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ne in the underlying markets, and the other in the derivatives markets, simultaneously. Underlying asset put or call Derivative call or put = Forward Contracts ? an agreement to buy or sell at a specified future time a certain amount of an underlying asset at a specified price. ? an agreement to replace a risk by a certainty ? traded OTC ? long position the buyer in a contract ? short position the seller in a contract ? delivery price the specified price ? maturity specified future time Future TS TVTSTVK K 0 0 Long position Short position TTV S K??V K S?? Futures ?same as a forward contract ?have evolved from standardization of forward contracts ?differences – ? futures are generally traded on an exchange ? a future contract contains standardized articles ? the delivery price on a future contract is generally determined on an exchange, and depends on the market demands Options ? an agreement that the holder can buy from (or sell to) the seller (the buyer) of the option at a specified future time a certain amount of an underlying asset at a specified price. But the holder is under no obligation to exercise the contract. ? a right, no obligation ? the holder has to pay premium for this right ? is a contingent claim ? Has a much higher level of leverage Two Options ? A call option a contract to buy at a specified future time a certain amount of an underlying asset at a specified price ? A put option a contract to sell at a specified future time a certain amount of an underlying asset at a specified price. ? exercise price the specified price ? expiration date the specified date ? exercise the action to perform the buying or selling of the asset according to the option contract Option Types ? European options can be exercised only on the expiration date. ? American options can be exercised on or prior to the expiration date. ?Other options – Asia option etc. Total Gain of an Option TSTPTSK K 0 0 Call option put option ()TTP S K p?? ? ?()P K S p?? ? ?TPp [Total gain]= [Gain of the option at expiration][Premium] Option Pricing ?risky asset’ s price is a random variable ?the price of any option derived from risky asset is also random ?the price also depends on time t ?there exists a function such that ?known ?How to find out ( , )V S t ( , )ttV V S t?()()TTTS K c allVK S put??? ?? ???0( , 0) ?p V S?? Types of Traders ? Hedger to invest on both sides to avoid loss ? Speculator to take action characterized by willing to risk with one39。s money by frequently buying and selling derivatives (futures, options) for the prospect of gaining from the frequent price changes. ? Arbitrage based on observations of the same kind of risky assets, taking advantage of the price differences between markets, the arbitrageur trades simultaneously at different markets to gain riskless instant profits Hedger Example ? In 90 days, A pays B 163。1000,000 with $1,650,000 90 days later ? Purchase a call option to buy 163。) 90day later Rate ($/ 163。s strike price, ? T the option39。rT rT rTT T T TTTTTV V c V K e S K K e eS S KS