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.
Highlights
The currency is sold at a high price, and purchased at the lower future currency value, resulting in a gain for the put buyer
Currency put options are only profitable with declining currency values
The Gain on a Currency Put = (Exercise Price − Spot Exchange Rate) − Put Purchase Price. This outcome suggests that an investor, forecasting future currency depreciation, purchases a put option at the purchase price, sells the underlying currency at a high exercise price and buys back the currency at the lower future spot exchange rate, earning a gain
Summary
Currency put options are only profitable with declining currency values. The Gain on a Currency Put = (Exercise Price − Spot Exchange Rate) − Put Purchase Price. Short sellers attempt to gain from depreciating currencies They borrow currencies, sell at high prices, and repay with cheap currency. Repeated short selling devalues currencies, raising concerns by regulatory authorities who view the devaluation as a loss of national wealth. An informed investor short sells currency in the foreign currency market, earns the modest gains, ceases short selling upon restrictions imposed by regulatory authorities. He or she still has unsatiated demand for depreciating currencies, which may be fulfilled in the unregulated options market. We present each joint short selling and put buying strategy in terms of its utility to the individual investor.
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