Question

Find the hedge ratio a 1-period at-the-money put option on ¥300,000. The spot exchange rate is ¥100 = $1.00. In the next period, the yen can increase in dollar value by 15 percent or decrease by 10 percent. The risk-free rate in dollars is i$ = 5%; The risk-free rate in yen is i¥ = 1%.

A.-0.44

B.-0.66

C.-0.60

D.-0.40

Answer 1

Spot rate $1.00 = Yen 100

Put option is availabe at the money. It means spot rate and strike rate is same

So strike rate $1.00 = 100 Yen

In next period, Upside value = spot rate*(1+increase %)

=100*(1+15%) = 115

In next period, downside value = spot rate*(1-decrease %)

=100*(1-10%) = 90

Value of put option = Strike price - value in next period (but it cannot be negative, maximum it can be 0)

If value increase, then

VP =100-115 = 0

If Value decreases then

VP = 100-90 =10

Hedge ratio formula= (VP at upside price-VP at downside price)/(Upside price - downside price)

=(0-10)/(115-90)

=-0.4

So Hedge ratio is -0.40