Choosing put option parameters based on quantiles from the distribution of portfolio value

Peter Bell

MPRA Paper from University Library of Munich, Germany

Abstract: This paper explores how a put option changes the probability distribution of portfolio value. The paper extends the model introduced in Bell (2014) by allowing both the quantity and strike price to vary. I use the 5% quantile from the portfolio distribution to measure riskiness and compare different put options. I report a so-called ‘quantile surface’ that shows the quantile across different combinations of quantity and strike price. I find that it is possible to maximize the quantile by purchasing a put with quantity equal to one and strike deep in the money; however, the distribution with such a put option collapses to a single point because the option hedges all variation in stock price. This result is analogous to full-insurance in insurance economics, but has practical limitations. The quantile surface also shows that certain put options will decrease the quantile, which is equivalent to increasing the riskiness of the portfolio, and leads me to ask: what return will an investor receive in return for bearing that extra risk? I find that one such put option will cause the distribution to have an asymmetric shape with positive skewness, which is interesting to some speculators.

Keywords: Portfolio; put option; probability distribution; quantile; optimization; risk management; speculation (search for similar items in EconPapers)
JEL-codes: C00 C69 D81 G00 G11 (search for similar items in EconPapers)
Date: 2014-09-09
New Economics Papers: this item is included in nep-rmg
References: Add references at CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/58428/1/MPRA_paper_58428.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:58428

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().