On Contingent Claims that Insure Ex‐post Optimal Stock Market Timing

Goldman, M. Barry; Sosin, Howard B.; Shepp, Larry

doi:10.1111/j.1540-6261.1979.tb02102.x

Cited by 39 publications

(16 citation statements)

References 10 publications

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“…A standard lookback put gives the right to sell at the highest price recorded during the option's life. Lookbacks were first studied by Goldman, Sosin, and Gatto (1979) and Goldman, Sosin, and Shepp (1979) who derived closed-form pricing formulae under the lognormal assumption. In addition to standard lookback options, Conze and Vishwanathan (1991) introduce calls on maximum and puts on minimum.…”

Section: Path-dependent Options Under the Cev Processmentioning

confidence: 99%

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Pricing and Hedging Path-Dependent Options Under the CEV Process

Давыдов¹,

2001

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M uch of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.

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Section: Path-dependent Options Under the Cev Processmentioning

confidence: 99%

“…Rubinstein and Reiner (1991) extend Merton's result to other types of barrier options. Goldman et al (1979), Goldman et al (1979), and Conze and Vishwanathan (1991) provide closed-form pricing formulae for lookback options.…”

Section: Introductionmentioning

confidence: 99%

Pricing and Hedging Path-Dependent Options Under the CEV Process

Давыдов¹,

2001

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“…Most models assume the continuous time version mainly because this leads to analytical solutions; see, for example, Gatto et al (1979), Goldman et al (1979), and Conze and Viswanathan (1991), for continuous lookback options; and see, for example, Merton (1973), Kat (1994a, 1994b), Rubinstein and Reiner (1991), Chance (1994), and Kunitomo and Ikeda (1992) for various formulae for continuously monitored barrier options under the classical Brownian motion framework. Recently, Boyle and Tian (1999) and Davydov and Linetsky (2001) have priced continuously monitored barrier and lookback options under the CEV model using lattice and Laplace transform methods, respectively; see Kou andWang (2003, 2004) for continuously monitored barrier options under a jump-diffusion framework.…”

Section: Barrier and Lookback Optionsmentioning

confidence: 99%

Chapter 8 Discrete Barrier and Lookback Options

Kou

2007

Financial Engineering

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“…The continuous versions of all of these options can be priced in closed form. See, in particular, Merton [48], Rubinstein and Reiner [54], Chance [18], Boyle and Lau [10], Rich [51], Carr [16], and Heynen and Kat [31,32] for various kinds of barrier options, and for various kinds of lookbacks see Conze and Viswanathan [23], Garman [27], Goldman, Sosin, and Gatto [29], Goldman, Sosin, and Shepp [30], and Heynan and Kat [33].…”

Section: Continuity Correctionsmentioning

confidence: 99%

Connecting discrete and continuous path-dependent options

Broadie

Glasserman

Kou³

1999

Finance and Stochastics

178

143

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Abstract. This paper develops methods for relating the prices of discrete-and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete-and continuous-time prices which dramatically improve convergence to the accurate price.

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On Contingent Claims that Insure Ex‐post Optimal Stock Market Timing

Cited by 39 publications

References 10 publications

Pricing and Hedging Path-Dependent Options Under the CEV Process

Pricing and Hedging Path-Dependent Options Under the CEV Process

Chapter 8 Discrete Barrier and Lookback Options

Connecting discrete and continuous path-dependent options

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