Posted on 18 August 2009
Tags: Arbitrage Free Price of Lookback Options, Arbitrage Free Price of Lookback Options with Fix Strike, Black-Scholes model, call option, European Lookback call option, European Lookback options, European options, Fix Strike, Lookback call, Lookback Option, Lookback Option with Fix Strike, Lookback put, minimum asset's price, payoff functions, standard European options, underlying asset price
In this article I have explained you about the lookback option with fixed strike.
Lookback Option with Fix Strike
The option’s strike price is fixed as for the standard European options.It differs in a way that at maturity the option is not exercised at the price: the maximum difference between the optimal underlying asset price and the strike is the payoff.
For the call option, the holder opt to exercise at the point when the underlying asset price is at its highest level whereas if we talk about put option the holder opt to exercise at the underlying asset’s lowest price. Respectively for the Lookback call and the Lookback put, the payoff functions are given by:
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where the maximum asset’s price is denoted by Smax during the life of the option, minimum asset’s price is denoted by Smin during the life of the option, and strike price is denoted by K.
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Posted on 18 August 2009
Tags: Arbitrage free price of Lookback options with floating strike, Black-Scholes model, European Lookback options, floating strike, foreign currencies, foreign exchange, foreign exchange market, forex, FX market, Lookback call option, Lookback Option, Lookback option with floating strike, Lookback options, Lookback put option, maximum asset's price, minimum asset's price, pricing method, standard normal cumulative distribution function, Strike price, underlying asset's price at maturity
A type of exotic options with path dependency, among many other kind of options are referred to as the Lookback options. The payoff depends on the optimal (maximum or minimum) underlying asset’s price that occur over the life of the option. By this option the holder is allowed to “look back” over time in order to determine the payoff. There are two kinds of Lookback options:
Here I will explain you Lockback option with floating strike and Arbitrage free price of Lookback options with floating strike.]
Lookback Option with Floating Strike
As the name suggests, the strike price of option is floating and it is determined at maturity. the optimal value of the underlying asset’s price during the option life is referred to as the floating strike. The the maximum difference between the market asset’s price at maturity and the floating strike is its payoff. The strike price is fixed at the lowest asset’s price of the option’s life,for the call and whereas for the put, it is fixed at the highest asset’s price.
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