Path Dependent Option

Explained:

path dependence


 

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Some exotic options are said to be path dependent. Their terminal value (at exercise or expiration) depends upon the value of the underlier, not only at that time, but also at prior points in time. In this sense, the option's terminal value depends upon the "path" take by the underlier over the life of the option.

A call option is not path dependent. Its value at exercise or expiration depends on the value of the underlier only at that point in time..

By comparison, an Asian option is path dependent. Its value at expiration depends on the average value of the underlier over the life of the option. A barrier option is also path dependent. The option's value at expiration depends upon both the value of the underlier at expiration but also on whether past values of the underlier ever hit a barrier. Chooser and Lookback options are also path dependent.

Pricing or calculating the Greeks is typically more difficult for path dependent options than for non-path dependent options.

Related Internal Links

Asian option An path dependent option whose expiration value depends on the average value of an underlier over the life of the option.

barrier option A path dependent option that terminates or is activated by the underlier reaching some "barrier" level.

derivative instrument An instrument which derives its value from the value of other financial instruments. Article includes a list of vanilla and exotic derivatives.

Greeks A set of factor sensitivities, which includes delta and gamma.

lookback option A path dependent option whose payout depends upon the maximum or minimum underlier value achieved during the entire life of the option.

option A type of derivative instrument.

option pricing theory The body of financial theory used to value options and other derivative instruments.

option spreads Positions combining one or more options in a single underlier.

volatility A metric of  variability in a stochastic process.

volatility skew A condition where implied volatilities vary by strike.

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Related Books

Haug (1997) and Briys (1998) discuss classic pricing methodologies for path dependent options. Das (2003) and Taleb (1996) provide the traders' perspective.

Complete Guide to
Option Pricing Formulas

Espen G. Haug

quality

 
technical  

1997

  

Options, Futures, and Exotic Derivatives

quality

 
technical  

1998

  

Swaps/Financial Derivatives

Satyajit Das

quality

 

technical  

2003

  

Dynamic Hedging

Nassim Taleb
quality

 
technical  

1996

  

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