第二十二章期權(quán)與公司理財：基本概念-文庫吧資料
2025-01-04 23:26本頁面
【正文】 cise price of $40,Buy the stock at $40 financed with some debt: FV = $X,Buy a call option with an exercise price of $40,$0,$40,$40P0,$40,Buy the stock at $40,[$40P0],In market equilibrium, it mast be the case that option prices are set such that:,Otherwise, riskless portfolios with positive payoffs exist.,Value of stock at expiry,Value at expiry,22.7 Valuing Options,The last section concerned itself with the value of an option at expiry.,This section considers the value of an option prior to the expiration date. A much more interesting question.,Option Value Determinants,Call Put Stock price + – Exercise price – + Interest rate + – Volatility in the stock price + + Expiration date + + The value of a call option C0 must fall within max (S0 – E, 0) C0 S0. The precise position will depend on these factors.,Market Value, Time Value and Intrinsic Value for an American Call,CaT Max[ST E, 0],Profit,loss,E,ST,Market Value,Intrinsic value,ST E,Time value,Outofthemoney,Inthemoney,ST,The value of a call option C0 must fall within max (S0 – E, 0) C0 S0.,22.8 An Option?Pricing Formula,We will start with a binomial option pricing formula to build our intuition.,Then we will graduate to the normal approximation to the binomial for some realworld option valuation.,Binomial Option Pricing Model,Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. S0= $25 today and in one year S1is either $28.75 or $21.25. The riskfree rate is 5%. What is the value of an atthemoney call option?,$25,$21.25,$28.75,S1,S0,Binomial Option Pricing Model,A call option on this stock with exercise price of $25 will have the following payoffs. We can replicate the payoffs of the call option. With a levered position in the stock.,$25,$21.25,$28.75,S1,S0,C1,$3.75,$0,Binomial Option Pricing Model,Borrow the present value of $21.25 today and buy 1 share. The net payoff for this levered equity portfolio in one period is either $7.50 or $0. The levered equity portfolio has twice the option’s payoff so the portfolio is worth twice the call option value.,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,Binomial Option Pricing Model,The levered equity portfolio value today is today’s value of one share less the present value of a $21.25 debt:,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,Binomial Option Pricing Model,We can value the option today as half of the value of the levered equity portfolio:,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,If the interest rate is 5%, the call is worth:,The Binomial Option Pricing Model,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,If the interest rate is 5%, the call is worth:,The Binomial Option Pricing Model,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,Binomial Option Pricing Model,the replicating portfolio intuition.,Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.,The most important lesson (so far) from the binomial option pricing model is:,The RiskNeutral Approach to Valuation,We could value V(0) as the value of the replicating portfolio. An equivalent m
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