The pricing of forward-starting asian options

Bouaziz, Laurent; Briys, Éric; Crouhy, Michel

doi:10.1016/0378-4266(94)00031-x

Cited by 63 publications

(39 citation statements)

References 9 publications

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“…Yor (1992, 1993) compute the moments of all orders of (1/θ ) T T −θ S(u) du and obtain the Laplace transform of the Asian option price process. Kemna and Vorst (1992) in a discretetime case and Bouaziz, Bryis, and Crouhy (1994) in a continuous-time case provide bounds for the price of an Asian option, but do not consider a hedging strategy.…”

Section: Asian Optionsmentioning

confidence: 99%

Robustness of the Black and Scholes Formula

Karoui

Jeanblanc‐Picquè

Shreve

1998

Mathematical Finance

340

247

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Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption may result in a misspecification of the volatility. However, if the misspecified volatility dominates the true volatility, then the misspecified price of the option dominates its true price. Moreover, the option hedging strategy computed under the assumption of the misspecified volatility provides an almost sure one-sided hedge for the option under the true volatility. Analogous results hold if the true volatility dominates the misspecified volatility. These comparisons can fail, however, if the misspecified volatility is not assumed to be a function of time and the stock price. The positive results, which apply to both European and American options, are used to obtain a bound and hedge for Asian options.

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Section: Asian Optionsmentioning

confidence: 99%

Robustness of the Black and Scholes Formula

Karoui

Jeanblanc‐Picquè

Shreve

1998

Mathematical Finance

340

247

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“…This exact approach has also been applied to the pricing of insurance futures contracts by Cummins and Geman (1993). Along this analytical approach, a number of other approaches coexist in the literature such as numerical approaches or price approximations : Carverhill and Clewlow (1990); Kemna and Vorst (1990); Ruttiens (1990); Turnbull and Wakeman (1991); Levy (1992); Bouaziz et al (1994); Rogers and Shi (1995).…”

Section: Introductionmentioning

confidence: 99%

Path dependent options on yields in the affine term structure model

Leblanc

Scaillet

1998

Finance and Stochastics

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Abstract. We give analytical pricing formulae for path dependent options on yields in the framework of the affine term structure model. More precisely, European call options such as the arithmetic average call, the call on maximum and the lookback call are examined. For the two last options approximate formulae using the law of hitting times of an Ornstein-Uhlenbeck process are proposed. Numerical implementation is also briefly discussed and results are given in the case of the arithmetic average option.

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“…It is easy to see that ordinary European calls and puts can easily be valued in 0 ( n ) time. However, the valuation of Asian calls and puts is a well-known hard problem in finance and much research has been directed at this problem [3,11,25,27,28]. All known valuation methods for these options either use some form of Monte Carlo estimation or use analytic approximations with no error analysis.…”

Section: Pricing Formulas and Results In The Papermentioning

confidence: 99%