Theory of Rational Option Pricing: II (Revised: 1-96)
This paper investigates the properties of contingent claim prices in a one dimensional diffusion world and establishes that (i) the delta of any claim is bounded above (below) by the sup (inf) of its delta at maturity, and (ii), if its payoff is convex (concave) then its current value is convex (concave) in the current value of the underlying. These properties are used as the foundation for a detailed study of the properties of option prices. Interestingly, although an upward shift in the term structure of interest rates will always increase a call’s value, a decline in the present value of the exercise price can be associated with a decline in the call price. We provide a new bound on the values of calls on dividend-paying assets. We establish that when the underlying’s instantaneous volatility is bounded above (below), the call price is bounded above (below) by its Black-Scholes value evaluated at the bounding volatility level. This leads to a new bound on a call’s delta. We also show that if changes in the value of the underlying follow a multidimensional diffusion (i.e., a stochastic volatility world), or are discontinuous or non-Markovian, then call option prices can exhibit properties very different from those of a Black-Scholes world: they can be decreasing, concave functions of the value of the underlying.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (215) 898-7616
Fax: (215) 573-8084
Web page: http://finance.wharton.upenn.edu/~rlwctr/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:fth:pennfi:11-95. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel)
If references are entirely missing, you can add them using this form.