高级公司金融pricingderivatives(编辑修改稿)

高级公司金融pricingderivatives(编辑修改稿)内容摘要：

ng stock, Microsoft, does not pay dividend. Let’s consider the following two strategies:  Strategy 1: a long position in a call on Microsoft and a short position in a put on the same stock.  Strategy 2: a long position in a forward on Microsoft The two strategies have the same cash flow at maturity so they should have the same value now. If c0 , p0 and f denote the value of call option, put option and forward respectively, f = c0 p0 = S0 –PV(K) PutCall Parity and Forward Contract Value ST K 45176。 STK Long Call Short Put Cost of Acquiring the Investment Today Cash Flow at the Expiration Date if S at That Time Is STK STK Strategy 1: Buy call and write put c0 – p0 ST K ST K = Long position in a call and short position in a put = c0 p0 = 0 (K ST) = ST K 0 Strategy 2: Tracking portfolio S0 –PV(K) ST K ST K = Buy stock and borrow present value of K = S0 PV(K) = ST K = ST K Tracking Portfolio as a Proof  A long position in a stock and a short position in a riskless asset with face value of K replicates a forward as well as a call (long) and put (short) PutCall Parity and a Minimum Value for a Call The putcall parity shows that: c0 p0 = S0 –PV(K) Sine the price of a put will never be negative, then, There is a minimum value for a call option: the price of a call option will never be lower than the value of a forward contract on the same underlying asset. )(00 KPVSc Premature Exercise of American Call American option should be worth more than European option because it has more rights. Does prematurely exercising of American option create value for investors? For underlying stock paying no dividend, the answer is no. The putcall parity shows that KSKPVSc  000 )(Value of option Value of early exercising Premature Exercise of American Call Example: Arbitrage when a call sells for its exercise value.  Consider an American call option with a $40 strike price on Intel stock. Assume that the stock sells for $45 a share and pays no dividends to expiration. The option sells for $5 on year before expiration. Risk free rate is 10 percent. How to arbitrage?  Solution: short sell an Intel stock (+$45), buy the American option ($5) and put the remaining cash ($40) on risk free asset. – At maturity if Intel stock price is higher than $40 the investor exercise the option to close short position in stock and earn 40*10% – If stock price is lower than $40, the investor does not exercise option. She can use the money on risk free asset to buy stock and earns 40*(1+10%) ST Premature Exercise of American Call When premature exercise of American call can occur?  Early exercise may be better if the underlying asset pays cash before maturity.  It may be better for CEO to exercise the executive stock option and sell the stock to reduce the weight of their wealth on the pany. Relating the price of American call to that of the European Call  If the right of early exercising add no value, the price of an American call on a nondividend paying stock should be the same as that of an European call. PutCall Parity for European Options on Dividend Paying Stocks If the underlying stock pays riskless dividend before maturity, the future cash flows of longing a call and shorting a put (c0p0) is still equal to those of longing a forward (f). But from forward valuation we know that for a dividend paying underlying stock, f = S0PV(K)PV(Div). The putcall parity for European options on dividend paying stock c0p0=S0PV(K)PV(Div) Portfolio Insurance Mutual fund or pension fund managers would like to have their portfolios insured so that they can enjoy the soaring of the stock but have a minimum value F when extremely bad situations occur. The payoff of the insured portfolio is similar to that of a call option. Actually it can be deposed into a call option and a risk free asset. The portfolio insurance can be achieved using the putcall parity. Portfolio Insurance Value ST F F Insured Portfolio Call Risk free asset Portfolio Insurance The current price of an insured portfolio is c0 + PV(F). The putcall parity shows that, To have the portfolio insured, fund managers have to acquire a put. The insurance can be constructed either by purchasing a exchange traded put option (put option on index) or by tracking portfolio. c0 p0=S0 PV(K) c0 + PV(K) = S0 + p0 Binomial Pricing Model Tracking and Valuation: static vs. dynamic strategies  Static strategy: buy and hold a position in a tracking portfolio until maturity. To track a forward contract an investor only needs to buy an underlying stock and short risk free asset at beginning and hold this position to maturity.  Dynamic strategy: the holdings in the tracking portfolio (often the weights in the ponents of tracking portfolio) need to change frequently in order to perfectly track payoff.  The static tracking strategy can be used only if the payoff of the tracked derivative at maturity is a linear function of that of the underlying asset. Binomial Process If the price of the underlying security follows a binomial process, the investor can still perfectly track the derivative’s future cash flows even if it’s payoff is not linear in the price of the underlying asset. With binomial process, the underlying security’s price moves up or down over time, but can take only two values at the next point. An Example: Value of a Structured Bond The structured bond in this example is a specific case of structure notes. The payoff at maturity (1 year later, next period) of the structure bond depends on Samp。 P 500 index. It is posed of two parts. One is the $100 principal plus percent interest. In additi。