Question

Cosmo, a Japanese exporter, wishes to hedge its $15 million in dollar receivables coming due in 60 days. In order to reduce its net cost of hedging to zero, however, Cosmo sells a 60-day dollar call option for $15 million with a strike price of ¥98/$ and uses the premium of $314,000 to buy a 60-day $15 million put option at a strike price of ¥90/$.a.Graph the payoff on Cosmo's hedged position over the range ¥80/$-¥110/$. What risk is Cosmo subjecting itself to with this option hedge?

Answer 1

Cosmo expects to receive USD 15 mn in 60 days and wants to hedge its exposure without any cost incurred on hedging. Accordingly, executes two options with same option premium such that the net option premium is 0.

1. Sells a Call option
2. Buys a Put Option

Sells a Call Option

Strike Price	98	Yen/USD
Notional	15	mn USD
Premium (USD)	$314,000	Received

Payoff from Sell Call = Option Premium Received – [ 15mn * Max (Market Price – Strike Price , 0) ]

Payoff from Sell Call = $ 314,000 – [ 15mn * Max (Market Price – 98, 0) ]

Buys a Put Option

Strike Price	90	Yen/USD
Notional	15	mn USD
Premium (USD)	$314,000	Paid

Payoff from Buy Put = – Option Premium Paid + [ 15mn * Max (Strike Price – Market Price, 0) ]

Payoff from Buy Put = – $ 314,000 + [ 15mn * Max (90 – Market Price, 0) ]

Total Payoff from these two options would be:

Total Payoff = Payoff from Sell Call + Payoff from Buy Put

Total Payoff = $314,000 – [ 15mn * Max (Market Price – 98, 0) ] – $314,000 + [ 15mn * Max (90 – Market Price, 0) ]

Total Payoff = [15mn * Max (90 – Market Price, 0)] – [15mn * Max (Market Price – 98, 0)]

(Note: This Payoff will be in Yen, as we are executing an option on exchange rate)

Based on the above formula, the payoffs have been calculated below:

Market Price	Total Payoff	Total Payoff (Mn Yen)
80	150000000	150
85	75000000	75
90	0	0
95	0	0
98	0	0
100	-30000000	-30
105	-105000000	-105
110	-180000000	-180

Sample Calculations:

Market Price = 85 | Total Payoff = [15mn * Max(90-85,0)] - [15mn * Max(85-98,0)]

Total Payoff = [15mn * 5] - [15mn * 0] = 75 mn

Market Price = 105 | Total Payoff = [15mn * Max(90-105,0)] - [15mn * Max(105-98,0)]

Total Payoff = [15mn * 0] - [15mn * 7] = - 105 mn

Based, on the table above, the graphical repsentation of payoffs over the range of 80-110 Yen/USD can be made as:

X Axis: Movement of Yen/USD from 80-110

Y Axis: Payoff from option position

Risk to Cosmo:

With this option hedging, Cosmo is exposed to the unlimited market risk wherein the Yen depreciates over 98Yen/USD.

With the graph shown above, it is quite evident that Cosmo expects the Yen to remain in the range of 90-98/USD. However, if the Yen cross 98 mark, then the Call Option sold will incur losses as the buyer of call option will exercise the option.

As shown in the graph, this market risk is unlimited and the losses will keep on increasing as the Yen depreciates further.