TITLE:
The Valuation of Currency Put Options
AUTHORS:
Rebecca Abraham
KEYWORDS:
Short Selling, Currency, Put Option, Lognormal, Weiner, Laplace
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.11,
August
24,
2018
ABSTRACT: Investors who seek to profit from depreciating
currencies may invest in put options. Upon option exercise, the currency is
sold at a high price, and then purchased at the lower future currency value,
resulting in a gain for the put buyer. A series of such transactions yields a
stream of income for the put investor. Alternatively, the investor could short
sell the currency, reaping gains from the difference between the high short
sale price and the low future purchase price. This paper derives the
theoretical formulations for combined short sale and puts purchase strategies for the
US dollar, the Euro, the Australian dollar and the New Zealand dollar, and the
Mexican peso. Utility functions are based upon an assumption of declining risk
aversio with negative rescale factors and positive threshold factors in a
hyperbolic cosine distribution. This distribution intersects with the cosine
distribution of short sale prices on the U. S. dollar, the lognormal
distribution of short sale prices on the Euro, the Weiner process for shorts on
the Australian dollar and the New Zealand dollar, and the Laplace currency
distribution for peso shorts. Similar utility functions intersect with
Levy-Khintchine jump processes to provide put option prices for each type of
foreign currency.