Question

Consider the following option contract on the Euro:

It is a put option for 125,000 euros, with settlement prices in terms of US dollars per one euro (i.e., if exercised, euros will be exchanged for the appropriate number of dollars) The strike price is 1.2000 dollars per euro, and the premium is 0.0300 dollars per euro.

(a) Suppose a trader entered a long position by buying seven of these put option contracts. What would be the trader’s profit or loss if the spot rate upon the option expiration is 1.1950 dollars per euro?

(b) A different options trader took a short position in this put option (for seven contracts). What would be the trader’s profit or loss if the spot rate upon the option expiration is 1.2050 dollars per euro?

(c) Another trader writes seven of these put option contracts. What would be this trader’s profit or loss if the spot rate upon the option expiration is 1.1900 dollars per euro?

(d) Suppose that soon after taking these positions (but before their expiration), the value of the dollar would depreciate substantially, well beyond expectations. Would it benefit the long position in this option or the short position?

Answer 1

a) The put options worth at expiration is given by max(K-S,0) where K is the strike price and S is the spot rate at expiration of the option

Value of the option per Euro = max(1.2-1.195,0) = $0.005

Cost per Euro = $0.03

So, Net profit per Euro = $0.005-$0.03 = -$0.025

So, Net profit for 7 contracts of Euro 125000 each = -$0.025*125000*7 = -$21875

So, there will be a net loss of $21875

b) For short position holder

net profit per Euro = premium per Euro - max(K-S,0) = 0.03-max(1.2-1.205,0) = $0.03

So, Net profit for 7 contracts of Euro 125000 each = $0.03*125000*7 = $26250

So, there will be a net profit of $26250

c) Writing an option is the same as selling the option or taking a short position in the option

net profit per Euro = premium per Euro - max(K-S,0) = 0.03-max(1.2-1.19,0) = $0.02

So, Net profit for 7 contracts of Euro 125000 each = $0.02*125000*7 = $17500

So, there will be a net profit of $17500

d) When the value of the dollar depreciates substantially before expiration , the put option becomes worthless.

as worth of the option = max(K-S,0) =0 as S becomes substantially larger than K

So, this benefits the short position holder as they get the premium without the risk of the put options getting exercised