The payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. Ó»ª"õ The options mentioned above are generally called “vanilla” options to express the fact that they are standardized and less interesting than “exotic” options *4]. The owner of a Russian option on a stock receives the historical maximum value of the asset price when the option is exercised and the option has no pre-set expiration date. The initial stock price is 50, the stock price volatility is 40%, the risk-free interest rate is 10% and the life of the option is 3 months. In this paper, we will introduce a numerical method to price the European lookback floating strike put options where the underlying asset price is modeled by a generalized regime-switching jump diffusion process. A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. Viewed 86 times 5. Fixed lookback options have a specified strike price, while floating lookback options have a strike price determined by the asset path. An option that allows the buyer to choose as the option strike price any price of the underlying asset that has occurred during the life of the option. Note that satisfies the functional form for the American lookback call option given by . This option will always be … Math- ematically, the pricing American lookback option can be formulated into the free boundary problem with a free boundary. American options and other path-dependent options, not just for discrete barrier and lookback options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. This paper considers the default probability of American lookback option in a mixed jump-diffusion model, where the underlying asset price has to cross two-sided predetermined strikes to activate the American lookback option. By solving a system of coupled MJD-fBm, we obtain an explicit formula for the Laplace transform of the default time. Active 5 years, 7 months ago. Use, Smithsonian Broadly speaking, general methods will be less efﬁcient than the methods which take advantage of the special struc-tures of discrete barrier and lookback options… Lookback option. and Vorst A.C.P. Fixed lookback options have a specified strike price, while floating lookback options have a strike price determined by the asset path. for Pricing Barrier Option 1998 2. Journal of International Money … Farlex Financial Dictionary. (2001). The inter-relations between the price functions of these American lookback options are explored. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options and pricing model of dynamic protection fund. In this paper, we will introduce a numerical method to price the European lookback floating strike put options where the underlying asset price is modeled by a generalized regime-switching jump diffusion process. •A ﬁxed strike lookback call (put) is a call (put) option on the maximum (minimum) realized price. ¿yJæÂdÉàIÍÓ@³'åý+%Ï¬UÞýX,3³XX®âù~:¯Ø±' 4ÏL0î ØTsmøP¶+WtïrçÊ\î«?2®|ÌWOdÞ/®lêö\( Ýw4°6áÆ(àGJ°ÞZ°##X«GRÍâ^Â{ i ©A©â»n_Ô¹°ÙÐÿçz}l;Wæix_oÞ +ë-jLÂ z(\NZúù×0Z Ú"w«Ý-]yWê¸,sbò7. The respective terminal payoﬀ of the ﬁxed strike lookback call and put are max(MT T0 − X,0) and max(X− mT T0,0), whereXis the strike price. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative An option (lookback option) that can be exercised at any time before, and including, expiration date. We study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price. Astrophysical Observatory. American lookback options can be thought of as a combination of American options and lookback options. LookBack Options - Introduction • call option on the stock with strike $100, expiration T • current stock price $100, two possible states at T: $110 (state A) and $90 (state B) • payoff of the call: $10 in state A and $0 in state B • option price between $0 and $10 • suppose state A comes with probability p, state B with probability 1-p, a options monte-carlo derivatives option-pricing quantitative-finance american-options jump-diffusion stochastic-volatility-models black-scholes fourier-transform sabr european-options levy-processes heston-model asian-option bermudan-option swing-option lookback-option variance-swap barrier-option ²pA{>* Ask Question Asked 5 years, 7 months ago. Financial Instruments Toolboxâ¢ software supports two types of lookback options: fixed and floating. Lookback options, in the terminology of finance, are a type of exotic option with path dependency, among many other kind of options. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options and pricing model of dynamic protection fund. ÚÉ¼h÷X{AÐºëLÍÜöfîbÉ)( ?¾|~T\ The local times of American lookback option Consider lookback options where the lookback period is taken to be the whole life of the option. KEYWORDS: United States North America District of Columbia Virginia INDUSTRY KEYWORDS: Lookback option is a well-known path-dependent option where its payoﬀ depends on the historical extremum prices. 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