Question

Problem 1 (Hedging)

A US exporter expects to receive £1 million in 2 months for her exports to the UK. The current exchange rate is US$2.30/£. She is worried that the pound might depreciate over the next 2 months and wants protection against its decline but she also want to benefit from a possible rise in £ over the next 2 months. Put options and call options on the £, with 2-month maturity are available.

1. What should she do?

2. Suppose the 2-month put options exercisable at US$2.50/£ are trading at US$0.01. What would be her cash revenue, given your answer in part a), if at the 2 month end the spot exchange rate turns out to be

   1. US$2.00/£

   2. US$3.00/£

3. What would be her minimum cash revenue, no matter what the spot rate at the end of 2 months turn out to be?

4. What would be the upfront cost (fee) for undertaking the appropriate options contract?

5. What would she do if the expected £1 million at the 2-month end are not received and what would be her loss if that happens?

Answer 1

Options are a type of derivative which gives the buyer of option a right and not an obligation to buy or sell the underlying at an agreed price on or before the due date. Call Option gives the buyer a right to buy and a Put Option gives the buyer a right to sell.

In the given question, the US exporter will receive 1 million in 2 months. She wants to protect against the depreciation of Pound but also wants to benefit from a possible rise in Pound. Call Option and Put Option on Pound are available for 2 months maturity.

1. She should buy a Put Option at an Exchange Rate below which she does not want to receive the amount in US$. By doing this, if the Actual Spot Rate after 2 months is below the Exercise Price of the Put Option then she will exercise the option and receive the USD at the Exercise Price thus not losing due to the depreciation of Pound. If the Actual Spot Rate after 2 months is above the Exercise Price then she will not exercise the Put Option and sell the Pounds received at Spot Rate and benefit from the appreciation of Pound.

2a. 2-month Put Option exercisable at US$2.50/£ is trading at US$0.01.

Thus, the Cost of Put Option for 2,000,000 = US$0.01 * 2,000,000.

                                                                  = US$ 20,000.

If the Spot Price at the end of 2 months turns out to be US$2.00/£, then the exporter will exercise the Put Option.

She will sell Pounds received at the Spot Rate = 2,000,000 * US$2.00/£

                                                                    = US$ 4,000,000.

Put Option on Expiry Date = ( Exercise Price - Spot Price) * Amount

                                       = ( US$2.50/£ - US$2.00/£) * 2,000,000

                               = US$ 1,000,000.

Profit on Put Option = Amount received on Expiry of Option - Cost of Option

                             = US$ 1,000,000 - US$ 20,000

                             = US$ 980,000.

Thus, Exporter will receive US$ 4,000,000 in Cash Market and Profit of US$ 980,000 in Derivatives market. Thus, in Net she will receive US$ 4,980,000.

2b. If the Spot Price at the end of 2 months turns out to be US$ 3.00/£, then the exporter will not exercise the Put Option.

She will sell the Pounds received in the Spot Rate = 2,000,000 * US$ 3.00/£

                                                                         = US$ 6,000,000.

Loss on Put Option = Cost of Option ( As the Option is not exercised, no amount is received or paid on expiry of Option)

                             = US$ 20,000.

Thus, Exporter will receive US$ 6,000,000 in Cash Market and Loss of US$ 20,000 in Derivatives Market. Thus in Net she will receive US$ 5,980,000.

3. If the Actual Spot Rate Actual Spot Rate after 2 months is below the Exercise Price of the Put Option then she will exercise the option and receive the USD at the Exercise Price. If the Actual Spot Rate after 2 months is above the Exercise Price then she will not exercise the Put Option and sell the Pounds received at Spot Rate which will be more than the Exercise Price.

The minimum amount the exporter will receive in Cash Market is the Exercise Price of the Put Option bought by the exporter.