• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 추계 학술발표회 논문집
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• pp.153-158
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• 2005

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will derive explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity.

• 응용통계연구
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• 제22권1호
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• pp.59-73
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• 2009

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will propose an outside floating-strike lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at some percentage of the lowest (or highest) price of the other underlying asset. In addition, this paper will derive explicit pricing formulas for these outside floating-strike lookback options. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples will be discussed.

• East Asian mathematical journal
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• 제32권3호
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• pp.301-310
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• 2016

Lookback options, in the terminology of nance, are a type of exotic option with path dependency whose the payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. In this paper, we exploit Mellin transform techniques to find a closed-form solution for European lookback options in Black-Scholes model.

• Communications for Statistical Applications and Methods
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• 제11권2호
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• pp.213-225
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• 2004

A fixed-strike lookback option is an option whose payoff is determined by the maximum (or minimum) price of the underlying asset within the option's life. Under the Black-Scholes framework, the time-t price of an equity asset follows a geometric Brownian motion. Applying the method of Esscher transforms, this paper will derive explicit pricing formulas for fixed-strike lookback call and put options, respectively. In addition, this paper will show a relationship (duality property) between the pricing formulas of the call and put options. Finally, this paper will derive explicit pricing formulas for the fixed-strike lookback options when their underlying asset pays dividends continuously at a rate proportional to its price.

• 응용통계연구
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• 제21권3호
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• pp.485-495
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• 2008

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will present explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying asset pays dividends continuously at a rate proportional to its price.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.819-835
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• 2012

A floating-strike lookback call (or put) option gives the holder the right to buy (or sell) at some percentage of the lowest (or highest) price of the underlying asset. This paper will propose an outside lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at its guaranteed floating-strike price that is some percentage times the smaller (or the greater) of a specific guaranteed amount and the lowest (or highest) price of the other underlying asset. In addition, this paper derives explicit pricing formulas for these outside lookback options. Section 3 and Section 4 assume that the underlying assets pay no dividends. In contrast, Section 5 derives explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples are also discussed.

• 대한수학회보
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• 제60권2호
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• pp.361-388
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• 2023

In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.