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Path-Dependent Option Valuation When the Underlying Path Is Discontinuous (1997)
| Venue: | The J. of Financial Engineering, v.8, N |
| Citations: | 3 - 0 self |
BibTeX
@ARTICLE{Zhou97path-dependentoption,
author = {Chunsheng Zhou},
title = {Path-Dependent Option Valuation When the Underlying Path Is Discontinuous},
journal = {The J. of Financial Engineering, v.8, N},
year = {1997},
volume = {1},
pages = {73--97}
}
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Abstract
The payoffs of path-dependent options depend not only on the final values, but also on the sample paths of the prices of the underlying assets. A rigorous modeling of the underlying asset price processes which can appropriately describe the sample paths is therefore critical for pricing path-dependent options. This paper allows for discontinuities in the sample paths of the underlying asset prices by assuming that these prices follow jump diffusion processes. A general yet tractable approach is presented to value a variety of path-dependent options with discontinuous processes. The numerical examples show that ignoring the jump risk may lead to serious biases in pathdependent option pricing. Jumps are an important feature of the price processes of financial assets, and are especially pronounced for certain types of assets, such as small-cap stocks and exchange rates. 1 For this reason, Merton's (1976) groundbreaking work, which explicitly admits jumps in the underlying asset prices ...
Keyphrases
path-dependent option valuation path-dependent option underlying path sample path underlying asset price discontinuous process certain type serious bias financial asset tractable approach jump diffusion jump risk underlying asset price process small-cap stock underlying asset numerical example exchange rate important feature rigorous modeling price process pathdependent option pricing final value
