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Barrier Options (barrier + option)
Selected AbstractsA General Approach to Hedging Options: Applications to Barrier and Partial Barrier OptionsMATHEMATICAL FINANCE, Issue 3 2002Hans-Peter Bermin In this paper we consider a Black and Scholes economy and show how the Malliavin calculus approach can be extended to cover hedging of any square integrable contingent claim. As an application we derive the replicating portfolios of some barrier and partial barrier options. [source] Robust Hedging of Barrier OptionsMATHEMATICAL FINANCE, Issue 3 2001Haydyn Brown This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion. We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight. [source] A NEW METHOD OF PRICING LOOKBACK OPTIONSMATHEMATICAL FINANCE, Issue 2 2005Peter Buchen A new method for pricing lookback options (a.k.a. hindsight options) is presented, which simplifies the derivation of analytical formulas for this class of exotics in the Black-Scholes framework. Underlying the method is the observation that a lookback option can be considered as an integrated form of a related barrier option. The integrations with respect to the barrier price are evaluated at the expiry date to derive the payoff of an equivalent portfolio of European-type binary options. The arbitrage-free price of the lookback option can then be evaluated by static replication as the present value of this portfolio. We illustrate the method by deriving expressions for generic, standard floating-, fixed-, and reverse-strike lookbacks, and then show how the method can be used to price the more complex partial-price and partial-time lookback options. The method is in principle applicable to frameworks with alternative asset-price dynamics to the Black-Scholes world. [source] A modified static hedging method for continuous barrier options,THE JOURNAL OF FUTURES MARKETS, Issue 12 2010San-Lin Chung This study modifies the static replication approach of Derman, E., Ergener, D., and Kani, I. (1995, DEK) to hedge continuous barrier options under the Black, F. and Scholes, M. (1973) model. In the DEK method, the value of the static replication portfolio, consisting of standard options with varying maturities, matches the zero value of the barrier option at n evenly spaced time points when the stock price equals the barrier. In contrast, our modified DEK method constructs a portfolio of standard options and binary options with varying maturities to match not only the zero value but also zero theta on the barrier. Our numerical results indicate that the modified DEK approach improves performance of static hedges significantly for an up-and-out call option under the BS model even if the bid,ask spreads are considered. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] THE DEPENDENCE STRUCTURE OF RUNNING MAXIMA AND MINIMA: RESULTS AND OPTION PRICING APPLICATIONSMATHEMATICAL FINANCE, Issue 1 2010Umberto Cherubini We provide general results for the dependence structure of running maxima (minima) of sets of variables in a model based on (i) Markov dynamics; (ii) no Granger causality; (iii) cross-section dependence. At the time series level, we derive recursive formulas for running minima and maxima. These formulas enable to use a "bootstrapping" technique to recursively recover the pricing kernels of barrier options from those of the corresponding European options. We also show that the dependence formulas for running maxima (minima) are completely defined from the copula function representing dependence among levels at the terminal date. The result is applied to multivariate discrete barrier digital products. Barrier Altiplanos are simply priced by (i) bootstrapping the price of univariate barrier products; (ii) evaluating a European Altiplano with these values. [source] A General Approach to Hedging Options: Applications to Barrier and Partial Barrier OptionsMATHEMATICAL FINANCE, Issue 3 2002Hans-Peter Bermin In this paper we consider a Black and Scholes economy and show how the Malliavin calculus approach can be extended to cover hedging of any square integrable contingent claim. As an application we derive the replicating portfolios of some barrier and partial barrier options. [source] Robust Hedging of Barrier OptionsMATHEMATICAL FINANCE, Issue 3 2001Haydyn Brown This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion. We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight. [source] A modified static hedging method for continuous barrier options,THE JOURNAL OF FUTURES MARKETS, Issue 12 2010San-Lin Chung This study modifies the static replication approach of Derman, E., Ergener, D., and Kani, I. (1995, DEK) to hedge continuous barrier options under the Black, F. and Scholes, M. (1973) model. In the DEK method, the value of the static replication portfolio, consisting of standard options with varying maturities, matches the zero value of the barrier option at n evenly spaced time points when the stock price equals the barrier. In contrast, our modified DEK method constructs a portfolio of standard options and binary options with varying maturities to match not only the zero value but also zero theta on the barrier. Our numerical results indicate that the modified DEK approach improves performance of static hedges significantly for an up-and-out call option under the BS model even if the bid,ask spreads are considered. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] Efficient quadrature and node positioning for exotic option valuationTHE JOURNAL OF FUTURES MARKETS, Issue 11 2010San-Lin Chung We combine the best features of two highly successful quadrature option pricing streams, improving the linked issues of numerical precision and abscissa positioning. Coupling the recombining abscissa (node) approach used in Andricopoulos, A., Widdicks, M., Duck, P., and Newton, D.P. (2003) (AWDN as well as AWND, 2007) with the Gauss-Legendre Quadrature (GQ) method of Sullivan, M.A. (2000) yields highly accurate and efficient option prices for a range of standard and exotic specifications including barrier options and in particular for NGARCH, CEV, and jump-diffusion processes. The improvements are due to manner in which GQ positions nodes and the use of these values without interpolation. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] Path-dependent currency options with mean reversionTHE JOURNAL OF FUTURES MARKETS, Issue 3 2008Hoi Ying Wong This paper develops a path-dependent currency option pricing framework in which the exchange rate follows a mean-reverting lognormal process. Analytical solutions are derived for barrier options with a constant barrier, lookback options, and turbo warrants. As the analytical solutions are obtained using a Laplace transform, this study numerically shows that the solution implemented with a numerical Laplace inversion is efficient and accurate. The pricing behavior of path-dependent options with mean reversion is contrasted with the Black-Scholes model. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:275,293, 2008 [source] Static hedging and model risk for barrier optionsTHE JOURNAL OF FUTURES MARKETS, Issue 5 2006Morten Nalholm The article investigates how sensitive different dynamic and static hedge strategies for barrier options are to model risk. It is found that using plain-vanilla options to hedge offers considerable improvements over usual , hedges. Further, it is shown that the hedge portfolios involving options are relatively more sensitive to model risk, but that the degree of misspecification sensitivity is robust across commonly used models. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:449,463, 2006 [source] | ||||||||||