How to Advance Your Career

1. How to Advance Your Career Gautam Goswami Fordham University

2. Overview • An aspiring banker is asked by a customer to quote prices on a DM currency option or a futures contract that would guarantee a receipt of $.3597 (.36) per DM. The New York Times is the only available information source, but no quotation for a DM put option with a strike price of $0.36 appears in the paper, and the futures price per DM is $.3530. • With additional information from the paper on the DM call option with a strike price of $0.36 and the yields on the treasury bills, the aspiring banker must satisfy the need of the customer.

3. Objectives • (1) How to read currency option and futures prices in the newspaper, • (2) The concept of put-call parity which is used to derive the premium on the currency put option from the given premium on a call option with the same strike price, and • (3) Encourage students to become a little bit more innovative with a futures transaction.

4. Analysis 1. Reading Currency Option and Futures Prices • As a first step, the aspiring banker must analyze the customer’s needs. The customer wants to sell DM 125,000 next December at a guaranteed exchange rate of DM 2.78. Stated in dollar terms, the customer wants a contract that guarantees $.3597 per DM. To satisfy that need, the banker will have to arrange either a DM put option with a strike price of $.36 or a currency future priced at $.36 that matures in December.

5. Analysis • Exhibit 1 of the case shows that December-maturing currency futures closed at $.3530 for the day. So as it is, the currency futures do not guarantee the customer a receipt of $.36 per DM. • Exhibit 3 of the case gives currency option prices, but there is no DM put option with a strike price of $.36 maturing in December. As a point of reference, the December $.35 put option is priced at 1.32 cents per DM transacted and the December $.36 call option is priced at 1.00 cent per DM transacted.

6. Analysis • Exhibit 2 of the case shows the yields of treasury bills with different maturities. Later the yield can be used with put-call parity to derive a premium on a put option from a premium on a call option, but at this moment, it is enough to know that since the currency option matures on the third Wednesday of the contract month, the yield on a treasury bill that matures 148 days hence on December 19 is the relevant discount rate (7.54%).

7. Analysis 2. Derivation of the Put Option Premium from the Call Option Premium • To derive the December $.36 put option price, students may be tempted to extrapolate from the December $.35 put option price of 1.32 cents per DM. This is a mistake. There is no easy way to get a pricing model to figure out the implied volatility and then using it to price the $.36 put option.

8. Analysis • The correct way is to use the put-call forward parity (PCFP) relationship which is based on the arbitrage technique of conversions and reversals. • The PCFP says a long put is equivalent to a long call plus a forward or futures contract. This parity is easily verified in the profit diagram of option contracts as shown in Figure 1.

9. Analysis • Algebraically the relationship can be expressed as follows: • C-P = • Where: • C = call price (1.50), • P = put price (1.32), • F = forward price (35.30), • E = exercise price (35), and • r = rate of discount (.0754).

10. Analysis • It is important to discount the right-hand side to present value because the premia are paid up front. In contrast, the forward and exercise prices are paid at the maturity date in the middle of December.

11. Analysis • This relationship can be verified by using the $.35 December option: • L. H. S. of equation R. H. S. of equation C – P 1.50- 1.32=.18 DM=.29 DM