Question

1. From the perspective of the writer of a put option written on €62,500. If the exercise price is $1.55/€, and the option premium is $0.03.

a. At what exchange rate do you start to lose money?

b. What is your maximum profit?

c. What is your maximum loss?

d. If the spot exchange rate is $1.54/€ calculate the intrinsic value and the time value of the put option.

e. Draw the profit graph for the writer of this put option

Please help me with all the parts step by step

Answer 1

Solution :

Euro = 62,500 Exercise price is = $1.55 / Euro , Option premium = $0.03

The investor is selling the put option means she is expecting that exchange rate will not go below the Exercise price - premium received

Part A )

If exchange rate goes below 1.55 - 0.03 = $1.52 / Euro then the investor will start to lose money

Payoff of short put option = min(ST – X, 0) + premium received

Part B ) Maximum profit can only be the premium received in case of writing an option. This can be seen from the pay-off equation

So maximum profit per option = $0.03 when the exchange rate remains above $1.55 / Euro

Total profit = 62500 * 0.03 = $1875

Part C )  

Maximum loss in case of writing a put option

Payoff of short put option = min(ST – X, 0) + premium received

When spot rate becomes Zero then Payoff per option = - Exercise price + premium = -1.55+0.03 = $-1.52  

Total maximum loss = -1.52 *62500 = $95000

Part D ) Spot rate = $1.54/ Euro, Exercise = $1.55/ Euro

In case of put option

Intrinsic Value = Strike Price - Price of Underlying Asset = $1.55/ Euro - $1.54/ Euro, = $0.01 / Euro

Time Value = Option Premium - Intrinsic Value = 0.03 - 0.01 = $0.02 / Euro

Part E )

Pay-off graph has been prepared in excel and details are given