How to Advance Your Career Gautam Goswami Fordham University.
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Transcript of How to Advance Your Career Gautam Goswami Fordham University.
![Page 1: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/1.jpg)
How to Advance Your Career
Gautam Goswami
Fordham University
![Page 2: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/2.jpg)
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.
![Page 3: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/3.jpg)
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.
![Page 4: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/4.jpg)
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.
![Page 5: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/5.jpg)
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.
![Page 6: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/6.jpg)
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%).
![Page 7: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/7.jpg)
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.
![Page 8: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/8.jpg)
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.
![Page 9: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/9.jpg)
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).
tr
EF
)1(
![Page 10: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/10.jpg)
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.
![Page 11: How to Advance Your Career Gautam Goswami Fordham University.](https://reader036.fdocuments.us/reader036/viewer/2022082417/56649d215503460f949f7200/html5/thumbnails/11.jpg)
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
tr
EF
)1(
360148
)0754.1(
3530.35