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financial risk management solution

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  LECTURE # 6 INTRODUCTION TO FINANCIAL ENGINEERINGObjective: After attending this lecture and studying the relevant material, the student will be able to understand the basic concept of nancial engineering. The tools used for nancial risk management will be discussed briey. ã Futures ã Forwards ã Swaps ã ptions Derivatives: ã !n the last # years derivatives have become increasingly important in the world of nance ã A derivative security is an agreement between two parties to transact something (underlying asset) at a future date for some agreed upon price   ã Agreement between tw !arties ã  $ou and a bank, %ank and a corporation, Two banks, il producers and consumers T transact smet ing ã Shares of stock, &rude oil, 'lectricity, An interest rate, r another derivative At sme time in t e $t$re an% at sme &'e% !rice( ã  These agreements e(pire at the e(piration date.    This price has di)erent names depending upon the nature of the agreement, Future price *in future contracts+, Forward price *in forward contracts+, '(ercise  strike price *in option contracts+ ) * t ese agreements are ca++e% %erivative ã %ecause the value of the -agreement derives from the value of the -underlying asset T*!es  Derivatives ã Amng man* variatins  $t$re cntracts, ++wing are t e majr t*!es:  – Frwar% cntracts  – F$t$re Cntract  – O!tins  – -wa!sE'c ange .ar/et an% Over0t e0C$nter .ar/ets ã A derivatives e(change is a market where individuals trade standardi/ed contracts that have been dened by the e(change. The &hicago %oard of  Trade *&%T+ was established in 0121 to bring farmers and merchants together. 3erivative traded outside e(changes by nancial institutions, fund managers, and corporate treasurers in what is termed the over-the-counter market Over0t e0c$nter mar/et ã !t is a telephone4 and computer4linked network of dealers, who do not physically meet  ã Financial institutions often act as market makers ã  Telephone conversations in the over4the4counter market are usually taped. ã 5arket participants are free to negotiate any mutually attractive deal *6ey advantage of T&+ ã A disadvantage is that there is usually some credit risk in an over4the4countertrade Frwar% Cntract ã De&nitin:  an agreement to buy or sell an asset at a certain future time for a certain price ã A forward contract is traded in the over4the4counter market ã A party assuming to buy the underlying asset is said to have assumed a long4position ã  The other party assumes a short-position and agrees  to sell the asset 1i% O2er Spot1# 1#.07 045onth forward 89.9 1#.#7 :4moths 89.2 89.79 4months 89.0 89.:7 ;4month 89 89.07 ã  The table shows <uotes made by a bank for e(change rates between dollar and rupee ã  The bank stands ready to buy =S dollars for >s.1# immediately, for >s.89.9 after a moth and for 89.2 after months ã  The bank also is ready to sell a dollar for 1#.07 now, for 1#.#7 after month and so on ã  The payo) from a long position in a forward contract on one unit of an asset is S T  -K  ã where K is the delivery price and ã S  T  is the spot price of the asset at maturity of the contract.   The triangle area below the S  T ?ine is the payo) for the long position holder inthe forward agreement. ã Similarly, the payo) from a short position in a forward contract on one unit of an asset is K-S T   The triangle above the S  T line is the payo) for the short position holder in the forward agreement. Frwar% 3rice an% De+iver* 3rice ã The forward price is the market price that would be agreed to today for delivery of the asset ã !n the table, if a corporation contracts for buying dollar si( months from now *April :#0#+, the forward price of 89.07 becomes delivery price for the contract ã with the passage of time, delivery price will not change, but forward prices of contracts maturing in April :#0# may change+ 4w %erivatives are !rice% ã 3erivative contracts are priced so that there is no arbitrage opportunity Arbitrage  ã Any trading strategy re<uiring no e<uity that has some probability of making prot without any risk of loss@ow forward price are determined!n other words, how to price future contractsSee the e(ample. Frwar% 3rices an% -!t 3rices ã Suppose that the spot price of gold is B0### per ounce and the risk4free interest rate for investments lasting one year is 7C per annum. Dhat is a reasonable value for the one4year forward price of gold ã Suppose rst that the one4year forward price is B0 ## per ounce. A trader can immediately take the following actionsE ã 0. %orrow B0### at 7C for one year. ã :. %uy one ounce of gold. ã . 'nter into a short forward contract to sell the gold for B0 ## in one year ã  The trader earns a riskless prot of  The trader pays a total price for one ounce of gold  0### G *0###(7C interest+  B0#7# ã  The trader sell the gold for >s. 0 ## ã @is riskless prot is  0 ##40#7#  B:7# ã  The e(ample shows that B0 ## was too high a forward price This is called arbitrage. 3ue to arbitrage, what will happen toE ã 3emand for 04year forward contract of gold ã Forward price of the goldDhat should be the forward price gold one year from now !n this case, the determinants of forward price of gold areE ã Forward price  S o  G && ã Dhere S o  is the spotcurrentcash price today ã && is the cost of carry * in the previous e(ample && is the nancing cost  interest paid for buying gold+ ã F  B0### G *0###(.#7+  0###*0G.#7+  B0#7# T e case  cntin$$s cm!$n%ing ã ?ike in time value of money concept, when continuous compounding is the assumption, the interest rate formula becomesE ã Where e = 2! #2#$orward price for a non-dividend paying asset is ã %&ample' onsider a four-month forward contract to buy a ero-coupon bond that will mature one year from today The current price of the bond is *s+,(This means that the bond will have eight months to go when the forward contract matures) .ssume that the four-month ris/-free rate of interest (continuously compounded) is 01 per annum ã  T = 3 2 = ,,, ã r = 04 and S o  = +, The forward price4 rT  ei  = rT o eS  F   = 79.948930  333.006. ===  xrT o  eeS  F 
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