Problem 7.13 U.S. Dollar/Japanese Yen- what would be the premium expense, in home currency, for a Japanese firm to purchase an option to sell 750,000 US dollars, assuming the initial values listed in the FX option pricing workbook?

Pricing Currency Options on the Japanese yen

A Japanese firm wishing to buy

A U.S.-based firm wishing to buy

or sell dollars (the foreign currency)

or sell yen (the foreign currency)

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

JPY 105.64

S0

$0.01

Strike rate (domestic/foreign)

X

JPY 100.00

X

$0.01

Domestic interest rate (% p.a.)

rd

0.09%

rd

1.45%

Foreign interest rate (% p.a.)

rf

1.45%

rf

0.09%

Time (years, 365 days)

T

1

T

1

Days equivalent

365

365

Volatility (% p.a.)

s

12.00%

s

12.00%

Call option premium (per unit fc)

c

JPY 7.27

c

$0.00

Put option premium (per unit fc)

p

JPY 3.06

p

$0.00

(European pricing)

Call option premium (%)

c

6.88%

c

3.06%

Put option premium (%)

p

2.90%

p

7.27%

A Japanese firm wishing to sell U.S. dollars would need to purchase a put on dollars. The put option premium listed above is JPY3.06/$.

Put option premium (JPY/US$)

JPY 3.06

Notional principal (US$)

$750,000

Total cost (JPY)

JPY 2,297,243