Suppose that we will receive USD $1$ mil a year from now. Given the following conditions, compare the expected value of our net payoff in AUD $($a year from now$)$ using the following methods: $1)$ hedging with a forward contract; $2)$ hedging with an option; and $3)$ staying unhedged. Which of the following statement is TRUE?

Spot rate now: AUD$1\mathrm{.}5/$USD

Spot rate a year from now: AUD$1\mathrm{.}4/$USD with $50\%$ probability and AUD$1\mathrm{.}6/$USD with $50\%$ probability

$1-$year forward rate: AUD$1\mathrm{.}48/$USD

$1-$year call option: AUD $0\mathrm{.}03$ mil as premium, to buy USD $1$ mil at $1\mathrm{.}55$

$1-$year put option: AUD $0\mathrm{.}04$ mil as premium, to sell USD $1$ mil at $1\mathrm{.}45$

Question $20$Answer

a$.$

The expected value of our net payoff is the highest hedging with a put option contract, yielding AUD $1\mathrm{.}485$ mil.

b$.$

The expected value of our net payoff is the highest hedging with a put option contract, yielding AUD $1\mathrm{.}525$ mil.

c$.$

The expected value of our net payoff is the highest hedging with a forward contract, yielding AUD $1\mathrm{.}48$ mil.

d$.$

The expected value of our net payoff is the highest staying unhedged.

e$.$

The expected value of our net payoff is the highest hedging with a call option contract, yielding AUD $1\mathrm{.}525$ mil.