson extrapolation technique. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:791,817, 2007 [source]

Analytic approximation formulae for pricing forward-starting Asian options

THE JOURNAL OF FUTURES MARKETS, Issue 5 2003
Chueh-Yung Tsao
In this article we first identify a missing term in the Bouaziz, Briys, and Crouhy (1994) pricing formula for forward-starting Asian options and derive the correct one. First, illustrate in certain cases that the missing term in their pricing formula could induce large pricing errors or unreasonable option prices. Second, we derive new analytic approximation formulae for valuing forward-starting Asian options by adding the second-order term in the Taylor series. We show that our formulae can accurately value forward-starting Asian options with a large underlying asset's volatility or a longer time window for the average of the underlying asset prices, whereas the pricing errors for these options with the previously mentioned formula could be large. Third, we derive the hedge ratios for these options and compare their properties with those of plain vanilla options. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:487,516, 2003 [source]

A generalization of Rubinstein's "Pay now, choose later"

THE JOURNAL OF FUTURES MARKETS, Issue 5 2008
Jia-Hau Guo
This article provides quasi-analytic pricing formulae for forward-start options under stochastic volatility, double jumps, and stochastic interest rates. Our methodology is a generalization of the Rubinstein approach and can be applied to several existing option models. Properties of a forward-start option may be very different from those of a plain vanilla option because the entire uncertainty of evolution of its price is cut off by the strike price at the time of determination. For instance, in contrast to the plain vanilla option, the value of a forward-start option may not always increase as the maturity increases. It depends on the current term structure of interest rates. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:488,515, 2008 [source]

The Term Structure of Simple Forward Rates with Jump Risk

MATHEMATICAL FINANCE, Issue 3 2003
Paul Glasserman
This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives. [source]

Pricing and hedging of quanto range accrual notes under Gaussian HJM with cross-currency Levy processes

The valuation of reset options with multiple strike resets and reset dates

THE JOURNAL OF FUTURES MARKETS, Issue 1 2003
Szu-Lang Liao
This article makes two contributions to the literature. The first contribution is to provide the closed-form pricing formulas of reset options with strike resets and predecided reset dates. The exact closed-form pricing formulas of reset options with strike resets and continuous reset period are also derived. The second contribution is the finding that the reset options not only have the phenomena of Delta jump and Gamma jump across reset dates, but also have the properties of Delta waviness and Gamma waviness, especially near the time before reset dates. Furthermore, Delta and Gamma can be negative when the stock price is near the strike resets at times close to the reset dates. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:87,107,2003 [source]

Pricing credit derivatives under stochastic recovery in a hybrid model

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2010
Stephan Höcht
Abstract In this article, a framework for the joint modelling of default and recovery risk is presented. The model accounts for typical characteristics known from empirical studies, e.g. negative correlation between recovery-rate process and default intensity, as well as between default intensity and state of the economy, and a positive dependence of recovery rates on the economic environment. Within this framework analytically tractable pricing formulas for credit derivatives are derived. The stochastic model for the recovery process allows for the pricing of credit derivatives with payoffs that are directly linked to the recovery rate at default, e.g. recovery locks. Copyright © 2009 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]