chap007尤恩,國(guó)際財(cái)務(wù)管理,英文第五版(編輯修改稿)
2025-02-04 23:21 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 the call is inthemoney, it is worth ST – E. If the call is outofthemoney, it is worthless, and the buyer of the call loses his entire investment of c0. Inthemoney Outofthemoney 718 Basic Option Profit Profiles E ST Profit Loss – p0 E – p0 Long 1 put E – p0 If the put is inthemoney, it is worth E – ST. The maximum gain is E – p0. If the put is outofthemoney, it is worthless, and the buyer of the put loses his entire investment of p0. Outofthemoney Inthemoney Short 1 put 719 Market Value, Time Value, and Intrinsic Value for an American Call E ST Profit Loss Long 1 call The red line shows the payoff at maturity, not profit, of a call option. Note that even an outofthemoney option has value—time value. Intrinsic value Time value Inthemoney Outofthemoney 720 European Option Pricing Relationships Consider two investments: 1 Buy a European call option on the British pound futures contract. The cash flow today is –Ce. 2 Replicate the upside payoff of the call by: ? Borrowing the present value of the dollar, exercise price of the call in the . at i$ , the cash flow today is ? Lending the present value of ST at i163。, the cash flow today is E (1 + i$) ST (1 + i163。) – 721 European Option Pricing Relationships Ce Max ST E (1 + i163。) (1 + i$) – , 0 ? When the option is inthemoney, both strategies have the same payoff. ? When the option is outofthemoney, it has a higher payoff than the borrowing and lending strategy. ? Thus, ? Using a similar portfolio to replicate the upside potential of a put, we can show that: Pe Max ST E (1 + i163。) (1 + i$) – , 0 722 Binomial Option Pricing Model Imagine a world where the spot exchange rate is S0($/€) = $€ today and in the next year S1($/€) is either $€ or $€. €10,000 will change from $15,000 to either $18,000 or $12,000. A call option on €10,000 with strike price S0($/€) = $ will payoff either $3,000 or zero. If S1($/€) = $€ the option is inthemoney since you can buy €10,000 (worth $18,000 at S1($/€) = $€ ) for only $15,000. $15,000 $18,000 = €10,000 $ € $12,000 = €10,000 $ € C1up = $3,000 C1down = $0 723 Binomial Option Pricing Model We can replicate the payoffs of the call option by taking a long position in a bond with FV = €5,000 along with the right amount of dollardenominated borrowing (in this case borrow the PV of $6,000). The portfolio payoff in one period matches the option payoffs: $6,000 $9,000 $ value of bond FV = €5,000 pay debt portfolio $15,000 – $6,000 – $6,000 = $3,000 = $0 C1($/€) $3,000 $0 724 Binomial Option Pricing Model The replicating portfolio’s dollar cost today is the sum of today’s dollar cost of the present value of €5,000 less the cash inflow from borrowing the present value of $6,000: $ $6,000 (1 + i$) € €5,000 – (1 + i€ ) When S0($/€) = $€, i$ = %, and i€ = 5%, the most a willing buyer should pay for the call option is $1,. That’s what it would cost him today to build a portfolio that perfectly replicates the call option payoffs—why pay more to buy a readymade option? $1, = $7, ? $5, 725 The Hedge Ratio ? We replicated the payoffs of the call option with a levered posit
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