Simulating Path-Dependent Options

Babsiri, Mohamed El; Noel, G. T.

doi:10.3905/jod.6.2.65

Cited by 25 publications

(11 citation statements)

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“…With only 100 time subintervals, the enhanced method is much faster and more accurate than the Monte Carlo method. Beaglehole, Dybvig, and Zhou [1997] and Babsiri and Noel [1998] show that the standard Monte Carlo method is not reliable for pricing barrier options. It is important to adapt it with enhancements based on, for instance, distributions of extreme values.…”

Section: E X H I B I T 4 Double Knock-in Call Prices On Stock-unenhanmentioning

confidence: 98%

“…Beaglehole, Dybvig, and Zhou [1997] describe a Monte Carlo method for barrier options that draws random numbers from the distribution for maximum (minimum) of a Brownian bridge. Babsiri and Noel [1998] simulate the terminal value of the underlying stock price and use the cumulative distribution function for the extreme of the logarithmic price conditional on the terminal price to draw random values of the extremes. Both these articles show that the use of distributional information improves the accuracy of Monte Carlo methods in pricing barrier options.…”

Section: The Pricing Of Barrier Optionsmentioning

confidence: 99%

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Pricing Barrier Options with One-Factor Interest Rate Models

Kuan¹,

Webber²

2003

JOD

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A numerical integration method may be used to price barrier options using one-factor interest rate models when the transition distribution function of the underlying rate is known but explicit pricing formulas are not available.For the Hull and White model, barriers on bonds are transformed to smooth time-dependent barriers on the short rate. For the swap market model, time-dependent barriers are imposed on forward swap rates. The first passage time densities of the underlying interest rate are solved for numerically from integral equations.Comparison to barrier options on equity where there are analytical formulas confirms that the method is faster and more accurate than a Monte Carlo method.Unlike lattice methods, the numerical integration method does not require finding optimal positioning of lattice nodes. The method has advantages over Monte Carlo and lattice methods when the barriers are time-dependent and the underlying process is a more general diffusion process.T he pricing of barrier options is often discussed. Single-barrier and doublebarrier options are the most commonly investigated. When the underlying asset is assumed to be lognormally distributed as in the Black and Scholes [1973] model, pricing formulas are available for both single-and double-barrier options. The pricing of options with time-dependent barriers in the interest rate market, where the underlying state variables are usually assumed to follow more general diffusion processes, is less well established.We focus on the problem of pricing barrier options on zero-coupon bonds and barrier swaptions in one-factor interest rate models. Computational examples are given for the Hull and White model [1990] and the swap market model (see Jamshidian [1997]). Both models take initial term structures as inputs. By including the current forward rate curve or bond price curve in the models, other interest rate options can be priced consistently with initial term structures. This is an essential practical requirement in the interest rate markets to avoid arbitrage and to permit consistent hedging.In the Hull and White model, the short rate is the only factor, and there are explicit expressions for zero-coupon bonds. These features allow us to transform barriers on the underlying zero-coupon bond or forward swap rate to time-dependent barriers on the short rate.The lognormal swap market model is widely used because it allows easy calibration to swaption prices through Black's formula. As we are interested in cases for which there are no analytical pricing formulas, we will price swaptions with time-dependent barriers in the swap market model.In general, the first passage time densities of interest rates to time-dependent barriers can be solved only numerically. We use the algorithm suggested by Park and Schuurmann [1976, 1980] to solve for first passage time densities. Given these densities, we are able to value single

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Section: E X H I B I T 4 Double Knock-in Call Prices On Stock-unenhanmentioning

confidence: 98%

Section: The Pricing Of Barrier Optionsmentioning

confidence: 99%

Pricing Barrier Options with One-Factor Interest Rate Models

Kuan¹,

Webber²

2003

JOD

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show abstract

“…A barrier option is cheaper than its underlying plain-vanilla option because the payoff of the barrier option is less than or equal to that of the plain-vanilla option. Barrier options have been considered by Reiner and Rubinstein (1991), Heynen and Kat (1994b), Nelken (1996), Lin (1998), El Babsiri andNoel (1998), Zhang (1998) and Kwok (1998). To increase the participation rate, let us now apply an up-and-in barrier option to new EIAs as an alternative to point-to-point EIAs.…”

Section: Up-and-in Barrier Eiamentioning

confidence: 98%

Pricing equity-indexed annuities with path-dependent options

Lee

2003

Insurance: Mathematics and Economics

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“…There are variations on these options which are used in practice whose pricing can be easily accommodated by the methods used here. A hotdog option (see Babsiri and Noel (1998)), is a double knock-out barrier option whose barriers are time dependent. We extend their methods to more general price processes using pathwise imputation.…”

Section: Pricing Path Dependent Optionsmentioning

confidence: 99%